Laboratory Exercises

GNSS Data Processing

Laboratory

Slides

gA

GE

rese

arc

h g

rou

p o

f A

str

on

om

y a

nd

gAGE

Geo

mati

cs

http://www.gage.upc.edu

@ J. Sanz Subirana & J.M. Juan Zornoza

Barc

elo

na,

Spain

Authorship statement

The authorship of this material and the Intellectual Property Rights are owned

by J. Sanz Subirana and J.M. Juan Zornoza.

These slides can be obtained either from the server http://www.gage.upc.edu,

or [email protected]. Any partial reproduction should be previously

authorized by the authors, clearly referring to the slides used.

This authorship statement must be kept intact and unchanged at all times.

5 March 2017

Contents

Tutorial 0: UNIX environment, tools and skills. GNSS standard files formats.

Tutorial 1: GNSS data processing laboratory exercises.

Tutorial 2: Measurements analysis and error budget.

Tutorial 3: Differential positioning with code measurements.

Tutorial 4: Carrier ambiguity fixing.

Tutorial 5: Analysis of propagation effects from GNSS observables based on laboratory exercises.

Tutorial 6: Differential positioning and carrier ambiguity fixing.

List of Acronyms.

Tutorial 0UNIX enviroment, Tools and Skills.

GNSS Standard File Formats

J. Sanz Subirana and J.M. Juan Zornoza

November 27, 2013

Tutorial 0.1. UNIX Environment, Tools and Skills


Objectives

To present a (very limited) set of UNIX instructions in order tomanage files and directories, as well as some basic elements ofawk/gawk programming and the graphical plotting environmentgraph.py. The aim is not to teach UNIX or programming lan-guages, but to provide some basic tools needed to develop thepractical sessions.

Note: The following exercises are very elementary and can beomitted if the reader already has some basic knowledge of UNIXand gawk.

Files to usesxyz.eci

Programs to usegraph.py

Development

This session has been organised as a series of guided exercises to be done inthe established order, which introduces the main instructions for use in thefollowing sessions.

1. First instructions

(a) Show the name of the directory where you are located.Execute: pwd

(b) Examine the directory content.Execute: ls -lt

(c) Go to the personal directory or home directory (‘∼’).Execute: cd or cd ∼

(d) Go to the GNSS directory (inside the home directory)1

Execute: cd GNSS

(e) Access the HTML directory and view its contents.Execute:

cd HTML

ls -lt

(f) Go back to the home directory.Execute: cd ∼

1If the installation has been done properly according to instructions in the installationguide, the following three directories will be found: FILES, PROG and HTML. These directories,together with the Notepad files, will appear in the home/GNSS directory.

1

gAGE/UPC

(g) Show a text line on the screen:Execute:echo "Have a nice day"

(h) Direct the contents to a file:Execute:

echo "Have a nice day" > test

ls -ltr

echo "you too" >> test

(i) Show the contents of the file on the screen:Execute:cat test

Try to execute this too: echo test. What happens?

(j) Edit a fileExecute:2

textedit test

2. Directory management

(a) From any directory where you are located, go to the GNSS directoryand check that you are in it. Create the directory working insidethe GNSS directory. Access it. Go back to the directory immediatelyabove (in this case the GNSS directory) by executing ‘..’).Execute:

cd ∼/GNSSpwd

mkdir working

cd working

pwd

cd ..

pwd

3. File management

(a) Go to the working directory (which is inside the GNSS directory).Copy the file test from the home directory (‘∼’) to your currentdirectory (symbolised by ‘.’).Execute:

cd ∼/GNSS/workingcp ∼/test .

ls -lt

(b) Copy the file test to the file file1.3 Check the contents of file1.Execute:

cp test file1

ls -lt

more file1

2Any text editor can also be used.3As file file1 does not exist, a new file will be created with this name and with the

same contents as file test.

2


(c) Create a ‘link’4 from file file2 to file test. Check the file contents.Check the contents of file2.Execute:

ln -s test file2

ls -lt

more file2

(d) Using a text editor (e.g. gedit or similar), edit file2 and change theword day to the word YEAR. Save the changes and exit gedit. Next,check the contents of file test and its link file2. Have the contentsof the original file test been modified through its link file2?Execute:

gedit file2

more test

more file1

(e) Remove file file1 and its link file2. Check if they have beendeleted. Create the directory other. Remove the directory other.Execute:

ls -lt

rm file1 file2

ls -lt

mkdir other

ls -lt

rm -r other

ls -lt

(f) Find information on the ‘mkdir’ and ‘rm’ commands in the help pages(i.e. in the UNIX manual).Execute:

man mkdir

man rm

4. Programming environment gawk5

(a) From within the working directory, create a link from file sxyz.eci

(which is placed in the directory GNSS/FILES/TUT0) to a file withthe same name in the working directory.Execute:

cd ∼/GNSS/workingln -s ∼/GNSS/FILES/TUT0/sxyz.eci .

ls -lt

The file sxyz.eci contains three columns of coordinates, in a geo-centric inertial system, of a set of satellites at different epochs. Itcontains the following fields:

SATELLITE time(sec) X(km) Y(km) Z(km)

4This differs from the previous case because file2 is not a new file, just a pointer tofile test. Thus, the ‘link’ file2 represents the minimum space expense, independent ofthe file test size. Execute man ln to see the meaning of different types of links.

5gawk is the GNU implementation of awk (from the Free Software Foundation).

3

gAGE/UPC

(b) Execute the instructions cat, more and less in order to display thefile contents sxyz.eci. What differences can be seen among theseinstructions?6

Execute:

cat sxyz.eci

more sxyz.eci

less sxyz.eci

cat sxyz.eci | less

(c) Using the programming language gawk, print (on screen) the firstand third fields of file sxyz.eci.Execute:

gawk ’{print $1,$3}’ sxyz.eci |more

or

cat sxyz.eci |gawk ’{print $1,$3}’ |more

(d) Now print all the fields at the same time.Execute:

cat sxyz.eci | gawk ’{print $0}’ | more

(e) The following instruction generates the file prb1 which contains datafrom a single satellite. Which satellite is selected?Execute:

cat sxyz.eci | gawk ’{if ($1==5) print $0 }’ > prb1

more prb1

(f) What is the meaning of the values in the second column of file prb2

generated by the next instruction?Execute (in a single line):7

cat sxyz.eci | gawk ’{if ($1==5)

print $2,sqrt($3**2+$4**2+$5**2)}’> prb2

more prb2

(g) Discuss the structure of the following instruction that makes a ‘print’with a particular format (where %i=integer, %f= float, %s= string).Execute:

cat sxyz.eci |gawk ’{printf"%2i %02i %11.3f %i %s \n",$1,$1,$3,$3, $1}’|more

(h) Access the manual pages of gawk.Execute:

man gawk

6The command ‘|’ allows us to connect the output of a process with the input of another.For example, the output of cat can be sent to more.

7The sentence line is a single line, although it may appear as two lines because oftypesetting constraints.

4


5. Graphics environment graph.py

(a) Program graph.py is in directory∼/GNSS/PROG/src/gLAB src. Linkthis program to the current directory "." (i.e. directory working).Execute:

ln -s ∼/GNSS/PROG/src/gLAB src/graph.py .

(b) For the previously generated file prb1, plot the third field (x coordi-nate) as a function of the second one (time in seconds).Execute:8

graph.py -f prb1 -x2 -y3

(c) Using file sxyz.eci, plot satellites #5 and #9.Execute:9

graph.py -f sxyz.eci -x2 -y3 -c ’($1 == 5)’

-f sxyz.eci -x2 -y3 -c ’($1 == 9)’

(d) Repeat the previous plot for the interval [20 000 : 30 000] on the x-axis.Execute:

graph.py -f sxyz.eci -x2 -y3 -c ’($1 == 5)’

-f sxyz.eci -x2 -y3 -c ’($1 == 9)’

--xn 20000 --xx 30000

(e) Using file prb1, plot on the same graph the x (third field), y (fourthfield) and z (fifth field) coordinate as a function of time (second field).Execute:

graph.py -f prb1 -x2 -y3 -f prb1 -x2 -y4 -f prb1 -x2 -y5

(f) Using file prb1, plot on the same graph the distance of the satellitesfrom Earth’s mass centre (r =

√x2 + y2 + z2) as a function of time.

Execute:

graph.py -f prb1 -x2 -y’math.sqrt($3*$3+$4*$4+$5*$5)’

(g) For the same file used in the previous cases (prb1), write the title"orbit", x label "sec" and y label "m".Execute:

graph.py -f prb1 -x2 -y3 -t "orbit" --xl "sec" --yl "m"

8Depending on the PATH configuration, it would be necessary to execute ‘./graph.py’instead of ‘graph.py’. Another possibility is to include the current directory ‘.’ in the PATH

variable of the current terminal. This is done in the bash environment by executing export

PATH="./:$PATH". On the other hand, if we want to make this PATH update permanent,then the sentence export PATH="./:$PATH" must be included at the end of file ‘.bashrc’in the home directory. When working in tcsh instead of bash, the equivalent sentences areas follows: execute set PATH=./:${PATH} in the current directory (for a non-permanentchange), or add the sentence set path=(./ $path) to the end of file /etc/csh.cshrc tomake the PATH update permanent. Note that, in this last case, administrator privileges areneeded to edit the /etc/csh.cshrc file.

9Note that, in the Windows OS, instructions like ’($1=="5")’ must be written as"($1==’5’)"; that is, replacing (") by (’).

5

gAGE/UPC

(h) Visualise the different forms of graphic representations in the follow-ing instructions (with points, lines and other symbols or colours).

Execute:

graph.py -f prb1 -x2 -y3 -s.

graph.py -f prb1 -x2 -y3 -s-

graph.py -f prb1 -x2 -y3 -s-.

graph.py -f prb1 -x2 -y3 -s--

graph.py -f prb1 -x2 -y3 -so

graph.py -f prb1 -x2 -y3 -s+

graph.py -f prb1 -x2 -y3 -sp

graph.py -f prb1 -x2 -y3 -so --cl r

graph.py -f prb1 -x2 -y3 -s. --cl g

(i) Save the plot in a POSTSCRIPT file "orbit.ps" and in a PNG! (PNG!)

file "orbit.png".Execute:

graph.py -f prb1 -x2 -y3 --sv orbit.ps

graph.py -f prb1 -x2 -y3 --sv orbit.png

(j) Check "help" in graph.py.Execute:

graph.py -help

6

Tutorial 0.2. GNSS Standard File Format


By Adria Rovira Garcıa

gAGE/UPC & gAGE-NAV, S.L.

Objectives

To become familiar with the different format standard(s) involvedin the GNSS data sets. To provide the user with a reliable andpowerful tool to learn the standard formats in a very easy andfriendly way, aided by explanatory tool tips. These tips will betriggered automatically when the mouse is hovered over a field.The explanations include a description of the field, the format inwhich it is written and, if applicable, its units.

Files to useLaunchHTML.html, GLONASS Navigation Rinex v2.11.html,SP3 Version C.html, Observation Rinex v3.01.html,ANTEX v1.3.html, Observation Rinex v2.11.html,IONEX v1.0.html, Observation Rinex v2.10.html,SP3 Version C.html, RINEX CLOCKS v3.00.html,SBAS Navigation Rinex v3.01.html,GPS Navigation Rinex v2.11.html

Programs to useAny Web browser (Firefox can be used, as well).

Development

1. RINEX measurement files: v2.10

This standard gathers the GNSS observations collected by a receiver. Thefile is divided clearly into two different sections: the header section andthe observables section. While in the header global information is givenfor the entire file, the observables section contains the code and carriermeasurements, among others, stored by epoch.

Open file Observation Rinex v2.10.html with a Web browser and an-swer the following questions (the answer is provided at the end of eachquestion).

(a) Hover the mouse over the title ‘Observation RINEX 2.10 Format’,where some general information is given. Which was the first insti-tution to develop this format?

→ The Astronomical Institute of the University of Berne.

(b) What was the reason for developing such a standard?

→ The exchange of GPS data from several different GPS receivers.

7

gAGE/UPC

(c) Which type of optimisation has been applied to this standard?

→ Minimum space requirements, keeping the observation records as shortas possible.

(d) What is the maximum record (i.e. line) length?

→ Files are kept to 81-character lines.

(e) The header section contains a set of labels. Where are they located?

→ The header labels are located between the 61st and the 80st columnof each line.

(f) Where can a collection of currently used formats be found?

→ On the IGS website:http://igscb.jpl.nasa.gov/components/formats.html .

(g) The header section of this file is dual coloured in order to distinguishheader information from header labels. What is the first and the lastheader label of the header section?

→ The first label is ‘RINEX VERSION / TYPE’ while the last label is ‘ENDOF HEADER’.

(h) What is the difference between the ‘RINEX VERSION / TYPE’ and the‘COMMENT ’ labels?

→ While the first one is a mandatory label, the second is optional andmay not appear in some RINEX files.

(i) Hover over the first field in the ‘RINEX VERSION / TYPE’ line; whatis the main advance in this RINEX version?

→ Version 2 has been prepared to contain GLONASS or other satellitesystem observations apart from GPS satellites.

(j) Where is the antenna located approximately? In which referencesystem?

→ The approximate antenna position is (478 902 8.4701, 176 610.0133,419 501 7.0310) in the WGS-84 system.

(k) Hover over the first field in the ‘LEAP SECONDS’ line; what is thedifference between the various satellite systems, when counting leapseconds?

→ The Glonass time system is tied to UTC, so leap seconds are needed,for instance, to mix Galileo or GPS with Glonass data.

(l) How many satellites are present in the current file? To which satellitesystem do they belong?

→ There are 14 different satellites:14 GNSS satellites = 10 GPS + 3 Glonass + 1 SBAS.

8


(m) Line ‘PRN / # OF OBS ’ has to be consistent with the observableslisted in line ‘# / TYPES OF OBSERV’. What are these observations?Do all satellites contain the same observables in this example?

→ The observables are: L1, L2, P1, P2, C1, S1, S2.Glonass and SBAS satellites only have: L1, C1, S1.

(n) How does the standard indicate the end of the header?

→ The last field of the header is a record of 60 empty characters.

(o) The data section of this file is again dual coloured in order to distin-guish blocks of data. According two the different colours used, howmany epochs are included in this file?

→ There are two different epochs, each with a different colour.

(p) The first line of an epoch contains information on a whole block ofmeasurements. When is the first epoch of the file?

→ The first epoch corresponds to 5/3/2010 at 00:00:00.

(q) How many satellites are present in the first epoch? Is there anyparticular feature occurring due to this number?

→ The first epoch contains 14 different satellites. Because there aremore than 12 satellites, the list of epoch satellites is divided into twodifferent lines.

(r) Measurements follow the order stated in line ‘# / TYPES OF OBSERV’line. The satellite order is given in the first line of the epoch. Whatare the units for the observables?

→ L1, L2: cycles of the carrier.P1, P2, C1: metres.S1, S2: receiver dependent.

(s) Hover over the first L1 measure of satellite G13. The measure is giventogether with two indicators. What are these indicators? What dothey represent?

→ Loss of Lock Indicator: Depending on its value, it can show a cycleslip, an opposite wavelength factor, or an anti-spoofing measurement.Signal Strength: Projected into the [1-9] interval.

2. RINEX measurement files: v2.11

Open file Observation Rinex v2.11.html with a Web browser.

(a) Hover over the ‘WAVELENGTH FACT L1/2’ line records. The first linestates the default values for the wavelength measures for the L1and L2 frequencies. Which satellite system do the default valuesapply to? Interpret the second line of the ‘WAVELENGTH FACT L1/2’records.

→ The Default Wavelength Factor applies for GPS only.Three satellites (G14, G18, G19) have a full cycle factor in the firstfrequency (L1) and half a cycle factor in the second frequency (L2).

(b) Hover over the first record of line ‘# / TYPES OF OBSERV’. Whatobservation types are defined in RINEX version 2.11? In what unitsare these observations measured?

9

gAGE/UPC

→ Pseudorange measures: C and P code [m]

Carrier phase: L [cycles of the carrier]

Doppler frequency: D [Hz]

Signal-to-noise ratio: S [receiver-dependent].

(c) What value is set in the ‘RCV CLOCK OFFS APPL’ record? Where canthe Receiver Clock Offset be found later in the RINEX file?

→ It has a value of 1, which means that an offset is applied in thereceiver clock. The value of this offset is reported in the last recordof the first line of each epoch.

3. RINEX Measurement files: v3.01

Open file Observation Rinex v3.01.html with a Web browser.

(a) This RINEX version is newer than version 2. At first glance theheader section is larger and the observation data records are reor-ganised to be column readable. Which satellite system does this filebelong to? What type of file is it?

→ This file contains GPS, Glonass and SBAS observations, so it is amixed file. It is an observation data file. Note that the possible valuesmay have changed from the previous version.

(b) The date record in ’PGM / RUN BY / DATE’ also has been redesigned.What is the date format now? What has changed in the versions?

→ In version 2.11, there was no a strict rule stating date file creation.In version 3.01, the date has to follow the structure Year/Month/Day

- Hour/Minute/Second - Time zone.

(c) A ‘MARKER TYPE ’ record has been added to the header. What typeof marker type would report a station at the North Pole?

→ The North Pole is located in the middle of the Arctic Ocean, almostpermanently covered with constantly shifting sea ice. It suits the‘FLOATING ICE’ marker type.

(d) An extensive description of the ANTENNA can now be obtainedfrom this new standard. What type of antenna information is avail-able?

→ Antenna Number. Antenna Type + Radome Identifier.ARP: (Height, East Eccentricity, North Eccentricity).ARP: (X,Y,Z) when mounted on a vehicle.Antenna Phase Centre: (North, East, North) w.r.t. the ARP.Antenna Bore-sight: (North, East, North) or (X,Y,Z).Antenna Zero Direction: Azimuth or Vector.

(e) A new ‘SYS / # / OBS TYPES’ record has been added in this file.What observations are present for the SBAS satellites?Hover over the observation descriptors. How many pseudorange codedescriptors are present for the sixth Beidou (Compass) frequency?

→ Glonass and SBAS satellites have the same four observation types:L1C S1C C1C S1C. RINEX v3.01 defines C6I, C6Q, C6X pseudor-ange code descriptors for Beidou.

(f) A new ‘SIGNAL STRENGTH UNIT ’ record has been added to stan-dardise RINEX SSI. What indicator would have a signal-to-noiseratio of 33 dBHz at the output of the correlator?

10


→ From the RINEX table, it would present a 5 SSI value.

(g) Records ‘SYS / DCBS APPLIED’ and ‘SYS / PCVS APPLIED’ informif DCB or PCV has been applied. What programs/files have beenused in these files?

→ DCBs are corrected using the CC2NONCC program10 with the input filep1c1bias.hist. PCVs are corrected using the PAGES program withinput file igs05.atx.

(h) Hover over the ‘SYS / SCALE FACTOR’ data records. What is thepurpose of implementing such a scale factor?

→ The purpose of the scale factor is to increase resolution of the phaseobservations.

(i) Find the week number in the ‘LEAP SECONDS’ line. What is thereason for the week roll-over? When it did happen first?

→ Because it is a 10-bit number.It happened on 22/08/1999 at 00:00:00 GPS time.

(j) Hover over any observation data record. Why are there lines of 80characters, and lines that are longer?

→ While the epoch headers retain a record length of 80 characters, theobservation record length limitation of RINEX versions 1 and 2 hasbeen removed.

4. RINEX navigation files: v2.11 (GPS)

The standard navigation messages broadcast by the GNSS satellites dis-cussed here can vary slightly from one satellite system to another. Forexample, while the GPS navigation RINEX contains pseudo-Keplerian el-ements that permit the calculation of the satellite’s position, Glonass navi-gation RINEX contains the satellite’s position, velocity and Sun and Moonacceleration in order to integrate the satellite orbits using the Runge–Kutta numerical method.

Open file GPS Navigation Rinex v2.11.html with a Web browser.

(a) As usual, this file is divided into a header section and a data recordsection. The header section is shorter than in the observation RINEX.How short can a GPS navigation message RINEX header be?

→ The shortest header contains just three lines: ‘RINEX VERSION /

TYPE’, ‘PGM / RUN BY / DATE’ and ‘END OF HEADER’.

(b) What ionospheric corrections are given?

The alpha0, alpha1, alpha2, alpha3 and the beta0, beta1, beta2,beta3 coefficients for the Klobuchar model.

(c) How many leap seconds are used in the file? When is it recommendedto state the number of leap seconds?

→ Fifteen leap seconds. It is recommended for mixed GPS/Glonass files.

(d) This file contains the ephemerides for two different satellites, eachblock of ephemeris having a separate colour. Where is the satelliteidentifier found? What satellites are present in the file?

10Program CC2NONCC is available from https://goby.nrl.navy.mil/IGStime/cc2noncc/ .

11

gAGE/UPC

→ The satellite identifier is found in the first record of the ephemerisblock. The PRN identifiers present in the file are PRN 6 and PRN 13.

(e) The first line of each ephemeris block contains three records to com-pute the satellite clock offset to the GPS time. What are these threecoefficients?

→ They are the polynomial coefficients to compute the satellite clockoffset from the GPS system time. These coefficients are: bias, driftand drift rate from the GPS time.

(f) GPS orbits are nearly circular. In the third line can be found thebroadcast orbit eccentricity. What are the orbit eccentricities for thefile satellites?

→ PRN 6 has an eccentricity of 0.006 267 404 183 75.PRN 13 has an eccentricity of 0.002 002 393 477 60.

(g) The last non-blank field (second record in the eighth row) states thevalidity period for each ephemeris block. What is the value if it isnot known? In this case, what is the fitting interval?

→ The value is zero when the fitting interval is unknown. In this case,the fitting interval is [t0 − 2 h, t0 + 2 h].

5. RINEX navigation files: v2.11 (Glonass)

Open file GLONASS Navigation RINEX v2.11.html with a Web browser.

(a) How do you identify this file as a Glonass navigation message?

→ The RINEX file type value is a ‘G’.

(b) Does this file include any ionospheric information?

→ The Glonass navigation message does not broadcast ionospheric cor-rections.

(c) What correction has to be applied to correct Glonass system time toUTC for the SU time zone?

→ Tutc = Tsv + TauN - GammaN*(Tsv-Tb) + TauC.

(d) Each of the other lines of Glonass navigation files contain threerecords with satellite position, velocity and Sun–Moon acceleration.In which units are they given? What information gives the fourthrecord of each line?

→ Units are: km, km/s and km/s2.Message Frame Time, Satellite Health, Frequency Number, Informa-tion Age.

(e) Frequency information is found in the third row of each ephemerisblock. What are the channel numbers of the two satellites present inthe file? Which are the associated frequencies?

12


→ R3 used the 21st frequency slot, so

1602 + 0.5625 ∗ 21 = 1613.8125 MHz.R11 used the 4th frequency slot, so

1602 + 0.5625 ∗ 4 = 1604.2500 MHz.

6. RINEX navigation files: v3.01 (SBAS)

Open file SBAS Navigation RINEX v3.01.html with a Web browser.

(a) The SBAS broadcast navigation message is given in a new version(v3.01). The first change is observed in the first header line, wherethe file type and the satellite system are now clearly divided. Whatis the difference between the older version 2.11 in representing thenavigation messages?

→ In the older navigation message version, the satellite system recordwas unused. In version 2.11, file type N or G would directly representa GPS or Glonass navigation message.In version 3.01, file type N represents a navigation message, wherethe satellite system record specifies which of the G, R, S, E, M satellitesystem(s) is involved.

(b) The ‘TIME SYSTEM CORR’ line allows the satellite system time to betransformed to UTC time through a correction. What are the coef-ficients of the formula? Which is the augmentation system of thisnavigation message?

→ The formula is: CORR(t) = a0 + a1*DELTAT

Particularised:

CORR(t)= 0.1331791282E-06 + 0.107469589E-12*(t-552960)

The augmentation system is EGNOS.

(c) This file contains ephemerides for a geostationary satellite. Whatis the difference in time between the two records? Where can it befound?

→ The epoch time is located in the first line of each data epoch.The first epoch corresponds to 18/12/2010 at 00:01:04.The second epoch corresponds to 18/12/2010 at 00:05:20.So, between them, the elapsed time is 4 minutes and 16 seconds.

(d) SBAS navigation files are similar to Glonass ones, in that both con-tain records of satellite position, velocity and accelerations. Whatis the flag for a healthy satellite? Which IODN corresponds to theephemeris present in the file?

→ A healthy satellite contains a 0.0 Health flag.The first ephemeris block has IODN: 23.The second ephemeris block has IODN: 24.

13

gAGE/UPC

7. Global Ionospheric Map files: IONEX v1.0

Using a GNSS tracking network it is possible to extract information aboutthe TEC of the ionosphere on a global scale. The IONEX format is a well-defined standard used to exchange ionospheric maps. It follows the samephilosophy as the RINEX format, even when the files are organised intoa header and a data section where the maps are allocated.

Open file IONEX v1.0.html with a Web browser.

(a) Hover over the third record of the first line. How many sources cancontribute to produce an IONEX map? And how many models?

→ Several satellite sources can be used: Envisat, Geostationary,Glonass, GPS, TOPEX/POSEIDON, Navy Navigation Satellite

(NNS) or IRI. Two different models are possible: BENt or ERS.

(b) This file contain two types of information lines: COMMENT linesand DESCRIPTION lines. What is the difference between the tworecords? Which model is used in this IONEX map? When is thismap valid?

→ Description lines give a brief description of the technique and modelused, while comment lines can contain any kind of information. TheIONEX map model of this file is based on spherical harmonics. Theionospheric map is for Day of Year (DoY) 288 of 1995.

(c) What information would you expect to appear in the ‘OBSERVABLESUSED’ line when using a theoretical model?

→ A blank line is given when a theoretical model is used.

(d) After COMMENT line(s) the IONEX Map Grid is described. Givedetails about: the number and dimension of the maps present inthe current file with its mapping function; the number of stationsand satellites used for the TEC computations; the grid size and thesatellite elevation cut-off.

→ The IONEX file contains five 3D TEC/RMS/HGT maps with a 1/ cos(z)mapping function.80 stations and 24 satellites have been used to produce this map.The grid extends from 200 to 800 km in height with an equidistantincrement of 50 km.The grid extends from 85◦ to −85◦ in latitude and from 0◦ to 355◦

in longitude in increments of 5◦.

(e) There are some auxiliary data in this file. What type of informationis given, and in which units?

→ The IONEX map gives the DCBs and their RMS for the satellitesused in the map.The DCBs are given between the GPS P1 and P2 codes in units ofnanoseconds (of L1−L2 delay).

(f) Once the header section ends, the ionospheric maps are detailed.How many ionospheric maps are presented in the current file?

→ There are three different maps: a TEC; an RMS error map of theassociated TEC map; and a final map containing the heights at whichthe TEC values are obtained.

(g) Hover over the first TEC values. What is the time for this map?

14


→ The first map corresponds to 15/10/1995 at 00:00:00.

(h) How can the exponent values be interpreted?

→ The exponent values indicate the 10 exponent to apply to the TECvalues:Exponent: -3 TEC field; 1000 TEC value: 1000 · 10−3 = 1 TECU.TECU is the given unit for TEC, where 1 TECU corresponds to1016e−/m2.

(i) How would an non-available TEC value be seen?

→ Non-available TEC values are given as 99999 values.

(j) How many TEC values fit in a single line and in which units arethese values given?

→ TEC rows are given in 16 fields per line, up to the grid limits.

(k) Hover over any of the RMS values. What is the default exponent forstating the RMS values of the TEC maps?

→ The default exponent is -1: 10−1 = 0.1 TECU, where 1 TECU cor-responds to 1016e−/m2.

8. RINEX clock files: v3.00

The standard files provide station and satellite clock data. Four typesof information are given in this format: data analysis results for receiverand satellite clocks derived from a set of network receivers and satelliteswith respect to a reference clock; broadcast satellite clock monitoring;,discontinuity measurements; and calibration(s) of single GNSS receivers.

Open file RINEX CLOCKS v3.00.html with a Web browser.

(a) This clock data file starts with a header section as usual. Hoverover the first and second comment records. What is the differencebetween the comments? What kind of information does the secondcomment give?

→ The first comment is generic, while the second is a Timescale Re-Alignment comment. This comment is required if ‘Ax’ data are given(AR or AS). In case clock values have been time-scale shifted, themethod applied to all receiver and satellite clocks should be noted.

(b) Hover over the ‘SYS / # / OBS TYPES’ records. Which observationdescriptors are present in this RINEX clock file?

→ This file contains four different descriptors from the GPS system:C1W, L1W, C2W, L2W.

(c) Records ‘SYS / DCBS APPLIED’ and ‘SYS / PCVS APPLIED’ describethe DCB and PCV. What programs are used to apply different cor-rections?

→ DCB corrections are applied using the CC2NONCC program, while PCVcorrections are applied using the PAGES program.

(d) Records ‘STATION NAME / NUM’ and ‘STATION CLK REF’ give infor-mation about the station. Which receiver identifier is present in thefile? What external clock of this station is used for calibration?

→ The station name is the USNO with a receiver identifier 40451S003.The external clock is the USNO, connected via a continuous cable.

15

gAGE/UPC

(e) What is the analysis centre of this file?

→ The analysis centre is the USNO, using the GIPSY/OASIS software.

(f) This file uses two different groups of ‘# OF CLK REF’ and ‘ANALYSISCLK REF’. When does each clock reference apply?

→ The data set is for the date 14/07/1994. USNO clock referenceapplies from 00:00:00 to 20:59:59. Afterwards, the clock referenceused is TIDB from 21:00:00 to 23:59:59.

(g) How many receivers are included in the data file? Which referenceframe is used to give station coordinates?

→ Five different stations are used in the file: GOLD (USA), AREQ (Peru),TIDB (Australia), HARK (South Africa), USNO (USA).

(h) The data record section of this file comes right after the ‘END OF

HEADER’ record. Each clock data record starts with a data typeidentifier. Which ones are present?

→ The following clock data records are present: AR (Receiver Analysis),AS (Satellite Analysis), CR (Receiver Calibration), DR (Receiver Dis-continuities). The only missing record is the MS (Satellite Monitor)record.

(i) What data records are present for all clock data types? Which datarecords are sometimes present?

→ Records ‘Clock Bias’ and ‘Clock Bias Sigma’ are always present.The ‘Clock Rate’, ‘Clock Rate Sigma’, ‘Clock Acceleration’ and‘Clock Acceleration Sigma’ are only present for the AR clock datatype.

9. APC files: ANTEX v1.3

These standard files in ANTEX contain satellite and receiver antenna cor-rections. Satellite data include satellite and block-specific PCO. Receiverdata include elevation and azimuth-dependent corrections for combina-tions of antennas and radomes.

Open file ANTEX v1.3.html with a Web browser.

(a) As usual, this file contains a header section. Hover over the recordpresent in line ‘PCV TYPE / REFANT’. Which PCV is used in this file?Which antenna is used as a reference?

→ PCVs are relative (i.e. not absolute, see section 5.6.1, Volume I).This ANTEX file uses the AOAD/M T antenna as a reference.

(b) The different blocks of information are clearly identified using colours.What are the opening and closing records of each block? Which an-tennas are described in the file?

→ The antenna blocks start with record ‘START OF ANTENNA’ and endwith ‘END OF ANTENNA’. This ANTEX file contains three differentantenna descriptions. The first one is from the GLONASS R08 satel-lite, the second from the GPS satellite G12 (modernised block 2) andthe third corresponds to the AOAD/M B antenna.

(c) Analyse Glonass antenna record ‘TYPE / SERIAL NO’. How is thesatellite code (CNNN) interpreted? When was the satellite launched?How many satellites were launched that year before this one? Repeatthe exercise with the GPS satellite.

16


→ The Glonass antenna corresponds to a GLONASS (R) satellite, num-bered 729. It was launched during the year 2008. According to theANTEX record, it is the 67th launched satellite. The GPS antennais onboard the 58th GPS SV. It is the 52nd satellite launched during2006.

(d) Line ‘DAZI’ shows the azimuth increment used to characterise theantenna’s azimuth phase pattern. For satellite R08, is the PCVazimuth dependent? What about the GPS one?

→ Because a DAZI value of 0.0 is given, the PCVs of R08 and G12 arenot azimuth dependent.

(e) ‘ZEN1 / ZEN2 / DZEN’ gives information on both AZI and NOAZI

phase patterns. What satellite grids are used to study the anten-nas? Is there any difference between receiver and satellite antennas?

→ Both satellite grids start at 0.0◦ and end at 14.0◦ in 1◦ steps. Receiverantennas use zenith degrees, satellite ones use nadir degrees.

(f) ‘# OF FREQUENCIES’ determines the number of frequencies for eachantenna block. What frequencies are described in the block for eachsatellite phase pattern?

→ Two different frequencies are described. The Glonass satellite de-scribes G1 and G2 frequencies, while the GPS satellites describe L1

and L2.

(g) The frequency section extends from ‘START OF FREQUENCY’ to ‘ENDOF FREQUENCY’ records. What information is given? Give the eccen-tricity vector for both satellites. What is the origin of this vector?

→ The eccentricities of the APC and the phase pattern values areR08=(-545.00,0.00,2300.00) and G12=(-10.16,5.87,-93.55).The vector points from the satellite centre of mass to the satelliteAPC.

(h) How many non-azimuth-dependent (NOAZI) phase pattern valuesare specified? Why?

→ Fourteen different NOAZI values are specified, due to the ‘ZEN1 /

ZEN2 / DZEN’ definition. Because DAZI is set to 0, NOAZI-dependentphase patterns are specified.

(i) The third antenna corresponds to a receiver antenna. What is thecalibration method? Which agency has created such corrections?

→ Calibrations have been converted from file igs 01.pcv. TUM is thecreator of the file.

17

gAGE/UPC

(j) This antenna has a non-zero DAZI record for the PCVs. What isthe value of this increment? Where else can we see this DAZI?

→ This antenna block has a 30◦ azimuth increment for the PCVs. So,this value will be given from 0 to 360 in increments of 30◦.Apart from giving the NOAZI values, this data set includes the DAZI

values, both of them using a 0.0 to 90 grid with a 5◦ step.

10. Precise orbit and clock files: SP3 version C

Precise orbital data (satellite position and velocity), the associated satel-lite clock corrections, orbit accuracy exponents, correlation informationbetween satellite coordinates and satellite clock are available in this for-mat.

Open file SP3 Version C.html with a Web browser.

(a) The structure of this file is different from the RINEX ones seen upto now. Hover the mouse over the ‘Extended Standard Product 3

Orbit Format’ title, where some general information is given. Whatadditional information is included regarding to the SP3-c version?

→ Satellite clock corrections, orbit accuracy exponents, comment lines,the GPS week and the first epoch seconds of a week.

(b) What was the main advance in the SP3-b version? Did this changesome previous characteristics?

→ Version B of the SP3 files accommodated Glonass orbits. SP3-b modi-fications were backwards compatible with SP3-a, with the exceptionof the satellite identification records, from an I3 field to an A1,I2

one.

(c) What is the main advance in the SP3-c version? How is this achieved?

→ Files now include not only clock accuracy information, but also infor-mation on the accuracy of (X,Y, Z) satellite coordinates, which isadded using columns 61 to 80 in each position and clock record.

(d) How is this format organised? Is there any optional record?

→ The format of an SP3 file is a header, followed by a series of epochtimes, each with a set of position and clock records listed for eachsatellite. Optional records are: satellite velocities, clock correctionrate of change, position and clock correlation record (EP record)

and velocity and clock rate-of-change correlation record (EV record).

(e) The first line of the SP3 file contains information about the entirefile. What is the version of the current file? What might be the nextSP3 version? Which flag mode is set in this file? What time is thefirst epoch? How many epochs are included in this file? What typeof orbit is used in the file? Which agency has created the file?

→ The version of the file is C-version. SP3 versions follow the alpha-bet, so next one might be the SP3-D version. The velocity mode flagis set. This means the records will follow the order P,V, P,V, ...

in case there are additional records, (EP or EV), which would be inthe middle.The first epoch dates from 08/08/2001 at 00:00:00.There are 192 epochs up to a maximum of 10 million.

18


The orbit type is HLM, which means it has been fitted by applying aHelmert transformation.IGS is the agency that created the file.

(f) What is the symbol identifying the start of the second line? WhichGPS week number corresponds to this file? Which interval is usedin this file?

→ The ## symbols.This file corresponds to the GPS week 1126.A 900 s interval is used.

(g) The next block (lines 3–7) states the satellites used in the file. Howmany have contributed? What does a zero value mean? How manydifferent satellites from different satellite systems are identified?

→ There are 31 different satellites.The 0 value indicates that all identifiers have been listed.Each identifier consists of the satellite system indicator followed bya two-digit integer.

(h) From lines 8 to 12, orbit accuracy of the satellites is listed followingthe previous block order (lines 3–7). How is this accuracy exponentinterpreted?

→ For example, if the accuracy exponent is 13 → 213 mm ' 8 m. Thisaccuracy represents one standard deviation of the entire file (persatellite).

(i) The next block comprises lines 13 and 14. Although it is mainlyunused, what information is given in the file?

→ This block states the file type and the system time used in the file.

(j) The next block comprises lines 15 and 16. What information is givenin the file? What is the reason for using such base numbers?

→ This block contains the floating-point base number used for computingthe standard deviations of satellite position, velocity, clock correctionand rate of change of the clock correction. Better resolution can beobtained using a floating-point number different from 2.

(k) After the ’comment’ section, the data records start with the pre-viously seen time of first epoch. What symbols mark the start ofcomments and the new epoch?

→ Comments start with symbols ‘/*’, while the new epoch starts withsymbol ‘*’.

(l) The second epoch line contains the position and clock data record.What parameters are given? Which units are used? Explain thedifferent flags applied to the first satellite.

→ Satellite (X,Y,Z) positions, the clock correction with its correspond-ing standard deviation exponents. There are four final flags.Satellite positions are given in kilometres, clock correction in mil-liseconds. The exponents generate corrections in millimetres and pi-coseconds.The first satellite has set: a discontinuity flag between the previousepoch and the current epoch; an orbit position and clock predictionflag; and a manoeuvre flag.

19

gAGE/UPC

(m) The third epoch line contains the extended position and clock cor-relation record. What information is given in the first four records?What is the difference with the previous line? Which correlationcoefficients are given next?

→ The standard deviations of the satellite position and clock correctionare given with greater resolution than the approximate values givenin the position and clock record.The correlations between the X/Y, X/Z, Y/Z satellite coordinates, andthe correlations between the X/C, Y/C, Z/C satellite coordinates andclock.

(n) The fourth epoch line contains the velocity and clock rate-of-changerecord. In which units are satellite velocities, clock rate of changeand their deviations expressed? What happens if the deviations areunknown or too big to represent?

→ Velocities are given in decimetres/second and clock rate of changein microseconds/second. Velocity deviation is in millimetres/secondand clock rate-of-change deviation in picoseconds/second.A value of 99 means the standard deviation was too large to represent,while a blank means it is unknown.

(o) The fourth epoch line contains the extended velocity and clock rate-of-change record. What correlation coefficients are given? Why arethe values given greater than one?

→ The correlations between the Vx/Vy, Vx/Vz, Vy/Vz satellite velocities,and correlations between the Vx/Clock, Vy/Clock, Vz/Clock satellitevelocities and clock.Because they have to be divided by 107.

20

Research group of Astronomy & GeomaticsTechnical University of Catalonia

gAGE/UPC ©gAGE/UPC http://www.gage.upc.eduSu©gAGE/UPC http://www.gage.upc.edu

Tutorial 1GNSS Data Processing Lab Exercises

Prof. Dr. Jaume Sanz Subirana and Prof. Dr. J. M. Juan Zornozaassisted by Dr. Adrià Rovira Garcia

Research group of Astronomy & Geomatics (gAGE)Universitat Politècnica de Catalunya (UPC)

Barcelona, Spain


gAGE/UPC


gAGE/UPC ©gAGE/UPC http://www.gage.upc.edu 3

OVERVIEW• Introduction• The gLAB tool suite• Examples of GNSS Positioning using gLAB• Laboratory session organization

LABORATORY Session• Starting-up your laptop• Basic: Introductory lab exercises• Medium: Laboratory Work Project:

Kinematic positioning of a LEO sat.• Advanced: Homework



• This practical lecture is devoted to analyze and assess different issues associated with Standard and Precise Point Positioning with GPS data.

• The laboratory exercises will be developed with actual GPS measurements, and processed with the ESA/UPC GNSS-Lab Tool suite (gLAB), which is an interactive software package for GNSS data processing and analysis.

• Some examples of gLAB capabilities and usage will be shown before starting the laboratory session.

• All software tools (including gLAB) and associated files for the laboratory session are included in the USB stick delivered to lecture attendants.

• The laboratory session will consist in a set of exercises organized in three different levels of difficulty (Basic, Medium and Advanced). Its content ranges from a first glance assessment of the different model components involved on a Standard or Precise Positioning, to the kinematic positioning of a LEO satellite, as well as an in-depth analysis of the GPS measurements and associated error sources.

Introduction



• IntroductionThe gLAB tool suite

• Examples of GNSS Positioning using gLAB• Laboratory session organization

LABORATORY Session• Starting-up your laptop• Basic: Introductory lab exercises• Medium: Laboratory Work Project:

Kinematic positioning of a LEO sat.• Advanced: Homework

OVERVIEW



• gLAB has been developed under the ESA Education Office contract N. P1081434.

The gLAB Tool suite

Main features:• High Accuracy Positioning

capability.• Fully configurable.• Easy to use.• Access to internal computations.

The GNSS-Lab Tool suite (gLAB) is an interactive multipurpose educational and professional package for GNSS Data Processing and Analysis.



• gLAB has been designed to cope with the needs of two main target groups:

– Students/Newcomers: User-friendly tool, with a lot of explanations and some guidelines.

– Professionals/Experts: Powerful Data Processing and Analysis tool, fast to configure and use, and able to be included in massive batch processing.

The gLAB Tool suite



• Students/Newcomers:– Easiness of use: Intuitive GUI.– Explanations: Tooltips over the different options of the GUI.– Guidelines: Several error and warning messages. Templates for

pre-configured processing.

The gLAB Tool suite



• Students/Newcomers:– Easiness of use: Intuitive GUI.– Explanations: Tooltips over the different GUI options.– Guidelines: Several error and warning messages.

Templates for pre-configured processing.

• Professionals/Experts:– Powerful tool with High Accuracy Positioning capability.– Fast to configure and use: Templates and carefully chosen defaults.– Able to be executed in command-line and to be included in batch

processing.

..

The gLAB Tool suite



• In order to broad the tool availability, gLAB Software has been designed to work in both Windows and Linux environments.

• The package contains:– Windows binaries (with an installable file).– Linux .tgz file.– Source code (to compile it in both Linux and Windows

OS) under an Apache 2.0 license.– Example data files.– Software User Manual.– HTML files describing the standard formats.

The gLAB Tool suite



Modelling module:• Fully configurable model.• Satellite positions.• Satellite clock error correction.• Satellite movement during signal flight

time.• Earth rotation during signal flight time.• Satellite phase center correction.• Receiver phase center correction.

(frequency dependent).• Relativistic clock correction.• Relativistic path range correction.• Ionospheric correction (Klobuchar,

NeQuick, IONEX).• Tropospheric correction

- Simple and Niell mappings.- Simple and UNB-3 nominals.

• Differential Code Bias corrections.• Wind up correction.• Solid tides correction (up to 2nd

degree).

Read files capability:• RINEX observation v2.11 & v3.00• RINEX navigation message.• SP3 precise satellite clocks and orbits files• ANTEX Antenna information files.• Constellation status.• DCBs files.• GPS_Receiver_Type files.• SINEX position files.

Pre-processing module:• Carrier-phase prealignment.• Carrier-phase / pseudorange consistency

check.• Cycle-slip detection (customizable

parameters)- Melbourne-Wübbena.- Geometry-free CP combination.- L1-C1 difference (single frequency).

• Pseudorange smoothing.• Decimation capability.• On demand satellite enable/disable.• Elevation mask.• Frequency selection.• Discard eclipsed satellites.

The gLAB Tool suite



Filtering module:

• Able to chose different measurements to process (1 or more), with different weights. This design could be useful in future Galileo processing, where processing with different measurements may be desired.

• Fixed or elevation-dependant weights per observation.

• Troposphere estimation on/off.• Carrier-Phase or Pseudorange

positioning.• Static/Kinematic positioning (full

Q/Phi/P0 customization).• Able to do a forward/backward

processing.• Able to compute trajectories (no

need for a priori position).

Output module:• Cartesian / NEU coordinates.• Configurable message output.

Other functionalities:• Computation of satellite coordinates

and clocks from RINEX and SP3 files.• Satellite coordinates comparison

mode. For instance RINEX navigation vs. SP3, or SP3 vs. SP3 (along-track, cross-track and radial orbit errors, clock errors, SISRE).

• Show input mode. No processing, only parsing RINEX observation files.

• Current version allows full GPS data processing, and partial handling of Galileo and GLONASS data.

• Future updates may include full GNSS data processing.

The gLAB Tool suite



GNSS learning material package

– GNSS Book: Complete book with theory and algorithms (Volume 1), and with a Lab. course on GNSS Data Processing & Analysis (Volume 2).

– gLAB tool suite: Source code and binary software files, plus configuration files, allowing processing GNSS data from standard formats. The options are fully configurable through a GUI.

Includes three different parts, allowing to follow either a guided or a self-learning GNSS course:



IntroductionThe gLAB tool suiteExamples of GNSS Positioning using gLAB

• Laboratory session organization

LABORATORY Session• Starting-up your laptop• Basic: Introductory laboratory exercises (Ex1, Ex2)• Medium: Laboratory Work Project (LWP):

Kinematic positioning of a LEO satellite• Advanced: Homework

OVERVIEW



• Standard and Precise Point Positioning

– To Illustrate how easy to process GNSS data using gLAB, a GPS receiver will be positioned in the next examples using:

• Example 1: Broadcast orbits and clocks (SPP, kinematic).• Example 2: Precise Orbits and clocks (PPP, static).• Example 3: Precise Orbits and clocks (PPP, kinematic).

– Solutions will be compared with an accurate reference value of receiver coordinates to asses the positioning error.

Note: the receiver coordinates were keep fixed during the data collection.

Basic: Introductory Lab. Exercises



We will work after the correlator: Our input data are code and carrier measurements and satellite orbits and clocks.

16

RINEX FILES

ResearchResearch group fof A tAstronomy && G ticsGeomaticsTechnicTechnicTechnicalalalTechnicTechnicTechnicTechnicTechnicTechnicalalalalalal UniversUniversUnivers yityityityUniversUniversUniversUniversUniversUniversityityityityityity ofofofofofofofofof CatalonCatalonCataloniaiaiaCatalonCatalonCatalonCatalonCatalonCataloniaiaiaiaiaia

gAGE/UPC 1616



• GNSS data files follow a well defined set of standards formats: RINEX, ANTEX, SINEX…

• Understanding a format description is a tough task.

• These standards are explained in a very easy and friendly way through a set of html files.

• Described formats:– Observation RINEX – Navigation RINEX– RINEX CLOCKS – SP3 Version C– ANTEX

More details at: http://www.gage.es/gLAB

GNSS Format Descriptions

Open GNSS Formatswith Firefox internet browser



SPP Template: Kinematic positioning with single freq. C1 code + broadcast orbits and clocks.

1. Select the SPP Template 2. Upload the RINEX files:

- Measurement: roap1810.09o- Navigation: brdc1810.09n

3. RUN gLAB

Default output file:gLAB.out

1

2

3Note: Reference coordinates are from RINEX

Example 1: Standard Point Positioning (SPP)



• Plotting Results

Positioning with few meters of error is achieved in kinematic SPP mode.• Receiver navigated as a rover in pure

kinematic mode.• Single frequency C1 code is used.• Broadcast orbits and clocks.

Example 1: Standard Point Positioning (SPP)



PPP Template: Static positioning with dual freq. code & carrier (ionosphere-free combination PC,LC) + post-processed precise orbits & clocks.

1. Select the PPP Template 2. Upload data files:

-Measurement: roap1810.09o- ANTEX: igs05_1525.atx- Orbits & clocks: igs15382.sp3- SINEX: igs09P1538.snx

3. RUN gLAB

Default output file:gLAB.out 1

2

3

Example 2: Static Precise Point Positioning (PPP)



• Plotting Results

•Coordinates are taken as constants in nav. filter.

•Dual frequency Code and Carrier measurements.

•Precise orbits and clocks.•Measurements modellingat the centimetrelevel.

Centimetre level accuracy over 24h data is achieved in PPP static mode

Example 2: Static Precise Point Positioning (PPP)



From default configuration of [PPP Template], • Select kinematics in the [Filter] panel. Run gLAB and plot results.

Decimetre error level navigation after the best part of an hourReceiver navigated as a rover

in a pure kinematic mode.

Example 3: Kinematic Precise Point Positioning



OVERVIEWIntroductionThe gLAB tool suiteExamples of GNSS Positioning using gLABLaboratory session organization

LABORATORY Session• Starting-up your laptop• Basic: Introductory laboratory exercises (Ex1, Ex2)• Medium: Laboratory Work Project (LWP):




• The laboratory session is organized as an assisted activity were a set of exercises must be developed individually or in groups of two.

• As they are conceived as self-learning work, a detailed guide is provided in the slides (pdf file) to develop the exercises.

• A set of questions is presented, and the answers are also included in the slides.

• Teachers will attend individual (or collective) questions that could arise during exercise resolution.

Laboratory session organization



• The exercises are organized in three different levels of difficulty. The student can choose the level of exercises to do, although at least an introductory exercise is recommended to learn basic gLAB usage.

• 1. Basic: Introductory exercises 1 & 2.They consist of simple exercises to assess the model components for Standard and Precise Point Positioning.“Background information" slides are provided, summarizing the main concepts associated with these exercises.

Brief summaries of fundamentals in backup slides




• 2. Medium: Laboratory work project.It consists of the kinematic positioning of a Low Earth Orbit satellite.Different positioning modes are analyzed and different modeling options will be discussed.

Given that session time is limited to 3h, students who feel comfortable using gLAB, can skip part of the previous basic exercises (Ex1, Ex2) and jump to the Lab. Work Project.




• 3 . Advanced: Labeled as “Homework exercises”

A set of additional exercises addressed to those students that already have a solid background on GPS data processing.These exercises are out of the scope of this 3h laboratory session, and are posed for a possible further discussion…As in the previous cases, the answers to the posed questions are also included as BACKUP slides.

gawk 'BEGIN{g=(77/60)^2}{print $6, $4, (g*($13-$14)-($15-$16))/(g-1)}' meas.txt > PC.txt

A minimum knowledge of UNIX (e.g., awk) is required for these homework exercises.




IntroductionThe gLAB tool suiteExamples of Positioning with gLABLaboratory session organization

LABORATORY SessionStarting-up your laptop

• Basic: Introductory laboratory exercises (Ex1, Ex2)• Medium: Laboratory Work Project (LWP):


OVERVIEW



This tutorial has been designed to be executed under UNIX (Linux) Operative System (OS). Which is a very powerful and robust environment.

Nevertheless, the necessary tools are provided for Windows or Macintosh users to install this software and to emulate a UNIX command line shell over Windows.

Installing the software

Macintosh users can install the software through the Virtual Machine.

Windows users can install the windows version of gLAB and the Cygwin emulator of a Linux command shell.

Linux users can install the native version of the software



Backup solutionfor Macintosh users:8GB of free space in disk are required to install this SW.

Inside the “Virtual Machine” folder, there are two folders and one file. Select the OSX Installers folder and follow the instructions of document“VirtualBoxInstaller_OSX.pdf”

Inside the “Windows” folder, there is the installable gLAB program. Follow the instructions of Software Installationfile.



The Medium and Advanced exercises of this tutorial have been designed to be executed under UNIX (Linux) Operative System(OS). Which is a very powerful and robust environment.

Nevertheless, Windows OS users can do the laboratory session by using Cygwin, which is a tool that allows to emulate a UNIX command line shell over Windows.

Indeed, after installing Cygwin, users can develop the laboratory session as if they were working on a UNIX system (as this tutorial was designed).

Installing the softwareWindows users



Installing gLAB + Cygwin1.- First step: Click over the icon

Check the folder:C:\gLAB



2.- Second Step: Completing the gLAB Setup Wizard

Cygwin and gLAB installation must be selected.



Once the installation finish, the icons of gLAB,CygwinTerminal and the GNSS Data Processing folder will appear.

Tutorial slides /cygdrive/c/gLAB/win/SUMMER_SCHOOL/WORK_FILES

UNIX (Linux) console to execute “command line” sentences



Sugg

este

d d

esk

conf

igur

atio

n to

star

t wor

king

ESA/ JRC INTERNATIONAL SUMMER SCHOOL ON GNSS 2015 Research group of Astronomy & GeomaticsTechnical University of Catalonia

gAGE/UPC Su

Barcelona, Spain, 31 August - 10 September 2015

Local Organiser: Supported by:



NOTE:Data files are available at the folder:C:\gLAB\win\SUMMER_SCHOOL\WORK_FILES



Windows Troubleshooting: Execute only if gLAB doesn’t runSome distributions of windows (e.g. Windows XP) do not install some dlls required to run gLAB_GUI. This problem is fixed by installing the "Microsoft Visual C++ 2008 Service Pack 1 Redistributable Package MFC Security Update“.

To install this package:1) Go to the DLL_fix folder, inside C:\gLAB directory. 2) Execute vcredist_x64

or vcredist_x86

Backup



IntroductionThe gLAB tool suiteExamples of GNSS Positioning using gLABLaboratory session organization

LABORATORY SessionStarting-up your laptopBasic: Introductory laboratory exercises (Ex1, Ex2)

• Medium: Laboratory Work Project (LWP): Kinematic positioning of a LEO satellite

• Advanced: Homework

OVERVIEW



Exercise 1: Model components analysis for SPP

– This exercise is devoted to analyze the different model components of measurements (ionosphere, troposphere, relativity, etc.). This is done both in the Signal-In-Space (SIS) and User Domains.

Basic: Introductory laboratory exercises

Given that session time is limited to 3h, students who feel comfortable using gLAB, can skip part of the basic exercises (Ex1, Ex2) and jump to the Lab. Work Project.



1. Compute SPP using files: chpi0010.04o,brdc0010.04nCachoeira Paulista station (in the south of Brazil: =-22.7º, =-45.0º). January 1st 2004.

Exercise 1: SPP Model components analysis

1

2

3

4

5gLAB.out



NEU Position Error plot from gLAB.out

North East Up

FULL SPP model

NEU plot template configuration



The different model components will be analyzed with gLAB:• Using the previous data

file, the impact of neglecting each model component will be evaluated in the Range and Position domains

• A baseline example of this analysis procedure for the ionosphericcorrection is provided as follows.

• The same scheme must be applied for all model terms.

The modeling options set in this panel are applied by default to the SPP solution.




Example of model component analysis: IONO.

Default configuration for SPP

In the Default configuration the output file was gLAB.out

Set output file as gLAB1.out

Disable Ionosphericcorrection

The procedure explained here is applicable for all the cases: iono, tropo…1. In Modeling panel,

disable the model component to analyze. (in this example: disable Ionospheric correction)

2. Save as gLAB1.outthe associated output file.

Notice that the gLAB.outfile contains the processing results with the FULL model, as it was set in the default configuration.

1

2

3



NEU Position Error plot from gLAB1.out

gLAB1.out

North East Up


No Iono. correction



gLAB1.out gLAB.outTime (sec) Vertical

Y-min, Y-max

Vertical Position Error plot from gLAB.out, gLAB1.out

Click Clear to restart plots1

2 3



Horizontal Position Error plot: gLAB.out, gLAB1.out

gLAB.out East: 19 North: 18

X-min, Y-min, Y-max


2 3gLAB1.out



Ionospheric model component plot: gLAB.out

gLAB.outSelect IONO

Note: Use the gLAB.out file.In gLAB1.out file this model component was switched off.

Code delay

Ionosphere delays code and advances carrier measurements.

Carrier advance



Summary: Iono. model component analysis

gLAB.out

gLAB1.out

gLAB.out

gLAB1.out

gLAB.out

Ionospheric correction (broadcast Klobuchar )Ionospheric delays are larger at noon due to the higher insulation.

Large positioning errors (mainly in vertical) appear when neglecting iono. corr.

Code delay Plot only

gLAB.out

gLAB1.out



• First order (~99.9%) ionospheric delay depends on the inverse of squared frequency:

where is the number of electrons per area unit along ray path (STEC: Slant Total Electron Content).

• Two-frequency receivers can remove this error source (up to 99.9%) using ionosphere-free combination of pseudoranges (PC) or carriers (LC).

• Single-frequency users can remove about a 50% of the ionospheric delay using the Klobuchar model, whose parameters are broadcast in the GPS navigation message.

240.3

ion If

eI N ds

2 21 2

2 21 2

1 2f L f LLCf f

I

ion

Ionospheric delayThe ionosphere extends from about 60 km over the Earth surface until more than 2000 km, with a sharp electron density maximum at around 350 km. The ionospheric refraction depends, among other things, of the location, local time and solar cycle (11 years).


Backup



keepgLAB1.outas output file

Set again: IonoDisable: Tropo

Example of model component analysis: TROPO.

The gLAB configuration can be set-up as follows, to repeat the processing without applying the tropospheric correction (but using the ionosphere again!):

• The same scheme must be applied for all other model terms (TGDs, relat...)



gLAB.out

gLAB1.out

gLAB.out

gLAB1.out

gLAB.out gLAB.out

gLAB1.out


Tropospheric correction (blind model)

Tropospheric and vertical error are highly correlated. A displacement of vertical component appears when neglecting tropospheric corrections.



Tropospheric delayThe troposphere is the atmospheric layer placed between Earth’s surface and an

altitude of about 60 km. The effect of troposphere on GNSS signals appears as an extra delay in the

measurement of the signal travelling from satellite to receiver. The tropospheric delay does not depend on frequency and affects both the

pseudorange (code) and carrier phases in the same way. It can be modeled by:– An hydrostatic component, composed of dry gases (mainly nitrogen and oxygen)

in hydrostatic equilibrium. This component can be treated as an ideal gas. Its effects vary with the temperature and atmospheric pressure in a quite predictable manner, and it is the responsible of about 90% of the delay.

– A wet component caused by the water vapor condensed in the form of clouds. It depends on the weather conditions and varies faster than the hydrostatic component and in a quite random way. For high accuracy positioning, this component must be estimated together with the coordinates and other parameters in the navigation filter.


Backup



gLAB.out

gLAB1.out

gLAB.outgLAB1.out

gLAB.out gLAB.out

gLAB1.out


Relativistic correction on satellite clock due to orbit eccentricity.This is an additional correction to apply at the receiver level. The satellite clock oscillator is modified on factory to compensate the main effect (~40 s/day).




Relativistic clock correction1) A constant component, depending only on nominal value of satellite’s orbit major semi-axis. It

is corrected modifying satellite’s clock oscillator frequency:

being f0 = 10.23 MHz, we have f=4.464 10-10 f0= 4.57 10-3 Hz. So, satellite should use f’0=10.22999999543 MHz.

2) A periodic component due to orbit eccentricity must be corrected by user receiver:

Being =G ME =3.986005 1014 (m3/s2) the gravitational constant, c =299792458 (m/s) light speed in vacuum, a is orbit’s major semi-axis, e is its eccentricity, E is satellite’s eccentric anomaly, and r and v are satellite’s geocentric position and speed in an inertial system.

2'100 0

20

1 4.464 102

f f v Uf c c

2 sin( ) 2 ( )arel e E metersc c

r v

Backup



gLAB.out

gLAB1.out

gLAB.outgLAB1.out

gLAB.out gLAB.out

gLAB1.out


P2-P1 Differential Code Bias (Total Group Delay [TGD]) correction.These instrumental delays can affect up to few meters, being the satellite TGDs broadcast in the navigation message for single frequency users.



Total Group Delay correction (TGD) (P2-P1 Differential Code Bias [DCB])

• Instrumental delays are associated to antennas, cables, as well as different filters used in receivers and satellites. They affect both code and carrier measurements.

• Code instrumental delays depend on the frequency and the codes used, and are different for the receiver and the satellites.

• Dual frequency users cancel such delays when using the ionosphere free combination of codes and carrier phases.

• For single frequency users, the satellite instrumental delays (TGDs) are broadcast in the navigation message. The receiver instrumental delay, on the other hand, is assimilated into the receiver clock estimation. That is, being common for all satellites, it is assumed as zero and it is included in the receiver clock offset estimation.


Backup



gLAB.out

gLAB1.out

gLAB.outgLAB1.out

gLAB.out gLAB.out

gLAB1.out


Satellite clock offsets

This is the largest error source, and it may introduce errors up to a thousand kilometers.



Satellite clock offsets

– They are time-offsets between satellite/receiver clocks time and GPS system time (provided by the ground control segment).

– The receiver clock offset is estimated together with receiver coordinates.

– Satellite clock offset values are provided:• In real-time, within the broadcast navigation message with a

few meters of erroror, • In post-process mode, by IGS precise products with

centimeter-level accuracy.


Backup



Exercise 2: Model components analysis for PPP

– This exercise is devoted to analyse the additional model components used in Precise Point Positioning (the ones which are not required by SPP). This is done in Range and Position Domains.

Basic: Introductory laboratory exercises

Given that session time is limited to 3h, students who feel comfortable using gLAB, can skip part of the basic exercises (Ex1, Ex2) and jump to the Lab. Work Project.



• Compute the kinematic PPP solution using files: chpi0010.04o, igs_pre1400.atx, igs12514.sp3

Note: The igs_pre1400.atx file contains the APC used by IGS before GPS week 1400.

1

2 Set Kinematic

Exercise 2: PPP Model components analysis

3



Kinematic PPP solution using files chpi0010.04o, igs_pre1400.atx, igs12514.sp3

gLAB.out

Set output file gLAB.outfor the FULL model, as in previous case.

4

5




• Additional model components are used now in the FULL model to assure a centimeter level modeling.

• Precise orbits and clocks instead of broadcast ones.

• Dual frequency Code and Carrier data instead of only single frequency code.

• Iono-free combination of codes and carriers to remove ionospheric error and P1-P2 DCBs.




• Code measurements are unambiguous but noisy (meter level measurement noise).

• Carrier measurements are precise but ambiguous, meaning that they have some millimetres of noise, but also have unknown biases that could reach thousands of km.

• Carrier phase biases are estimated in the navigation filter along with the other parameters (coordinates, clock offsets, etc.). If these biases were fixed, measurements accurate to the level of few millimetres would be available for positioning. However, some time is needed to decorrelate such biases from the other parameters in the filter, and the estimated values are not fully unbiased.

Code and carrier Measurement noise

Note: Figure shows the noise of code and carrier prefit-residuals, which are the input data for navigation equations.

Cycle-slip

Code is unambiguous, but noisy

Carrier is ambiguous, but precise

Zoom ofcarrier noise


Backup




Broadcast:• Few metres of

accuracy for broadcast orbits and clocks

Orbits & clocks accuracies

Precise:• Few centimetres

of accuracy for broadcast orbits and clocks

Backup



Example of model component analysis: Solid Tides

Default configuration for

PPP

In the Default configuration the output file was gLAB.out

Set output file as

gLAB1.out

DisableSolid Tides correction

Proceed as in the previous exercise:1. In Modeling panel,

disable the model component to analyze.

2. Save as gLAB1.out the associated output file.

Notice that the gLAB.outfile contains the processing results with the FULL model, as it was set in the default configuration.Make plots as in previousexercises (see slides 38-40).

1

2

3



gLAB1.out gLAB.out Time (sec) Vertical

Y-min, Y-max

Vertical Position Error plot from gLAB.out, gLAB1.out

Click Clear to restart plots

1

2 3

-0.4-0.4 0.4



Horizontal Position Error plot: gLAB.out, gLAB1.out

gLAB.out East: 19

North: 18

X-min, Y-min, Y-max

($1==“OUTPUT”)

Click Clear to restart plots

1

2 3gLAB1.out

-0.4 0.4 -0.4 0.4-0.4-0.4 0.4



Solid Tides model component plot: gLAB.out

gLAB.out SelectSOLIDTIDES


Solid Tides plot28SOLIDTIDES



Solid TidesIt comprises the Earth’s crust movement (and thence receiver coordinates variations) due to the gravitational attraction forces produced by external bodies, mainly the Sun and the Moon.

Sun

Moon

gLAB.out

gLAB1.out

gLAB.out

Solid Tides:These effects do not affect the GNSS signals, but if they were not considered, the station coordinates would oscillate with relation to a mean value.They produce vertical (mainly) and horizontal displacements.


gLAB.out

gLAB1.out



Receiver Antenna Phase center (APC)

GNSS measurements are referred to the APC. This is not necessarily the geometric center of the antenna, and it depends on the signal frequency and the incoming radio signal direction. For geodetic positioning a reference tied to the antenna (ARP) or to monument is used.

Receiver APC:The antenna used for this experiment, has the APC position vertically shifted regarding ARP.Thence, neglecting this correction, an error on the vertical component occurs, but not in the horizontal one.

(ARP)

APC

ARP

L2 Antenna Phase centerL1 Antenna Phase center

Antenna Reference Point (ARP)


gLAB.out

gLAB1.out

gLAB.out

gLAB1.out

gLAB.out



Satellite Mass Center to Antenna Phase Center

Satellite Mass Center(MC)

Broadcast orbits are referred to the antenna phase center, but IGS precise orbits are referred to the satellite mass center.

gLAB.out

Satellite MC to APC:The satellite MC to APC eccentricity vector depends on the satellite. The APC values used in the IGS orbits and clocks products are referred to the iono-free combination (LC, PC) . They are given in the IGS ANTEX files (e.g., igs05.atx).

Satellite AntennaPhase Center (APC)


gLAB.outgLAB.out

gLAB1.out gLAB1.out



Wind-up affects only carrier phase. It is due to the electromagnetic nature of circularly polarized waves of GNSS signals.As the satellite moves along its orbital path, it performs a rotation to keep its solar panels pointing to the Sun direction. This rotation causes a carrier variation, and thence, a range measurement variation.

Satellite rotationPhase

variation

gLAB.out

Wind-UpWind-up changes smoothly along continuous carrier phase arcs. In the position domain, wind-up affects both vertical and horizontal components.


gLAB.out

gLAB1.out

gLAB.out

gLAB1.out




LABORATORY SessionStarting-up your laptopBasic: Introductory laboratory exercises (Ex1, Ex2)Medium: Laboratory Work Project (LWP): Kinematic positioning of a LEO satellite

• Advanced: Homework

OVERVIEW



• A kinematic positioning of GRACE-A satellite is proposed in this exercise as a driven example to study and discuss the different navigation modes and modelling options for code or code & carrier positioning of a rover receiver.

More details at: http://op.gfz-potsdam.de/grace/index_GRACE.html

LWP: Kinematic positioning of a LEO satellite

GPS OmnidirectionalAntenna: Satellite Attitude and Orbit Control System

GPS Backup OmnidirectionalAntenna: AOCS

GPS 45º FOV Antenna: Radio Occultation Data



• The following “preliminary” questions are posed:– Could a LEO satellite like GRACE-A be kinematically positioned as a

rover receiver (i.e., car, aircraft...)? Why?– Would both Standard and Precise Positioning be achievable?

Note: The RINEX file graa0800.07o contains GPS dual freq. Measurements.

– Which model components should be set for each positioning mode?• Relativistic correction?• Tropospheric correction?• Ionospheric correction?• Instrumental delays (TGDs)?• Solid Tides correction?• Antenna phase centre corrections?• Others ???

– In case of successful positioning, which accuracy is expected?




The following positioning modes are proposed to be explored:

– Code positioning + broadcast orbits:1. Single frequency: C1 code (and no ionospheric corrections).2. Dual frequency: PC code combination (i.e., ionosphere-free

combination).– Code and carrier positioning + precise orbits and clocks:

3. Dual frequency: PC, LC combinations (i.e., ionosphere-free combinations).

4. GRAPHIC combination of C1 code and L1 carrier phase.5. Single frequency: C1 code and L1 carrier (and no ionospheric

corrections).

Data files: Measurements file: graa0800.07oGPS orbits and clocks:

Broadcast: brdc0800.07nPrecise: cod14193.sp3, cod14193.clk, igs05_1402.atx

GRACE-A Precise Reference Orbit file: GRAA_07_080.sp3




Example of computation with gLAB: Code positioning + broadcast orbits: Single frequency: C1 code.

Set calculateSelect files graa0800.07obrdc0800.07n

Set SPPSet data decimation to 30 seconds instead of 300 to have a higher number of output samples

Mode1: Single frequency C1 code with broadcast orbits & clocks

1

2

Set SPP

3



Example of computation with gLAB: Code positioning + broadcast orbits: Single frequency: C1 code.

Disable all messages except:

• Print INFO Messages• Print OUTPUT Messages

to avoid big output files

Run gLAB

From SPP template disable:• Ionospheric• Tropospheric

Set output file asgLAB.out




• Accuracy assessment of the computed solution:Complete the following steps to compare the output solution (from gLAB.out file) with the reference coordinates of file GRAA_07_080.sp3:

1. Convert the output gLAB.out file to sp3 format:

Execute (in Console): out2sp3 gLAB.outNote: this sentence generates the file: orb.sp3

(see file content with: less orb.sp3)

:

out2sp3 gLAB.out

2. Compare the computed coordinates orb.sp3 with reference GRAA_07_080.sp3. Note: Use the configuration file dif.cfg.

gLAB_linux –input:cfg dif.cfg –input:SP3 GRAA_07_080.sp3 –input:SP3 orb.sp3

Note: this sentence generates the file: dif.out

3. Plot dif.out file:The Graphic User Interface can be used for plotting




Set plotting ranges[Xmin, Xmax] [Ymin,Ymax]

Plotting dif.out

with the GUI

Upload file dif.out in Plot 1, Plot 2 & Plot 3

1

2

3

4




Questions

1. Is it reasonable to disablethe tropospheric and ionospheric corrections?

2. Like GPS satellites, LEOs are also affected by relativistic effects. Is it necessary to introduce an additional model term to account for this effect?

3. What could be the reason for the large error peaks seen in the plots?

Zoom




Answer to Question 1: Is it reasonable to disable the tropospheric and ionospheric corrections?– Troposphere:

The troposphere is the atmospheric layer placed between Earth’s surface and an altitude of about 60 km.

GRACE-A satellite is orbiting at about 450 km altitude, thence no tropospheric error is affecting the measurements.

– Ionosphere:The ionosphere extends from about 60 km over the Earth surface until more than

2000 km, with a sharp electron density maximum at around 350 km. GRACE-A satellite, orbiting at about 450 km altitude, is less affected by the

ionosphere than on the ground, but nonetheless a few meters of slant delay could be experienced. On the other hand, as the correction from Klobucharmodel is tuned for ground receivers, its usage could produce more harm than benefit (see HW1).

Homework:HW1: Assess the ionospheric delay on the GRACE-A satellite measurements. Compare with the Klobuchar model corrections.


Backup



Answer to Question 2: In this approach, is it necessary to introduce an additional model term to account for the relativity effect on LEO satellite?– GRACE-A clock is affected by general and special relativistic effects (due to the

gravitational potential and satellite speed). But this is not a problem, because the receiver clock is estimated along with the coordinates. Notice that this relativistic effect will affect all measurements in the same way, and thence, it will be absorbed into the receiver clock offset estimation.

Answer to Question 3: What could be the reason for the large error peaks seen in the plots?– The large error peaks are associated to bad GPS-LEO satellite geometries and

mismodelling. Notice that the satellite is moving at about 8 km/s and therefore the geometry changes quickly (see HW2). Also, the geometry is particularly poor when GRACE-A satellite is over poles.

Homework:HW2: Plot in the same graph the “True 3D error”, the “Formal 3D error” (i.e, the 3D-sigma) and the number of satellites used. Analyze the evolution of the error.


Backup




Execute (in Console): out2sp3 gLAB.out

orb.sp3



dif.out3. Plot dif.out file:

Example of computation with gLAB: Code positioning + broadcast orbits: Dual frequency: PC

code combination.

1

3

Complete the steps (from previous configuration):1. [Modeling]:

• Disable P1-P2 correction2. [Filter]:

• Dual Frequency• PC measurement

3. Run gLAB4. In console mode:

• Convert the gLAB.outto orb.sp3 format file.

• Compute differences with reference file GRAA_07_080.sp3

Mode 2. Dual frequency PC code with broadcast orbits & clocks

From previous configuration, disable (TGD):

• P1 – P2 Correction 2From previous configuration, set:

• Dual Frequency

• PC Measurement



Questions4. Why is the solution noisier

than the previous one with C1 code?

5. Discuss the pros and cons of the ionosphere-free combination of codes (PC), compared with C1 code.

6. How could the performance be improved?

Plotting• Make the same plots as in

the previous case.


Zoom



Questions4. Why is the solution noisier

than the previous one with C1 code?

5. Discuss the pros and cons of the ionosphere-free combination of codes (PC), compared with C1 code.

6. How could the performance be improved?

Plotting• Make the same plots as in

the previous case.


Zoom



Answer to Question 4: Why the solution is noisier than the previous one with C1 code?

The iono-free combination of codes P1 and P2 is computed as: ;

Thence, assuming uncorrelated P1, P2 measurements with equal noise , it follows:

Answer to Question 5: Discuss the pros and cons of the ionosphere-free combination of codes (PC).– Combination PC removes about the 99.9% of ionospheric delay, one of the most difficult error

sources to model, but two frequency signals are needed. On the other hand, PC is noisier than the individual codes C1, P1 or P2 (see HW3).

Answer to Question 6: How could the performance be improved?– Smoothing the code with the carrier and/or using precise orbits and clock products as well.

Homework:HW3: Assess the measurement noise on the C1, P1, P2 and PC code measurements.

2 21 1 2 2 1 2

2 21 2 1

f P f P P PPcf f

27760

3Pc


Backup



Example of computation with gLAB: Code & Carrier + precise orbits & clocks: Dual frequency (LC, PC)

Set calculateSelect files graa0800.07ocod14193.sp3cod14193.clkigs05_1402.atx

Set PPP Set SPP

Set data decimation to 30 seconds instead of 300 to have a higher number of output samples

Mode 3. Dual freq. LC, PC carrier and code with precise orbits & clocks

Set Precise (2 files)

1

2

3



From PPP configuration, disable:• Receiver Antenna Phase Center• Receiver Antenna Ref. Point• Ionospheric (already disabled)• P1 – P2 (already disabled)• Tropospheric• Solid Tides correction

Switch to Kinematic

Disable Estimate Troposphere





1. Run gLAB

2. Generatedif.out file

3. Make plotsas before

Set plotting ranges[Xmin, Xmax] [Ymin,Ymax]

Upload file dif.out in Plot 1, Plot 2 & Plot 3

1

2

3

4



orb.sp3




Disable all messages except:

• Print INFO Messages• Print OUTPUT Messagesto avoid big output files

Run gLAB

2

3

1





Questions7. Which is the improvement

in precise orbits and clocks accuracy, regarding the broadcast case?

8. How do carrier phase measurements allow to improve the accuracy?

9. Why do large peaks appear?10. Why does a 40-50 cm bias

appear in the radial component?

11. Why do wind-up and satellite antenna phase center offset corrections have to be applied? What about the solid tides correction?


Zoom



Answer to Question 7: Which is the improvement in precise orbits and clocks accuracy, regarding the broadcast case?– Broadcast orbits and clocks are accurate at the level of few meters.– Precise orbits and clocks IGS products are accurate at few centimeter level (see HW4).

Answer to Question 8: How do carrier phase measurements allow to improve the accuracy?– Code measurements are unambiguous but noisy (meter-level measurement noise).– Carrier measurements are precise but ambiguous (few millimetres of noise, but with

an unknown bias that can reach thousands of kilometres).– The carrier phase biases are estimated in the navigation filter along with the other

parameters (coordinates, clock offsets, etc.). If these biases were fixed, then measurements accurate at the level of few millimetres, would be available for positioning. However, some time is needed to decorrelate such biases from the other parameters in the filter, and the estimated values are not fully unbiased.

• Homework:HW4: Assess the broadcast orbits and clock accuracy using the precise products as the truth.


Backup



Answer to Question 9: Why do large peaks appear?– The peaks are related to massive cycle-slips experienced after each revolution (about

1.5 h). – After a cycle-slip happens, the filter has to restart the carrier ambiguity. This is not a

problem when it occurs on a single satellite (being the others well determined), as its ambiguity is estimated quickly. But when a massive cycle-slip occurs, the filter needs more time to converge (see HW5).

Answer to Question 10: Why does a 40-50 cm bias appear in the radial component?– This is the GRACE-A antenna phase centre offset. Please notice that we are

positioning the Antenna Phase Centre (APC), while the coordinates in the SP3 reference file (GRAA_07_080.sp3) are referred to the satellite Mass Centre (MC).

• Homework:HW5: Analyze the carrier phase biases convergence in this kinematic PPP positioning.


Backup



Answer to Question 11: Why do wind-up and GPS satellite antenna phase center offset corrections have to be applied? What about the solid tides correction?

– Wind-up correction: Wind-up only affects the carrier phase measurements, but not the code ones. This is due to the electromagnetic nature of circularly polarised waves of GPS signals.The correction implemented in gLAB only accounts for the satellite movement relative to a receiver with fixed coordinates. An additional correction to account for the GRACE-A motion along its orbital path could also be included, but since most part of this effect will be common for all satellites, it will be absorbed by the receiver clock offset estimation.

– GPS satellite antenna phase center: Precise orbits and clocks of IGS products are relative to the GPS satellite mass centre (unlike the broadcast ones, which are relative to the satellite antenna phase centre [APC]). Thence an APC offset vector must be applied.

– Solid tides correction: No Earth’s Solid Tides corrections are needed because the rover is not on the ground.


Backup



Example of computation with gLAB: Code and Carrier + precise orbits & clocks: Single frequency (GRAPHIC)



orb.sp3




From previous configuration, unset:• TGD correction

1

2

Complete the steps (from PPP configuration mode):1. [Model]:

• Disable P1 – P2 Corr.2. [Filter]:

• Single Frequency• C1C (C1 code [*])• G1C (GRAPHIC)• Set Kinematic Mode


• Convert the glab.outto orb.sp3 format file.


Make plots as before.

Mode 4. Single freq. with L1, C1 GRAPHIC comb. and precise orbits & clocks

FroFroFroFrFroFrorFrFrFrFrrFrFFrFFFFFFFFFFFFF m pm pm pm pm pm pmm revrevrevereverever iouiououiouiooioo s s ssssssssconnnoconfigfigurauratiotioon,n,n,n,,,,,,nn,,,,,,,,,,,,,,,,, nnunsuunsunsunsunnunsunsunsunsnsunsnunsuunsunsunsssunsnsssnnunsuuuuuuunssssnnnnunsnnuuuunsunsunsunsuunssunuuu et:et:et:et:et:et:et:eeet:et:etet:tet:tttteeeeeeeet::ttttteeet:teetteet:etet:eteeeet•••• TGDTGDTGDTGDTGDTGDTGDTGDGDGDTGDTGDTGDTGDGDTGDTGTGDGGGTGDTGTGTGDDDGTTGDTGDTGDT DTGGDGGGTT DDGTGDT coccc rre titicticticttiiitittiittitiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiionoonoooononooonononoonnonononononoonnonnnnoooo

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 [*] Note: C1C must be set due to gLAB architecture, but it is assigned a large sigma to avoid the C1 code noise and ionospheric error.

C1=100 meters

G1=0.5 meters

1C1CG1C

Single frequency

Skip thewarning

Kinematic




Questions

12. Which is the main benefit of the GRAPHIC combination?

13. Why is the solution noisier than the previous one with LC, PC?

14. Would the performance be improved directly using the L1, P1 measurements (like in the LC, PC case)?

Zoom



Answer to Question 12: Which is the main benefit of the GRAPHIC combination?– The GRAPHIC combination is defined as:

– Thence, since the ionospheric refraction has opposite sign in code P1 and carrier L1, GRAPHIC removes the ionospheric error.

– On the other hand the code noise is reduced by a factor 2 (i.e., ).– However, this is an ambiguous measurement due to the unknown carrier phase bias.– Note: Due to the gLAB filter design, a code measurement must also be provided to the

filter along with the GRAPHIC one. Nevertheless, a large sigma noise is set to this code in order to downweight this measurement in the filter (in this way the solution will be driven by the GRAPHIC combination).

Answer to Question 13: Why is the solution noisier than the previous one with LC, PC?– Unlike the previous case (where carrier phase data with few millimetres of error were

provided), now the most accurate measure provided to the filter is the GRAPHIC combination with tens of centimetres of error.

Answer to Question 14: Let’s see the next two exercises.

1 112

G P L

1/ 2G


Backup



Example of computation with gLAB: Code and Carrier + precise orbits & clocks: Single frequency (L1, C1)

Mode 5. Single freq. L1, C1 carrier and code with precise orbits & clocks

1

From previous configuration, complete the following steps:1. [Input]: Upload the brdc0800.07n

file in the P1-P2 correction.2. [Model]: Set P1-P2 correction, select

RINEX Navigation File as DCB source.

Note: TGDs (i.e, P1-P2 DCBs) are needed for single-frequency positioning.

21





orb.sp3




4

Complete the steps 3. [Filter]:

• Single Frequency measurements

• L1P (L1 carrier)• C1P (P1 code)


• Convert the gLAB.outto orb.sp3 format file.



3C1PL1P

Single frequency

Set C1P=1 meterL1P=0.01 meters

Skip thewarning

Example of computation with gLAB: Code and Carrier + precise orbits & clocks: Single frequency (L1, C1)




Questions

15. Explain why the solution has a more defined pattern, with large oscillations.

16. No ionospheric corrections have been applied in this run. What would happen if the Klobuchar model is applied?




Answer to Question 15: Explain why the solution has a more defined pattern, with large oscillations.– This effect is due to the error introduced by the ionosphere and the broadcast

differential code biases inaccuracy.

Answer to Question 16: No ionospheric corrections have been applied in this run. What would happen if the Klobuchar model is applied?– In general, the performance will degrade. As commented before, the correction from

Klobuchar model is tuned for ground receivers, only removes about the 50% of ionospheric delay, and its usage can produce more harm than benefit. (see HW6).

Homework:HW6: Apply the Klobuchar model and discuss the results.HW7: Generate a file with the satellite track (in a Earth-Fixed Earth-Centeredreference frame) to be viewed with .


Backup




LABORATORY SessionStarting-up your laptopBasic: Introductory laboratory exercises (Ex1, Ex2)Medium: Laboratory Work Project (LWP): Kinematic positioning of a LEO satelliteAdvanced: Homework

OVERVIEW



Proposed Homework exercises

HW1: Assess the ionospheric delay on the GRACE-A satellite measurements. Compare with the Klobuchar model corrections.

HW2: Plot in the same graph the “True 3D error”, the “Formal 3D error” (i.e, the 3D-sigma) and the number of satellites used. Analyze the evolution of the error.

HW3: Assess the measurement noise on the C1, P1, P2 measurements and the PC code combination.

HW4: Assess the broadcast orbits and clocks accuracy using the precise products as the truth.

HW5: Analyze the carrier phase biases convergence in this kinematic PPP positioning.



HW6: Apply the Klobuchar model to the L1, P1 positioning with precise orbits and clocks and discuss the results.

HW7: Generate a file with the satellite track (in a Earth-Fixed Earth-Centeredreference frame) to be viewed with .

( ......

Proposed Homework exercises



Backup slides

Homework help and answers



Configure gLAB as in Mode 1 and complete the following steps:

1. [Output]: set • Print INPUT Message• Print MODEL Message (see message content in the Tooltips)

2. Run gLAB.

3. Make plots:[Analysis] section:• Click on the preconfigured Ionospheric

combinations option.• Complete the [Plot1, Plot2, Plot3] panels

configuration as indicated in the next slide.

Note: This configuration will provide:Plot 1: L1-L2 as a function of time for ALL sat.Plot 2: L1-L2 as a function of time for PRN16.Plot 3: P2-P1 as a function of time for PRN16

HW1: Assessing the ionospheric delay on the GRACE-A satellite

Backup



$11-$12 L1-L2$10-$9 P2-P1

$11-$12 L1-L2

Plot 1

Plot 2

Plot 3


Note: This plot take some time to rise !

Backup



graph.py -f gLAB.out -c '($1=="INPUT")' -x4 -y'($11-$12)' --l "ALL" -f gLAB.out -c '($1=="INPUT")&($6==16)' -x4 –y '($10-$9)' -so --l "PRN16 P2-P1" -f gLAB.out -c '($1=="INPUT")&($6==16)' -x4 –y '($11-$12)' -so --l "PRN16 L1-L2" --xn 43000 --xx 67000 --yn -10 --yx 15

Plot HW1-a Comments:• The ionospheric delay (STEC) computed from L1-L2 (aligned)

carriers is shown in blue for all satellites.• The red circles show the L1-L2 delay for sat. PRN16• The green circles show the ionospheric delay on PRN16

computed from P2-P1 code measurements.As it is shown in the plot, the STEC variations are typically at

the meter level, but in some cases they increase up to several meters.

The code measurement noise and multipath in the P2-P1 combination is typically at the meter level, but in the ends of data arcs (low elevation rays) can reach up to a few meters.

1mL1-L2 delay=1.55 mL1 delay

The previous plot can be also generated in console mode as follows (see graph.py –help):


Backup



Working in console modeThe next commands compute the ionospheric delay from C1, L1 measurements:

1. Using the configuration file meas.cfg, read the RINEX and generate the MEAS message with data format:

Execute:

2. From file meas.txt, compute the ionospheric delay as

3. From previous file, plot the ionospheric delay for the time interval [43000:67000]. Show in the same plot: 1) ALL satellites, 2) PRN16 and 3) PRN21 (see Plot HW1-b in next slide).

graph.py -f I1.txt -x2 -y3 -s. --cl y --l "ALL" -f I1.txt -c '($1==16)' -x2 -y3 -so --cl r --l "PRN16" -f I1.txt -c '($1==21)' -x2 -y3 -so --cl g --l "PRN21" --xn 43000 --xx 67000 --yn -10 --yx 10

gLAB_linux -input:cfg meas.cfg -input:obs graa0800.07o > meas.txt

11 1 12I C L bias

gawk '{print $6,$4,($11-$14)/2}' meas.txt > I1.txt


[Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P]1 2 3 4 5 6 x x 9 10 11 xx 13 14 15 16 ]

Backup



Plot HW1-b: STEC variations of few meters are typically experienced , but in some cases they reach up to 8 meters of L1 delay.

Plot HW1-c: L1-C1 iono estimate is less noisier than the P2-P1. On the other hand, large discrepancies appear when comparing with Klobuchar corrections

Large discrepancies with Klobuchar appear




Plot HW1-c generation (working with the GUI and in console mode):

1. Using the gLAB configuration of exercise 1, activate the “Ionospheric Correction” option in the [Modelling] panel and run again gLAB. The program will output the file gLAB.out.

(see help and file format executing: gLAB_linux –messages, or gLAB_linux –help).

2. “grep” the MODEL messages of file gLAB.out, selecting the C1P [PRN, time Klob_iono] data:

Note: the Klob_data is shifted by “-3” meters to align the curves in the plot

3. Plot in the same graph the ionospheric delays of satellites PRN16 and PRN21 from I1.txt and klob.txt file (see Plot HW1-c in the previous slide).

Note: Both the Graphic User Interface (GUI) panel or the graph.py tool (in console mode) can beused for plotting.

grep MODEL gLAB.out |grep C1P|gawk '{print $6,$4,$25-3}' > klob.txt


Backup



Complete the following steps1. Configure gLAB as in Mode1 and set Print EPOCHSAT Messages in Output panel.

(see message content in the Tooltip, or executing gLAB_linux –messages).

Remember that IONO corrections were unable in Mode 1.

2. Run gLAB.The program will output the file gLAB.out.

3. Generate the dif.out file from gLAB.out as in the previous exercises.

Plot the results: In the same graph, plot the “3D error” [from file dif.out], the formal error (the 3-D sigma) and

the number of satellites used in the computation [from file gLAB.out].

graph.py -f dif.out -x4 -y9 -s- --l "3D error" -f gLAB.out -c '($1=="OUTPUT")' -x4 -y'($5*5)' -s- --cl r --l "5*sigma" -f gLAB.out -c '($1=="EPOCHSAT")' -x4 -y6 -s- --cl g --l "N. sat. used" --xn 43000 --xx 67000 --yn 0 --yx 20

HW2: Plot in the same graph the “True 3D error”, the “Formal 3D error” and the number of satellites used. Analyze the result.

Note:In the previous plot, the 3-D sigma is multiplied by 5 to enlarge the image.3 -D sigma PDOP

Backup



Large discrepancies with Klobuchar appearSTEC variations of few meters, but in somecases, reaching up to 8 meters of L1 delay.

Plot HW2-aPeriodic error peaks appear, mostly associated with losing a satellite and/or with bad geometries.

Plot HW2-b: Zoom of Plot HW2-a. Along the peaks associated to bad geometries, mismodelling is also producing some error trends.

HW2: Plot in the same graph the “True 3D error”, the “Formal 3D error” and the number of satellites used. Analyze the result.



A) The next commands compute the C1 code noise and multipath:1. Using the configuration file meas.cfg, READ the RINEX and generate the MEAS message with

data format:

Execute:

2. From meas.txt file,

Compute C1 code noise and multipath as:

3. From C1.txt file, Plot the C1 code noise and multipath for time interval [43000:67000]. Show in the same graph: 1) ALL satellites, 2) PRN16 and 3) PRN21 (see Plot HW3-a)

graph.py -f C1.txt -x2 -y3 -s. --cl y --l "ALL" -f C1.txt -c '($1==16)' -x2 -y3 -so --cl r --l "PRN16" -f C1.txt -c '($1==21)' -x2 -y3 -so --cl g --l "PRN21" --xn 43000 --xx 67000 --yn 8 --yx 28


gLAB_linux -input:cfg meas.cfg -input:obs graa0800.07o > meas.txt

gawk 'BEGIN{g=(77/60) 2}{print $6, $4 , $11-$14-2*($14-$16)/(g-1)}' meas.txt > C1.txt

HW3: Code measurements noise assessment: C1, P1, P2 and PC

121 1 ( 1 2)1CM C L L L

27760

Backup



B) The next commands compute the P1 code noise and multipath:1. Using the meas.txt file generated before, with the MEAS message data format:

Compute P1 code noise and multipath as:

2. From previous P1.txt file, Plot the P1 code noise and multipath for time interval [43000:67000]. Show in the same graph: 1) ALL satellites, 2) PRN16 and 3) PRN21 (see Plot HW3-b)

graph.py -f P1.txt -x2 -y3 -s. --cl y --l "ALL" -f P1.txt -c '($1==16)' -x2 -y3 -so --cl r --l "PRN16" -f P1.txt -c '($1==21)' -x2 -y3 -so --cl g --l "PRN21" --xn 43000 --xx 67000 --yn 8 --yx 28


gawk 'BEGIN{g=(77/60) 2}{print $6, $4 , $13-$14-2*($14-$16)/(g-1)}' meas.txt > P1.txt

121 1 ( 1 2)1PM P L L L

27760


Backup



C) The next commands compute the P2 code noise and multipath:1. Using the meas.txt file generated before, with the MEAS message data format:

Compute P2 code noise and multipath as:

2. From previous P2.txt file, Plot the P2 code noise and multipath for time interval [43000:67000]. Show in the same graph: 1) ALL satellites, 2) PRN16 and 3) PRN21 (see Plot HW3-c)

graph.py -f P2.txt -x2 -y3 -s. --cl y --l "ALL" -f P2.txt -c '($1==16)' -x2 -y3 -so --cl r --l "PRN16" -f P2.txt -c '($1==21)' -x2 -y3 -so --cl g --l "PRN21" --xn 43000 --xx 67000 --yn 8 --yx 28


gawk 'BEGIN{g=(77/60) 2}{print $6, $4 , $15-$16-2*g*($14-$16)/(g-1)}' meas.txt > P2.txt

222 2 ( 1 2)1PM P L L L

27760


Backup



D) The next commands compute the PC combination noise and multipath:1. Using the meas.txt file generated before, with the MEAS message data format:

Compute PC noise and multipath as:

2. From previous PC.txt file, Plot the PC combination noise and multipath for time interval [43000:67000]. Show in the same graph: 1) ALL satellites, 2) PRN16 and 3) PRN21 (see Plot HW3-d)

graph.py -f PC.txt -x2 -y3 -s. --cl y --l "ALL" -f PC.txt -c '($1==16)' -x2 -y3 -so --cl r --l "PRN16" -f PC.txt -c '($1==21)' -x2 -y3 -so --cl g --l "PRN21" --xn 43000 --xx 67000 --yn 8 --yx 28


PcM Pc Lc2 21 1 2 2 1 2

2 21 2 1

f L f L L LLcf f

gawk 'BEGIN{g=(77/60) 2}{print $6, $4, (g*($13-$14)-($15-$16))/(g-1)}' meas.txt > PC.txt


2 21 1 2 2 1 2

2 21 2

;1

f P f P P PPcf f

L

P

Backup



Comments• Large noise patterns appear at the end

of each data arc. This is due to interference cross-talk with other components. The figure at bottom shows the multipath map for the GRACE-A .

• P2 code is noisier than P1 or C1.• PC code combination is the noisiest one,

as expected.

C1 multipath map of sat. GRACE_A.

A GPS satellite track is shown in blue

This figure is from P. Ramos-Bosch PhD dissertation, gAGE/UPC 2008].

Plot HW3-a Plot HW3-b

Plot HW3-c Plot HW3-d




Complete the following steps:File brdc0800.07n contains the orbit and clocks data broadcast in the GPS navigation message. Files cod14193.sp3, cod14193.clk contain the precise orbits and clocks computed in post-process by “CODE” center (IGS precise orbits and clocks products program).

1. Execute the following sentence to compute the difference of satellite coordinates and clock offsets between both orbits and clocks sources:

2. Select the SATDIFF message of dif.tmp file:

3. Plot dif.out file as in the first exercise.

Note:

gLAB_linux -input:nav brdc0800.07n -input:SP3 cod14193.sp3 -input:ant igs05_1402.atx > dif.tmp

HW4: Broadcast orbits and clocks accuracy assessment using the IGS precise products as the accurate reference (i.e, the truth).

grep SATDIFF dif.tmp > dif.out

SATDIFF message content is shown in the table beside.(see gLAB_linux –messages).The IGS post-processed products are accurate at few cm level, thence they can be taken as the truth.

2 2 21( Rad Clk) ( Alon Cross )49SISRE

Backup



Comments• Meter level errors are found on

broadcast orbits and clocks.• The bias seen in the radial component is

due to the different APC’s used by the GPS ground segment (i.e, in broadcast orbits) and by IGS (precise products).

• This bias is compensated by a similar shift in clocks.

• For the Signal-In-Space-Range-Error (SISRE), please see the plot below.

Plot HW4-a1 Plot HW4-b1

Plot HW4-c1 Plot HW4-d1

Plot HW4-e1




CommentsThe previous computations have been repeated, but using the ANTEX file gps_brd.atx, instead of igs05_1402.atx.

This new ANTEX file contains the GPS antenna phase center offsets used by the GPS ground segment, not the IGS ones.

• Notice that the biases in the radial component have disappeared.

Plot HW4-a2 Plot HW4-b2

Plot HW4-c2 Plot HW4-d2

Plot HW4-e2




HW5: Analyze the carrier phase biases convergence in the kinematic PPP positioning.

Plot the results: Plot the ionosphere-free bias estimates as a function of time for the time interval [40000:70000]. Show in the same graph: 1) ALL satellites, 2) PRN16 and 3) PRN21 (see Plot HW5-d).

grep POSTFIT gLAB.out| gawk '{i=$6" "$4;a[i]=$13}END{for (i in a) print i,a[i]}' |sort -n > amb.out

graph.py -f amb.out -x2 -y3 -f amb.out -x2 -y3 -c '($1==16)' --l "PRN16" -f amb.out -x2 -y3 -c '($1==21)' --l "PRN21" --xn 40000 --xx 70000 --yn -10 --yx 10

Note: The GUI can be used instead of the “graph.py” command.

Complete the following steps1. Configure gLAB as in Mode 2 for the Kinematic PPP positioning. Activate the “Print POSTFIT

messages” in the OUPUT panel(see message content in the Tooltip, or executing gLAB_linux –messages).

2. Run gLAB.The program will output the file gLAB.out.

3. From gLAB.out, “grep” the POSTFIT message and generate the file amb.out, containing the estimates of ambiguities for each epoch. Take the last estimated value of the ambiguities for each epoch. This can be done by executing:



Comments

• Large peaks appear in the carrier phase biases due to massive cycle-slips: – Satellite tracking loses happen

periodically after each revolution.– These satellite loses produce massive

cycle slips which leads to a global reinitialization of carrier-phase biases in the navigation (Kalman) filter .

– After such ambiguities reinitialization, the filter needs some time to converge.

• Carrier phase ambiguities converge quickly thanks to the rapid variation of geometry due to the LEO movement along its orbital path.

Plot HW5-a Plot HW5-b

Plot HW5-c Plot HW5-d

Zoom

ZoomZoom

HW5: Analyze the carrier phase biases convergence in the kinematic PPP positioning.



Code and Carrier + precise orbits & clocks: Single frequency (L1, C1) + Klobuchar ionosphere

1

Configure gLAB as in Mode 5 and complete the following steps:1. [Input]: Upload the

• brdc0800.07n file to IONO• brdc0800.07n file to DCBs

2

2. [Model]: set• P1 – P2 corr.• IONO corr.

HW6: Single freq. L1, C1 carrier and code with precise orbits & clocks using Klobuchar ionospheric corrections





orb.sp3




4

Complete the steps

3. [Filter]:• Single Frequency

measurements:• L1P (L1 carrier)• C1P (P1 code)

4. In console mode:• Convert the gLAB.out

to orb.sp3 format file.• Compute differences

with reference file GRAA_07_080.sp3


3

C1PL1P

Single frequency

Set C1P= 1 meterL1P = 0.01 meters


Code and Carrier + precise orbits & clocks: Single frequency (L1, C1) + Klobuchar ionosphere



Comments• A clear degradation is seen when

applying the Klobuchar model to the LEO.• This is due to the large error introduced

by this model which was designed for ground receivers, not for LEO’s.

• Next plot compares the L1 delay computed from Klobuchar with the STEC experienced by the GPS signal.




HW7: Generate a file with the satellite track (in a Earth-Fixed Earth-Centered reference frame) to be viewed with Google Earth

Complete the following steps1. Select the satellite [longitude, latitude, height] coordinates of message OUTPUT in the gLAB.out

file. Generate a file with these coordinates (comma-separated).

2. Add the header (Prefix.kml) and the tail (Postfix.kml) files to the previous track.tmpdata file:

3. View the file with:

grep OUTPUT gLAB.out |gawk 'BEGIN{OFS=","} {print $16,$15,$17}' > track.tmp

cat Prefix.kml > grace_track.kmlcat track.tmp >> grace_track.kmlcat Postfix.kml >> grace_track.kml



Thanks for yourattention



Oth

er

Tuto

rials

are

ava

ilabl

e a

t ht

tp:/

/www

.gag

e.up

c.ed

u



• The ESA/UPC GNSS-Lab Tool suit (gLAB) has been developed under the ESA Education Office contract N. P1081434.

• The data set of GRACE-A LEO satellite was obtained from the NASA Physical Oceanography Distributed Active Archive Center at the Jet Propulsion Laboratory, California Institute of Technology.

• The other data files used in this study were acquired as part of NASA's Earth Science Data Systems and archived and distributed by the Crustal Dynamics Data Information System (CDDIS).

• To Pere Ramos-Bosch for his fully and generous disposition to perform gLAB updates in his afterhours.

• To Adrià Rovira-Garcia for his contribution to the edition of this material and gLAB updating.

• To Deimos Ibáñez for his contribution to gLAB updating and making the Windows installable version for this tutorial.

Acknowledgements


gAGE/UPC @ J. Sanz & J.M. Juan 1

Tutorial 2Measurements analysis

and error budget

Contact: [email protected] site: http://www.gage.upc.edu

Slides associated to gLAB version 2.0.0




The authorship of this material and the Intellectual Property Rights are owned by J. Sanz Subirana and J.M. Juan Zornoza.

These slides can be obtained either from the server http://www.gage.upc.edu,or [email protected]. Any partial reproduction should be previously authorized by the authors, clearly referring to the slides used.




This tutorial is devoted to analysing and assessing the GNSS measurements and their associated errors. This is done over four groups of test cases: 1.- Atmospheric propagation effects on GNSS signals. Analysis of the errors due to the

troposphere and the ionosphere.2.- Code measurement noise and multipath on C1, ionsphere-free and Melbourne-

Wübbena combinations.3.- Carrier smoothed code. Analysis of the code-carrier divergence of the ionosphere.4.- Broadcast orbits and clocks accuracy versus the IGS precise products.

The laboratory exercises will be developed with actual GPS measurements, and processed with the ESA/UPC GNSS-Lab Tool suite (gLAB), which is an interactive software package for GNSS data processing and analysis. All software tools (including gLAB) and associated files for the laboratory session are included in the CD-ROM or USB stick associated with this tutorial.

Aim of this tutorial


gAGE/UPC @ J. Sanz & J.M. Juan

Introduction: gLAB processing in command line.Test cases on Atmospheric Propagation Effects:Troposphere, Ionosphere. Test cases on Measurement Noise and Multipath: C1, Ionosphere-free and Melbourne Wübbena combinations.Test cases on Carrier Smoothed Code: Code-carrier divergence.Test cases on Broadcast Orbits and Clocks Accuracy

OVERVIEW

4



Console to execute “command line”

sentences

A “notepad”with the

command line sentence is provided to facilitate the

sentence writing: just “copy” and

“ paste” from

notepad to the working

terminal.

gLAB processing in command line



The different messages providedby gLAB and its content can befound in the [OUTPUT] section.

By placing the mouse on a givenmessage name, a tooltip appearsdescribing the different fields.

Backup

gLAB_linux -messages

In console mode: execute




Introduction: gLAB processing in command line.Test cases on Atmospheric Propagation Effects: Troposphere, Ionosphere.Test cases on Measurement Noise and Multipath: C1, Ionosphere-free and Melbourne Wübbena combinations.Test cases on Carrier Smoothed Code: Code-carrier divergence.Test cases on Broadcast Orbits and Clocks Accuracy

OVERVIEW

7



Test cases on Atmospheric Propagation Effects:

Troposphere, Ionosphere



Tropospheric delayThe troposphere is the atmospheric layer situated between the Earth’s surface and an

altitude of about 50 km.The effect of the troposphere on GNSS signals appears as an extra delay in the

measurement of the signal travelling from satellite to receiver.

The tropospheric delay does not depend on frequency and affects both the pseudo-range(code) and carrier phases in the same way. It can be modeled by:

• A hydrostatic component, composed of dry gases (mainly nitrogen and oxygen) inhydrostatic equilibrium. This component can be treated as an ideal gas. Its effects varywith the temperature and atmospheric pressure in a reasonably predictable manner, and itis responsible for about 90% of the delay.

• A wet component caused by the water vapor condensed in the form of clouds. It dependson the weather conditions and varies faster than the hydrostatic component and in a totallyrandom way. For high accuracy positioning, this component must be estimated togetherwith the coordinates and other parameters in the navigation filter.

9

Troposphere





-Measurement : roap1810.09o - ANTEX: igs05_1525.atx - Orbits & clocks: igs15382.sp3 - SINEX: igs09P1538.snx

3. RUN gLAB

Default output file:gLAB.out1

2

3

Exercise 1: Zenith Troposphere Delay estimation

10



Plotting Results• Coordinates are taken as

constants in nav. filter.• Dual frequency Code and

Carrier measurements.• Precise orbits and clocks.• Measurements modellingat the centimetrelevel.

Centimetre level accuracyover 24h data is achieved

in PPP static mode

11




The ZTD in this file is given in mm of delay. Thus, it is converted to m to compare with gLAB resultsgrep ROAP roap1810.09zpd | gawk -F\: '{print $3} ' | gawk '{print $1,$2/1000}' > roap_igs.trp

ftp://cddis.gsfc.nasa.gov/pub/gps/products/troposphere/new/2009/181/roap1810.09zpd.gz

1 2

The troposphere is estimated as a Random Walk process in the Kalman Filter. A process noise of 1cm/sqrt(h) has been taken.

12




gLAB_linux -input:cfg gLAB_p51_ex6S.cfg -input:obs roap1810.09o -input:SP3 igs15382.sp3 -input:ant igs05_1525.atx -input:snx igs09P1538.snx

graph.py -f gLAB.outK -x4 -y9 -s.- -c '($1=="FILTER")' -l "PPP Kinematic" -f gLAB.outS -x4 -y9 -s.- -c '($1=="FILTER")' -l "PPP Static" -f roap_igs.trp -s.- -l "IGS" --xl "time (s)" --yl "metres" --yn 2.40 --yx 2.55

-t "Session 5.1, Ex6b: Zenith tropospheric delay Estimation"


Equivalent command line sentences:



Questions: • What is the level of discrepancy between the estimated ZTD and the

accurate IGS determination?• What is the variation of ZTD in 24 hours due to the wet content?• What is the proportion of wet component compared with the dry (or

hydrostatic) component?





where STEC is the number of electrons per area unit along ray path (STEC: Slant Total Electron Content).

• Two-frequency receivers can remove this error source (up to 99.9%) using ionosphere-free combination of pseudo-ranges (PC) or carriers (LC).

• Single-frequency users can remove about 50-70% of the ionospheric delay using the Klobuchar model, whose parameters are broadcast in the GPS navigation message.

15

eSTEC N ds

2 21 2

2 21 2

1 2f P f PPCf f

1I

Ionospheric delayThe ionosphere extends from about 60 km over the Earth’ssurface up to more than 2000 km, with a sharp electron densitymaximum at around 350 km. The ionospheric refraction depends,among other things, on the location, local time and solar cycle (11years).

240.31I STECf

Ionosphere



Depict the ionospheric delays for the different satellites in view from station amc2 • This is a simple exercise aimed to illustrate how to use gLAB

to easily analyze GNSS measurements and theircombinations.

• gLAB will used to read the RINEX measurements file and togenerate a “text” with the measurements provided in acolumnar format (more suitable for making plots).

Exercise 2: Ionospheric delay analysis

• From “text” file, compute and plot the Ionosphericdelay for a given satellite, by using code and carrier measurements at f1, f2:

2 1 21

1 2

I

I

P P P I KL L L I Ambiguity

1 1 1

2 2 2

2 12 2

P L I ambiguityP L I ambiguity

16



The target is to generate this plot to depict the

ionospheric delay from code & carrier data

2 1 21

1 2

I

I


1 1 12 1P L I ambiguity

1 2 121

2 221 1 2

1 1.546 ; 11

/ (154 /120)f f


Carrier Phase L1-L2 (ambiguous but precise)

Code P2-P1 (unambiguous but noisier)

Ambiguity= P L

Iono

sphe

ric c

ombi

natio

n (m

eter

s)Exercise 2: Ionospheric delay analysis



1 1 21 1

2 2 21 2

P I K

P I K1 1 1 1

2 2 2 2

L I BL I B

, is in sat

erecSTEC N dl STEC TECUs

16 21 10 / 0.10 of 1- 2 delayTECU e m m L L

2 21 2 16

1 22 21 2

40.310 ; ( is in of delay)

f fI STEC I m L L

f f

21 21, 21sat

recK K K

As the satellite clocks are referred to the ionosphere-free combination of codes (PC), the cancels in such combination. Note: is broadcast in GPS nav. Message.1 21

satTGD K

Refers to all non-dispersive terms: geometric range, clocks, tropo. delay… (see [R-1]).

Ionospheric delay

Inter-frequency bias21satK 2 2

1 1 2 22 2

1 2C

f P f PPf f

i i i iB N bCarrier ambiguities

Ni is an integer number. bi is a real number (fractional part of ambiguity)

2 1

121

221 1 2

11 1.546

1

/f f

Code measurement content Carrier measurement content

Backup




1.- Read RINEX file with gLAB and generate a “measurements file” in a columnar format (the easiest to manipulate and plot content):

Using the configuration file meas.cfg, READ the RINEX and generate the MEAS file:

19

[Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 xx xx 14 15 16 ]

gLAB_linux -input:cfg meas.cfg -input:obs coco0090.97o -input:nav brdc0090.97n > coco.meas

-pre:dec 1 -print:none -print:meas

--model:satphasecenter --model:recphasecenter --model:satclocks --pre:cs:li --pre:cs:bw

gLAB configuration fileRINEX

Measurementfile

RINEX Navigation

file

OUTPUT: measurement file in columnar format





-pre:dec 1-print:none-print:meas

--model:satphasecenter--model:recphasecenter--model:satclocks--pre:cs:li--pre:cs:bw

RINEX Measurement

file

RINEX Navigation

file

Disable:--model:satphasecenter --model:recphasecenter

--model:satclocks

Set data decimation to 1s-pre: dec 1

Disable cycle-slip detectors:--pre:cs:li --pre:cs:bw

Input Files:coco0090.97obrdc0090.97n

MEAS file

Set default SPP config.

Backup




2.- Manipulate the file with the easy & powerful awk (or gawk) programming language (to compute the combinations of measurements):

From coco.meas file:

Compute different ionospheric combination of codes and carriers, and generate the obs.txt file containing the fields: [PRN,sec, P2-P1, (P2-L2)/5.09, (P1-L1)/3.09, L1-L2, Elev/10]

21

gawk '{print $6,$4,$15-$11,($15-$16)/5.09,($11-$14)/3.09,$14-$16,$7/10}' coco.meas > obs.txt

PRN#6

sec#4

(P2-P1)

#15 -- #11

(P2-L2)/5.09

#15 -- #16

(P1-L1)/3.09

#11-- #14

(L1-L2)

#14 -- #16

Elev/10#7

P1 L1 P2 L2 ] [Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 xx xx 14 15 16




3.-Plot results with “graph.py” (you can use the gnuplot as well)

From obs.txt file:

Show in the same plot the following iono. delays for satellite PRN01: P2-P1, (P2-L2)/5.09, (P1-L1)/3.09, L1-L2, Elev./10

22

graph.py -f obs.txt -c'($1==01)' -x2 -y3 --l "P2-P1" -f obs.txt -c'($1==01)' -x2 –y4 --l "(P2-L2)/5.09" -f obs.txt -c'($1==01)' -x2 -y5 --l "(P1-L1)/3.09" -f obs.txt -c'($1==01)' -x2 –y6 --l "L1-L2" -f obs.txt -c'($1==01)' -x2 –y7 --l "Elev/10" --yn -10 --yx 15 --xl "time (s)" --yl "meters of L1-L2 delay"

[PRN, sec, P2-P1, (P2-L2)/5.09, (P1-L1)/3.09, L1-L2, Elev/10] 1 2 3 4 5 6 7

File to plot

Condition:Select PRN01

(from 1-st field)

Fields to plot:#2 (x-axis)

versus#3 (y-axis)

Label:P2-P1




zoom

2 1 21

1 2

I

I



1 2 121

2 221 1 2

1 1.546 ; 11

/ (154 /120)f f





Questions: • Justify the expressions used to depict the Ionospheric delay (see

slides #16 to #18).• Justify the factors of 5.09 and 3.09 used in the P2-L2 and P1-L1

combinations to give the results of L1-L2 delay in metres.• Why is the STEC larger at low elevations?




cocoPRN01

Sky plots at different latitudes

=90º

=40º

=0º




A severe ionospheric storm was experienced on October 29-31,2003 producing an increase of the electron density which led tolarge ionospheric refraction values on the GPS signals. Suchconditions were beyond the capability of the GPS Klobucharmodel broadcast for single frequency users, producing largeerrors in the SPS (see details in [R-3]).

26

Ex. 3. Halloween storm: October 2003

Dual frequency users, navigating withthe ionospheric-free combination ofGPS signals were not affected bysuch ionospheric errors, as theionospheric refraction can beremoved up to 99:9% using dual-frequency signals.

.

Backup



Before the storm, on October 28, 2003, an intense solar eruption(a Solar Flare) was detected around 11h UT in an active regionwhich had grown one of the largest sunspots ever seen by theSOlar Helioscopic Observatory (SOHO). It appeared as a brightspike in the SOHO ultraviolet images.

27

This sudden enhancement of the solarradiation in the X-ray and extremeultra-violet band produced a suddenincrease in the ionospheric electrondensity on the daylight hemisphere,(see [R-3]).

Ex. 3.1: Solar Flare October 28, 2003



Exercise: Analyze the effect of the Solar Flare on the Slant TotalElectron Content (STEC) measurements of four permanent IGSreceivers ankr, asc1, kour and qaq1, covering a wide range oflongitude and latitude.

Data sets: ankr3010.03o, asc13010.03o,kour3010.03o, qaq13010.03o

28

ankr

qaq1

kour

asc1




Execute:

gLAB_linux -input:cfg meas.cfg -input:obs ankr3010.03o > ankr3010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs asc13010.03o > asc13010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs kour3010.03o > kour3010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs qaq13010.03o > qaq13010.03.meas

graph.py -f ankr3010.03.meas -x4 -y'($14-$16)' --l "ankr" -f asc13010.03.meas -x4 -y'($14-$16)' --l "asc1" -f kour3010.03.meas -x4 -y'($14-$16)' --l "kour" -f qaq13010.03.meas -x4 -y'($14-$16)' --l "qaq1" --xl "time (s)" --yl "meters of L1-L2" --xn 38500 --xx 40500 --yn -20 --yx 20 -t "28 Oct 2003 Solar flare"

ankr

qaq1

kour

asc1

[Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 xx 13 14 15 16 ]

29




ankr

qaq1

kour

asc1




Questions: • Why can we associate the sudden increase of TEC seen in the

plots with a Solar Flare?• What is the STEC variation rate due to the Solar Flare?• Can all solar flares be seen in this way?




Associated with the Solar Flare analysed in the previous exercise, a CoronalMass Ejection occurred, which sent a large particle cloud impacting theEarth's magnetosphere about 19 hours later, on October 29.

Subsequent impacts were still occurring several hours later. This materialinteracted with the Earth's magnetosphere, and a Storm EnhancementDensity (SED) appeared in North America and this later affected the northernlatitudes in Europe. Extra large gradients ofTEC associated with this phenomenon werealso produced, degrading the GPSpositioning performance.

The TEC evolution on October 30, 2003 (i.e.,Day 303 of year 2003) can be seen in themovie TEC 2003oct30 anim.gif.

Ex. 3.2: Halloween storm analysis



The measurement files garl3010.03o, garl3020.03o, garl3030.03o,garl3040.03o, garl3050.03o, garl3060.03o were collected by thepermanent receiver garl in Empire, Nevada, USA ( = 40.42 deg

=-119:36 deg) from October 28 to November 2, 2003.

Using these files, plot the STEC for all satellites in view and discussthe range of such variations. Analyse, in particular, the satellitePRN 04 and calculate the maximum rate of STEC variation inmm=s of L1 delay. Add the elevation of satellite PRN 04 in the plot.

The associated broadcast navigation files are brdc3010.03n, brdc3020.03n, brdc3030.03n, brdc3040.03n, brdc3050.03n, brdc3060.03n.




The next commands read a RINEX file and generate a text file (in columnar format) that enables easy plotting of the measurements and their combinations:

1. Using the configuration file meas.cfg, READ the RINEX and generate the MEAS message with data format:

Execute:

2. From meas.txt file, Compute the ionospheric combination of codes: PI=P2-P1.

Generate the file PI.txt with the following content: [PRN, hour, PI, elevation]

3. From PI.txt file,Plot the PI=P2-P1 for time interval [15 to 24].hours. Show in the same graph: 1) ALL satellites, 2) PRN 13, 28 and 29, and 3) The elevation of each satellite.(13, 28 and 29)

34


gawk '{print $6, $4/3600, $15-$13, $7}' amc23030.03.meas > PI.txt

Backup

gLAB_linux -input:cfg meas.cfg -input:obs amc23030.03o -input:nav brdc3030.03n > amc23030.03.meas

graph.py -f PI.txt -x2 -y3 --l "ALL" -f PI.txt -c'($1==28)' -x2 -y3 -so --l "28:P2-P1" -f PI.txt -c'($1==28)' -x2 -y4 --l "29:ELEV" -f PI.txt -c'($1==29)' -x2 -y3 -so --l "29:P2-P1" -f PI.txt -c'($1==29)' -x2 -y4 --l "13:ELEV" -f PI.txt -c'($1==13)' -x2 -y3 -so --l "13:P2-P1" -f PI.txt -c'($1==13)' -x2 -y4 --l "13:ELEV" --xn 15 --xx 25 --yn 0 --yx 85 --xl "time (s)" --yl "meters of L1-L2 delay" 34




amc2 station location

October 30, 2003


Questions: • What is the maximum STEC

variation rate seen in the plots?• How could we explain the

shape of the STECs seen for satellites PRN28 and PRN29?



Exercise: Analyze the ionospheric delays for 6 consecutive days including the Halloween storm

• This is a simple exercise aimed to illustrate the ionosphericdelay variation during the Halloween storm. A period of 6consecutive days (from October 28 to November 2, 2003)are analyzed using measurements collected in the “garl” station in North America.

• The STEC variations are depicted from the geometry-freecombination of codes P2-P1.

Note:

36

Ex. 3.3: Halloween storm evolution

2 1 21P P I K



gLAB_linux -input:cfg meas.cfg -input:obs garl3010.03o -input:nav brdc3010.03n > garl3010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3020.03o -input:nav brdc3020.03n > garl3020.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3030.03o -input:nav brdc3030.03n > garl3030.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3040.03o -input:nav brdc3040.03n > garl3040.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3050.03o -input:nav brdc3050.03n > garl3050.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3060.03o -input:nav brdc3060.03n > garl3060.03.meas

graph.py -f PI.txt –x2 –y3 --l "ALL P2-P1" -f PI.txt -c'($1==04)' –x2 –y4 --l "PRN04: ELEV" -f PI.txt -c'($1==04)' –x2 –y3 –so --l "PRN04: P2-P1" --xn 0 --xx 144

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ JJJJ. SanSanSannSannnnnnnnnnnzzzzzzzzzzzzzzzzzzzzz &&&& JJJJ.MMMMMMMMMMMMMMMM....... JuaJJJJJJJJJJJJJJJJJuaJJJJJJJJJJJuauaauJ aaannnnnnnnn

cat garl30?0.03.meas |gawk '{d=($3-301)*86400;$4=$4+d; print $6, $4/3600, $15-$13, $7}' > PI.txt

2.- Merge files and refer all the data to 0h of October 28th: Doy0301:

3.- Plot results:

1.- Read RINEX file: [Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 xx 13 14 15 16 ]


37



Zoom at time interval: 70 to 78 h graph.py -f PI.txt –x2 –y3 --l "ALL P2-P1" -f PI.txt -c'($1==04)' –x2 –y4 --l “04: EL" -f PI.txt -c'($1==04)' –x2 –y3 –so --l “04" --xn 0 --xx 144

graph.py -f PI.txt –x2 –y3 --l "ALL P2-P1" -f PI.txt -c'($1==04)' –x2 –y4 --l “04: EL" -f PI.txt -c'($1==04)' –x2 –y3 –so --l “04" --xn 70 --xx 78


38



Questions: • What is the maximum STEC seen before and after the storm?

And during the storm? • The STEC of satellite PRN04 shows a flat pattern after time 74

hours which does not change with the elevation. Try to explain this phenomenon.




Exercise: Analyze the single frequency positioning solution under the Halloween storm.

The following steps are recommended:1. Using files amc23020.03o,brdc3030.03n compute with gLAB

the following solutions:1. Solution with full SPS modeling. Name output file as: gLAB.out2. Solution with the ionospheric corrections disabled gLAB1.out3. Solution with the 2-freq. Ionosphere-free code (PC) gLAB2.out

2. Plot results

40

Ex. 3.4: Single frequency pos. effects

Note: The gLAB GUI or the command line sentences can also be used . A “notepad” with the command line sentence is provided to facilitate the sentence writing: just “copy” and “paste” from notepad to the working terminal



1. Compute SPP using files: amc23020.03o,brdc3030.03n

1

2

3

TechnTechnicalical UniveUnive yyrsityrsity ofof CatalCataloniaoniaRR

TechnTechnicalicalTechnTechnicalical UniveUniversityrsityUniveUniversityrsity ofofofof CatalCataloniaoniaCatalCataloniaonia

Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_Full.cfg -input:obs amc3030.03o -input:nav brdc3030.03n

By default, the output file name is gLAB.out

Ex. 3.4: Full processing gLAB.out



Ex. 3.4: Iono. Disabled gLAB1.out

Change output file name to gLAB1.out

Disable Ionospheric corrections

31

2

2. Reprocess the same files, with the iono. corrections disabled

TechnTechnicalical UniveUnive yyrsityrsity ofof CatalCataloniaoniaRR


Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_NoIono.cfg -input:obs amc3030.03o -input:nav brdc3030.03n


gAGE/UPC @ J. Sanz & J.M. Juan 43@@@@@@@@@@@@ JJJ... SanSanSanzz & J.M. JuaJuaJJuannn 43

3. Reprocess the same files, but with 2-frequency ionosphere-free (PC)

Ex. 3.4: Processing with PC gLAB2.out

Disable Ionospheric corrections and P1-

P2 corrections

1Select Dual Frequency

2

Change output file name to gLAB2.out 3

4TechnTechnicalical UniveUnive yyrsityrsity ofof CatalCataloniaonia

RRRTechnTechnicalicalTechnical UniveUniversityrsityUniversity ofofof CatalCataloniaoniaCatalonia

Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_IFree.cfg -input:obs amc3030.03o -input:nav brdc3030.03n

43



graph.py -f gLAB.out -x4 -y18 -s.- -c '($1=="OUTPUT")' -l "North error" -f gLAB.out -x4 -y19 -s.- -c '($1=="OUTPUT")' -l "East error" -f gLAB.out -x4 -y20 -s.- -c '($1=="OUTPUT")' -l "UP error" --yn -40 --yx 70 --xl "time (s)" --yl "error (m)" -t "NEU positioning error [SPP]: Full model"

44

Execute in a single line: (or use the gLAB GUI)

graph.py -f gLAB.out -x4 -y20 -s.- -c '($1=="OUTPUT")' --l "Full model" -f gLAB1.out -x4 -y20 -s.- -c '($1=="OUTPUT")' --l "No Iono." --cl r --yn -40 --yx 90 --xl "Time (s)" --yl "Up error (m)" -t "Vertical positioning error [SPP]"

graph.py -f gLAB1.out -x19 -y18 -so -c '($1=="OUTPUT")' --l "No Iono." --cl r -f gLAB.out -x19 -y18 -so -c '($1=="OUTPUT")' --l "Full mod" --cl b --xl "East error (m)" --yl "North error (m)" --xn -40 --xx 40 --yn -40 --yx 40 -t "Horizontal pos. error [SPP]"

graph.py -f gLAB.out -x4 -y'($10-$9+4)' -s. -c '($1=="INPUT")' -f gLAB.out -x4 -y25 -s. -c '($1=="MODEL")' --cl r --xl "time (s)" --yl "meters" --yn -5 --yx 80 -t "Ionospheric Combination"

@@@@@ JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ. SSannananSaaaSaaSSaSannSSS nnSSSanSSSanSSSSSanSSSSanSanSSanSSSanSannnSanSannSanSannSanSannSSSaSSanannnSSananSSanSanaaSaSaSSS nnaaaSanSSSSSSSS nSannaaSSSaaaaaaSSSSSSannnnnSanannnaaaaaaaSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS zzzzzzzzzzzzzzzzzzzzzzzz &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ..................MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM... JuauJuaJuaJJuaJuaJuJuaJuJuuJJ aJJJJJJJ n 4444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444

P2-P1 shifted +4 m

r

44

Ex. 3.4: Single freq. positioning effects



gLAB.out

gLAB1.out

gLAB.out

Code delay

gLAB.out

gLAB1.out

Ionospheric correction (broadcast Klobuchar )Ionospheric delays are larger at noon due to the higherinsulation.Klobuchar model is unable to mitigate the largeionospheric errors during the storm. Position domainerrors reach up to 40 meters with Klobuchar correctionsused.




2-freq.: Iono-free

1-freq.[SPS]: with Klobuchar


October 30, 2003

Ionospheric correction(broadcast Klobuchar )•The ionosphere-free combination(PC) of P1 and P2 codes is immuneto the ionospheric storm.• Although PC is three-times noisierthan P1 or P2, it provides positioningaccurate at the level of a few metersduring the storm.

2 21 1 2 2

2 21 2

Cf P f PP

f f




Questions: • Discuss the results seen in the previous plots. Is the Klobuchar

model able to remove the ionospheric error during the storm? What was the level of the error?

• What is the position domain error level for single frequency users?

• And for dual frequency users navigating with the ionosphere-free combination?

• Discuss pros and cons of using the ionosphere-free combination against the single-frequency code with Klobuchar (consider nominal conditions and perturbed conditions).




Introduction: gLAB processing in command line.Test cases on Atmospheric Propagation Effects:Troposphere, Ionosphere. Test cases on Measurement Noise and Multipath: C1, Ionosphere-free and Melbourne Wübbena combinations.Test cases on Carrier Smoothed Code: Code-carrier divergence.Test cases on Broadcast Orbits and Clocks Accuracy

OVERVIEW

48



Test cases on Measurement Noise and Multipath:

C1, Iono-free and Melbourne Wübbena combinations.



• Code measurements are unambiguousbut noisy (meter level measurementnoise).

• Carrier measurements are precise butambiguous, meaning that they havefew millimetres of noise, but also haveunknown biases that could reachthousands of km.

• Carrier phase biases are estimated inthe navigation filter along with the otherparameters (coordinates, clock offsets,etc.). If these biases were fixed,measurements accurate to the level offew millimetres would be available forpositioning. However, some time isneeded to decorrelate such biasesfrom the other parameters in the filter,and the estimated values are not fullyunbiased.

Code and carrier Measurements

Note: Figure shows the noise of code and carrier prefit-residuals, which are the input data for navigation equations.

Cycle-slip

Code is unambiguous,

but noisy

Carrier is ambiguous, but precise

Zoom ofcarrier noise

Backup

Measurement noise and multipath



The code multipath can be seen by plotting the difference of code and carrierionosphere-free combinations (PC-LC). The evolution of this difference can befollowed with a sampling rate of 1 Hz. Due to its geometric nature, the effectof multipath repeats with the receiver-satellite geometry.

The RINEX files UPC33600.08N, UPC33610.08N, UPC33620.08N containobservations at 1 Hz collected by a GPS receiver with fixed coordinates overthe same period of time on three consecutive days. The correspondingnavigation files are BRD3600.08N, BRD3610.08N, BRD3620.08N.

Using gLAB, read the RINEX files, plot the combination PC-LC and identifythe effect of multipath. Analyse the measurements of satellites PRN20 andPRN25 in the time interval 67000 < t < 68000s. Include the satellite'selevation in the plots.

Exercise 4. Code multipath



Complete the following steps to depict the noise and multipath in the PC combination:

1. Read the RINEX files, execute:

52

[Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 x x 9 10 11 xx 13 14 15 16 ]

gLAB linux -input:cfg meas.cfg -input:obs UPC33600.08 -input:nav BRD3600.08N > upc3360.meas

Exercise 4.1. PC Code multipath

2. Verify the following field contents in the generated file upc3360.meas and others:

3. Compute the difference of code and carrier ionosphere-free combinations: (i.e. apply next equation) :

PcM Pc Lc2 2

1 1 2 2 1 22 2

1 2 1f L f L L LLc

f f

2 21 1 2 2 1 2

2 21 2

;1

f P f P P PPcf f



graph.py -f upc3360.LcPc -c '($1==20)' -x2 -y3 -s- -l "DoY 360" -f upc3361.LcPc -c '($1==20)' -x2 -y3 -s- -l "DoY 361" -f upc3362.LcPc -c '($1==20)' -x2 -y3 -s- -l "DoY 362" -f upc3360.LcPc -c '($1==20)' -x2 -y4 -l "Elev (deg.)"

gawk 'BEGIN{g12=(154/120)**2}{if ($4>66000 && $4<69000) print $6,$4,(g12*$13-$15)/(g12-1)-(g12*$14-$16)/(g12-1),$7}' upc3360.meas > upc3360.LcPc (Similarly for the other two files upc3361.meas and upc3362.meas.)

2. Plot the results:

- Repeat the same plots, but shift the plot of the second day by 3m 56s = 236s and the third day by 2x(3m 56s) = 472s.

graph.py -f upc3360.LcPc -c '($1==20)' -x2 -y3 -s- -l "DoY 360" -f upc3361.LcPc -c '($1==20)' -x'($2+236)' -y3 -s- -l "DoY 361" -f upc3362.LcPc -c '($1==20)' -x'($2+472)' -y3 -s- -l "DoY 362" -f upc3360.LcPc -c '($1==20)' -x2 -y4 -l "Elev (deg.)"




• What is the reason for the observed 3m 56s displacement between thegraphs for two consecutive days?

• Repeat the previous plot for the satellite PRN25 and compare results.




OPTIONAL: Repeat the multipath analysis of the previous exercise usingfiles htv13450.04o, htv13460.04o, htv13470.04o collected by thepermanent receiver HTV1, and files galb3450.04o, galb13460.04o,galb13470.04o collected by the permanent receiver GALB. The associatedbroadcast orbit files are brdc3450.04n, brdc3460.04n, brdc3470.04n.




Complete the following steps to depict the noise and multipath in the Melbourne Wübbena combination:

56

Exercise 4.2. Melbourne-Wübbena multipath

Execute (in a single line):

MW N WM P L1 21 1 2 2

1 2 1WL Lf L f LL

f f

1 21 1 2 2

1 2

;1N

P Pf P f PPf f

gawk 'BEGIN{s12=154/120}{print $6,$4,(s12*$14-$16)/(s12-1)-(s12*$13+$15)/(s12+1),$7}' galb3450.meas > galb3450.MW (Similarly for the other files)

And plot results.



Exercise 4.2. Melbourne-Wübbena multipath



58

The C1 code multipath and receiver noise can be depicted using the following combination (that removes all frequency dependent and not dependent terms):

a) Generate the “meas” file: Select, for instance, PRN03

1 1 1 1 22 ( )CM C L L L

gLAB_linux -input:cfg meas.cfg -input:obs UPC33510.08O|gawk '{if ($6==03)print $0}'>upc3.meas

gawk '{print $4,$11-$14-3.09*($14-$16)-21.3}' upc3.meas> upc3.C1

c) Plot resuts for PRN03:

222

2 21 2

1 771.545 ;1 60

ff f

graph.py -f upc3.C1 -s- --l "C1 Raw" --xn 35000 --xx 40000 --yn -5 --yx 5 --xl "time (s)" --yl "meters" -t "PRN03, C1 Raw measurement noise and multipath"

[*] results are Shifted by “-21.3” to remove the carrier ambiguity

[Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ]

b) Using previous expression, compute the C1 multipath and code noise:

Exercise 4.3. C1 code multipath



Introduction: gLAB processing in command line.Test cases on Atmospheric Propagation Effects:Troposphere, Ionosphere.Test cases on Measurement Noise and Multipath: C1, Ionosphere-free and Melbourne Wübbena combinations.Test cases on Carrier Smoothed Code: Code-carrier divergence.Test cases on Broadcast Orbits and Clocks Accuracy

OVERVIEW

59



Test cases on Carrier Smoothed Code:

Code-carrier divergence



The noisy code P can be smoothed with the precise (but ambiguous) carrier Lmeasurements. This carrier smoothing can be done in real-time applying theHatch filter.

The previous algorithm can be interpreted as real-time alignment of carrier with code:

where

Carrier smoothed code

where [ if ], and [ if ].

1 1ˆ( ) ( ) ( 1) ( ) ( 1)

ˆThe algorithm is initialised with: (1) (1).

n k k N n N k N

nP k P k P k L k L kn n

P P

( )

1 1ˆ( ) ( ) ( 1) ( ) ( 1)

( )k

nP k P k P k L k L kn nL k P L

( ) ( 1)

1 1 1( ) ( ) ( ) ( )k k

nP L P k L k P L P k L kn n n

Carrier Phase L (ambiguous but precise)

Code P (unambiguous but noisier)

Ambiguity= P L

Iono

sphe

ricco

mbi

natio

n(m

eter

s)



The noisy code can be smoothed with the precise (but ambiguous) carriermeasurements. This carrier smoothing can be done in real-time applying theHatch filter.

The smoothing depends on the time smoothing constant or filter length. The morethe filter length is used, the more smoothed the code is, but (with singlefrequency measurements) a higher code-carrier divergence error is induced bythe ionosphere.

This is because the ionospheric refraction has an opposite sign on code andcarrier, its effect being twice on the difference of code and carrier. This doubleionospheric refraction is propagated forward through the filter, producing a bias.

The error induced by the code-carrier divergence of the ionosphere on thesingle frequency smoothed codes is assessed in this exercise for different filter

lengths.

Carrier smoothed code



The target of this exercise is to analyze the error induced by the divergence of the ionosphere (between code and carrier) into the Single-Frequency (SF) carrier smoothed code.

Ex.5.: Iono. Divergence on Smoothing

This effect will be analyzedanalytically and tested withsingle and double frequencyGPS measurements underlarge ionospheric gradients.

The Divergence Free (Dfree)and the Ionosphere Free(IFree) smoothed codes will becompared with the SF one.



Where includes all non dispersive terms (geometric range, clockoffsets, troposphere) and represents the frequency dependentterms (ionosphere and DCBs). is the carrier ambiguity, which isconstant along continuous carrier phase arcs, and account forcode and carrier multipath and thermal noise.

64

Time varying ionosphere induces a bias in the single frequency smoothed code when it is averaged in the smoothing filter. This effect is analysed as follows:

Let:


1 1 1

1 1 1 1

P IL I B

1I1B

1 1,

therefore,

1 1 1 12P L I B 12 : Code-carrier divergenceI

Substituting in Hatch filter equation (see slide #61):1 1P L

1 1 1ˆ

IP I bias

where, being the ambiguity term a constant bias, thence , and cancels in the previous expression

1B1 1B B

1 1 1 1( ) ( )

1 1 1( )

ˆ ( ) ( ) ( ) ( ) 2

( ) ( ) 2 ( )

I

k k

k

bias

P k L k P L k I k B I B

k I k I I k

where is the noise term after smoothing

1

Note: the carrier noise is neglected against code noise .1

1



Raw assessment of the induced bias on P1 smoothed code by ionosphere:

• Let assume a simple model where the STEC vary linearly with time:

where is the Hatch filter smoothing time constant (i.e., in previous eq.).

Exercise: Prove the previous statement.Solution: Let be and . The averaging in the Hatch filter can be implemented as:

Thence:


01 1 1 1 1 1( )( ) 2 ( ) 2I kI t I I t bias I I k I

N

( ) ( )f t I t ( )( )t

y t I

( ) ( ) ( )T Ty t T y t f t T 0( ) ( ) 1 1 1 1( ) ( ) ' ( )T

y t T y t y t f t T y y f tT

0

/1 1 1 1 1 1 1 1 1( ) ( )( ) ( ) 1 2 ( ) 2t

I tt tI t I I t I I t I e bias I I t I



• Divergence Free smoothing (DFree):With 2-frequency measurements, the ionosphere can be removed from acombination of two carriers:


1 1 1 2 12 1 1 1 12ˆ2 ( )P L L L B P I

22

2 21 2

ff f

12 1 1 22 ( )B B B B

• Ionosphere Free smoothing (IFree):Using both code and carrier 2-frequency measurements, it is possible to removethe frequency dependent effects using the ionosphere-free combination :

C C

C C C

PL B

2 21 1 1 2

2 21 2

2 21 1 1 2

2 21 2

C

C

f P f PPf f

f L f LLf f

,C CP L

C CP

DFree smoothed code is not affected by iono. temporal gradients, being the ionospheric delay the same as in the original code .1P

IFree smoothed code is not affected by either spatial or temporal gradients,but is 3-times noisier than the DFree, or the in the Single Freq. smoothed code.



67

Ex. 5.1: Iono. Divergence on Smoothing 1.- Multipath and measurement noise assessment on raw code measurements:


a) Generate the “meas” file for PRN03:

1 1 1 1 22 ( )CM C L L L



c) Plot the raw (unsmoothed) measurements for PRN03:

222

2 21 2

1 771.545 ;1 60

ff f




b) Using previous expression, compute the C1 multipath and code noise: :



Ex. 5.1: Iono. Divergence on Smoothing

2. Apply the Hatch filter to smooth the code using a filter length of N =100 sample(as the measurements are at 1Hz,this means 100 seconds smoothing). Then, asin the previous case, depict the multipath and noise of the smoothed code.

a) Smoothing code (T=100sec):

b) Plotting results and compare with the row C1.

gawk 'BEGIN{Ts=100}{if (NR>Ts){n=Ts}else{n=NR}; C1s=$11/n+(n-1)/n*(C1s+($14-L1p));L1p=$14; print $4,C1s-$14-3.09*($14-$16)-21.3}' upc3.meas > upc3.C1s100

graph.py -f upc3.C1 -s- --l "C1 Raw" -f upc3.C1s100 -s.- --cl r --l "C1 SF smoothed" --xn 35000 --xx 40000 --yn -5 --yx 5 --xl "time (s)" --yl "meters" -t "PRN03: C1 100s smoothing and iono div."



Ex. 5.1: Iono. Divergence on Smoothing 3 . Using 2-frequency carriers it is possible to generate a combination with the

same ionospheric delay (the same sign) as the code to avoid the code-carrierdivergence

a) Apply the Hatch filter to compute the DFree smoothed code

b) Plot results and compare with the row C1 code:

gawk 'BEGIN{Ts=100}{if (NR>Ts){n=Ts}else{n=NR}; C1f=$11;L1f=$14+2*1.545*($14-$16); C1fs=C1f/n+(n-1)/n*(C1fs+(L1f-L1p));L1p=L1f; print $4,C1fs-L1f-21.3}' upc3.meas > upc3.C1DFs100

1 1 1 2 12 ( )DFreeL L L L I B22

22 2

1 2

1 771.545 ;1 60

ff f

graph.py -f upc3.C1 -s- --l "C1 Raw" -f upc3.C1s100 -s.- --cl r --l "C1 SF smoothed (100s)" -f upc3.C1DFs100 –s.- --cl g --l "C1 DFree smooth(100s)" --xn 35000 --xx 40000 --yn -5 --yx 5 --xl "time (s)" --yl "meters"



Ex. 5.1: Iono. Divergence on Smoothing 4 . Generate the ionosphere-free combinations of code and carrier measurements

to compute the Ionosphere Free (IFree) smoothed code:

• Apply the Hatch filter to compute the IFree smoothed code

• Plot results and compare with the unsmoothed PC:

gawk 'BEGIN{g=(77/60)**2}{pc=(g*$13-$15)/(g-1); lc=(g*$14-$16)/(g-1); print $4,pc-lc-3.5}' upc3.meas > upc3.PC

27760

1 2 1 2;1 1IFree C IFree C

P P L LC P L L

gawk 'BEGIN{g=(77/60)**2}{pc=(g*$13-$15)/(g-1); lc=(g*$14-$16)/(g-1); if (NR>100){n=100}else{n=NR}; ps=1/n*pc+((n-1)/n*(ps+lc-lcp)); lcp=lc; print $4,ps-lc-3.5}' upc3.meas > upc3.PCs100

graph.py -f upc3.PC -s- --l "IFree raw" -f upc3.PCs100 -s.- --cl black --l "Ifree(100s)" --xn 35000 --xx 40000 --yn -5 --yx 5 --xl "time (s)" --yl "meters"



Ex. 5.1: Iono. Divergence on Smoothing 5 . Repeat previous plots but using: N=360, N=3600 and compare results. Plot also

the ionospheric delay (from L1-L2) (see more details in [R-1]):

STEC

Note that the y-range in bottom row

plots is 3 times larger than in

top plots

T=100s T=360s T=3600s

C1

PC

C1

PC

C1

PC



Questions: • Discuss a possible source of the large oscillations seen in the plots.• Using the expressions of slide #65, estimate the expected accumulated

ionospheric bias with smoothing time constant T=3600s.• Is the Divergence-Free smoothing immune to ionospheric temporal

gradients? And to spatial gradients? Why?• Is the Ionosphere-Free smoothing immune to temporal gradients? And to

spatial gradients?

Ex. 5.1: Iono. Divergence on Smoothing



Repeat the previous exercise using the RINEX file amc23030.03o_1Hz collected for the station amc2 during the Halloween storm. Take N=100(i.e. filter smoothing time constant =100 sec).

Ex.5.2.: Assessment on Halloween storm



Introduction: gLAB processing in command line.Test cases on Atmospheric Propagation Effects:Troposphere, Ionosphere.Test cases on Measurement Noise and Multipath: C1, Ionosphere-free and Melbourne Wübbena combinations.Test cases on Carrier Smoothed Code: Code-carrier divergence.Test cases on Broadcast Orbits and Clocks Accuracy

OVERVIEW

74



Test cases on Broadcast Orbits and Clocks

Accuracy



Satellite Mass Center to Antenna Phase Center

76

Satellite Mass

Center(MC)

Broadcast orbits are referred to the antenna phase center, but IGS precise orbits are referred to the satellite mass center.

Satellite MC to APC:The satellite MC to APCeccentricity vector depends onthe satellite. The APC valuesused in the IGS orbits andclocks products are referred tothe iono-free combination (LC,PC) . They are given in the IGSANTEX files (e.g., igs05.atx).

Satellite Antenna

Phase Center (APC)

Broadcast v.s. precise IGS Orbits and clocks



Complete the following steps:File brdc0800.07n contains the orbits and clocks data broadcast in the GPS navigation message.Files cod14193.sp3, cod14193.clk contain the precise orbits and clocks computed in post-process by “CODE” center (IGS precise orbits and clocks products program).

1. Execute the following sentence to compute the difference of satellite coordinates and clock offsets between both orbits and clocks sources:

2. Select the SATDIFF message of dif.tmp file:

3. Plot dif.out file as in the first exercise.

Note:

77

gLAB_linux -input:nav brdc0800.07n -input:SP3 cod14193.sp3 -input:ant igs05_1402.atx >dif.tmp

Ex.6.: Broadcast orbits and clocks accuracy assessment using the IGS precise products as the accurate reference (i.e. the truth).

grep SATDIFF dif.tmp > dif.out

SATDIFF message content is shown in the table beside.(see gLAB_linux –messages).The IGS post-processed products are accurate at few cm level, therefore they can be taken as the truth.

2 2 21( Rad Clk) ( Alon Cross )49SISRE



Comments• Meter level errors are found on broadcast

orbits and clocks.• The bias seen in the radial component is

due to the different APC’s used by theGPS ground segment (i.e, in broadcastorbits) and by IGS (precise products).

• This bias is compensated by a similarshift in clocks.

• For the Signal-In-Space-Range-Error(SISRE), please see the plot below.




CommentsThe previous computations have beenrepeated, but using the ANTEX filegps_brd.atx, instead of igs05_1402.atx.

This new ANTEX file contains the GPSantenna phase center offsets used by theGPS ground segment, not the IGS ones.• Notice that the biases in the radial

component have disappeared.

79




Questions: • What is the level of error of the broadcast orbits and clocks?• Why do the results improve using the gps_brd.atx, instead of igs05_1402.atx ANTEX file?

• Is there any correlation between radial orbit errors and clock errors?• Which orbit errors are expected to affect the differential positioning more (radial,

cross track, along track)?

Ex.6.: Broadcast orbit and clock accuracy assessment using the IGS precise products as the accurate reference (i.e. the truth).






R-1: J. Sanz-Subirana, J.M. Jaun-Zoroza, M. Hernández-Pajares. GNSS Data processing.Volume-I and Volume-II. ESA Publications Division, 2012.R-2: J. Sanz-Subirana, J.M. Jaun-Zoroza, M. Hernández-Pajares. Tutorial on GNSS DataProcessing Laboratory Exercises. ESAInternational Summer School on GNSS, 2010.R-3: Hernández-Pajares M., J.M. Juan, J. Sanz, "EGNOS Test Bed IonosphericCorrections Under the October and November 2003 Storms", IEEE Transactions onGeoscience and Remote Sensing, Vol.43(10), pp.2283-2293, 2005.

Bibliography



The ESA/UPC GNSS-Lab Tool suite (gLAB) has beendeveloped under the ESA Education Office contract N.P1081434.The other data files used in this study were acquired as part ofNASA's Earth Science Data Systems and archived anddistributed by the Crustal Dynamics Data Information System(CDDIS).To Adrià Rovira-Garcia for his contribution to the edition of thismaterial and gLAB updating.

83

Acknowledgements



Tutorial 3Differential Positioning

with code measurements





This tutorial is devoted to analysing and assessing the differential positioning with code pseudorange measurements. Four different permanent receivers and two baselines 280km and 51km are considered.

The atmospheric effects on differential positioning are the subject of the first session. The differential tropospheric and ionospheric delays are analysed for the two baselines considered and the absolute and differential user solution are computed and assessed.

The ephemeris error on differential positioning is the subject of the second session. A 2000 metres of Along-Track error is simulated by manipulating the broadcast message, and the impact of this error on range and user domains is assessed for absolute and differential positioning. A theoretical expression to predict the range error on a given baseline is also verified in the last part of this session. Detailed guidelines for self-learning students are provided in this tutorial and in its associated notepad text file.

All software tools (including gLAB) and associated files for the laboratory session are included in the CD-ROM or USB stick associated with this tutorial.




Introduction: gLAB processing in command line

Session A: Atmospheric effects• A1 Differential positioning of EBRE-CREU receivers (Long baseline: 288 km) • A2 Differential positioning of GARR-MATA receivers (Short baseline: 51 km)

Session B: Orbit error effects• B1 Differential positioning of EBRE-CREU receivers (Long baseline: 288 km) • B2 Differential positioning of GARR-MATA receivers (Short baseline: 51 km)• B3 Range domain orbit error.

OVERVIEW

4




sentences

A “notepad” with the



“ paste” from


terminal.




The different messages provided by gLAB and its content can be found in the [OUTPUT] section.

By placing the mouse on a given message name, a tooltip appears describing the different fields.

Backup









OVERVIEW

7



Session AAtmospheric effects

on differential positioning with code measurements



MATA

GARR

GARR-MATA: 51 kmEBRE-CREU: 288 km

Barcelona

Toulouse

MATA

Session A: Atmospheric effects



Data sets:Measurement files:

CREU0770.10o, EBRE0770.10o, GARR0770.10o, MATA0770.10oOrbit and clocks files: brdc0770.10n.

10

Receiver coordinates:

MATA 4776835.5870 202618.9947 4207574.6304 41.539929530 2.428858625 123.6209GARR 4796983.5767 160309.1177 4187340.3773 41.292941528 1.914040080 634.6040EBRE 4833520.1197 41537.2015 4147461.6263 40.820888849 0.492363266 107.8284CREU 4715420.3054 273177.8809 4271946.7957 42.318843076 3.315603563 133.4780

Data files and receiver coordinates

Session A: Atmospheric effects

Note: the receivers were not moving (static receivers) during the data collection.






OVERVIEW

11



Model Components computation• The script "ObsFile1.scr" generates a data file “STA.obs” with the following

content

12

1 2 3 4 5 6 7 8 9 10 11 12 13 14[sta sat DoY sec P1 L1 P2 L2 Rho Trop Ion Elev Azim Prefit]

• Run this script for EBRE and CREU receivers:

ObsFile1.scr EBRE0770.10o brdc0770.10nObsFile1.scr CREU0770.10o brdc0770.10n

• Generate the navigation equations system for absolute positioning for each receiver and compute the user solution (see next two slides).

A.1.1 Model components computation

A.1. Differential positioning of EBRE-CREU receivers (Long baseline: 288 km)



cat EBRE.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",

$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> EBRE.mod

Justify that the next sentence builds the navigation equations system for absolute positioning:

[Prefit]=[Los_k 1]*[dx]

time [Pref] [ Los_k 1] ------ ------------------------

30.00 -3.3762 0.3398 -0.1028 0.0714 130.00 -7.1131 0.1725 0.5972 0.0691 1 30.00 4.3881 -0.6374 0.0227 0.2725 1

11

2 2

ˆ 1PrefˆPref 1

Pref ˆ 1

T

T

n Tn

ρ

ρ dx

ρ

ˆ cos( )sin( ), cos( )cos( ), sin( )kk k k k kEl Az El Az Elρ

See file content in previous slide




The program kalman.f implements the kalman filter for code positioning (see source code).

The INPUT file is the file EBRE.mod generated in the previous slide. The OUTPUT is the user solution file: 1 2 3 4 5

[time dE dN dU, dt]

The filter configuration is done by the namelist kalman.nml.• The namelist kalman_wn.nml configures the filter to process the coordinates

and clock as white nose (i.e. Kinematic solution).• The namelist kalman_ct.nml configures the filter to process the coordinates

as constants and clock as white nose (i.e. static solution).

The program is executed as: cp kalman.nml_wn kalman.nml

cat EBRE.mod | kalman > EBRE.pos


A.1.2. Absolute positioning



Using the files EBRE.obs and CREU.obs, follow the next steps:

1. Build the navigation equations system for each receiver, for absolute positioning.

2. Compute the user solutions in kinematic mode.

3. Plot the results and compare the positioning errors.





2.- Computing the user solution for absolute positioning:

16

cp kalman.nml_wn kalman.nml

cat EBRE.mod | kalman > EBRE.pos

3.- Plotting results:graph.py -f EBRE.pos -x1 -y2 -s.- -l "North error"

-f EBRE.pos -x1 -y3 -s.- -l "East error" -f EBRE.pos -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "EBRE: Standard Point Positioning"

1.- Building the navigation equations system for absolute positioning: cat EBRE.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> EBRE.mod






17


cat CREU.mod | kalman > CREU.pos

3.- Plotting results:graph.py -f CREU.pos -x1 -y2 -s.- -l "North error"

-f CREU.pos -x1 -y3 -s.- -l "East error" -f CREU.pos -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "CREU: Standard Point Positioning"

1.- Building the navigation equations system for absolute positioning: cat CREU.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> CREU.mod







Questions: •What is the expected accuracy of the computed coordinates (in absolute positioning)?•Why are the patterns seen for the receivers EBRE and CREU are so similar?



The script Dobs.scr computes the single difference of measurementsfiles sta1.obs (reference station) and sta2.obs (user).

19

The output file (D_sta1_sta2.obs) has the following content:

1 2 3 4 5 6 7 8 9 10 11 12 13 14[sta2 sat DoY sec DP1 DL1 DP2 DL2 DRho DTrop DIon El2 Az2 DPrefit]

It can be executed by the sentence: Dobs.scr sta1.obs sta2.obs

Where: D(o)= (o)sta2 -- (o)sta1

EL2 and AZ2 are the satellite azimuth and elevation from sta2.

In our case, executing: Dobs.scr EBRE.obs CREU.obs

the OUTPUT file is generated. D_EBRE_CREU.obs


A.1.3. Differential positioning



cat D_EBRE_CREU.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",

$4,$5-$9-$10-$11 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> D_EBRE_CREU.mod

Justify that the next sentence builds the navigation equations system for differential positioning of CREU (user) relative to EBRE (reference station):

[DPrefit]=[Los_k 1]*[dx]

11 creu

2 2creu

creu

ˆ 1DPrefˆDPref 1

DPref ˆ 1

T

T

n Tn

ρ

ρ dx

ρ


Question: Is this combination equivalent to use $14? Why?


time [DPref] [ Los_k 1] ------ ------------------------

30.00 -3.3762 0.3398 -0.1028 0.0714 130.00 -7.1131 0.1725 0.5972 0.0691 1 30.00 4.3881 -0.6374 0.0227 0.2725 1



Using the files EBRE.obs and CREU.obs, follow the next steps:1. Compute the single differences of measurements and model

components.2. Build the navigation equations system for the differential

positioning of CREU receiver (user) relative to EBRE (reference station).

3. Compute the user solution in kinematic mode and in static mode.

4. Plot the results and discuss the positioning error found.


A.1.3.1. Differential positioning.Full model



3.- Computing the user solution for differential positioning:

22

cp kalman.nml_wn kalman.nmlcat D_EBRE_CREU.mod | kalman > EBRE_CREU.posK

2.- Building the navigation equations system for differential positioning: cat D_EBRE_CREU.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4,$5-$9-$10-$11,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'> D_EBRE_CREU.mod

1. Computing the single differences of measurements and model components.

Dobs.scr EBRE.obs CREU.obs

cp kalman.nml_ct kalman.nmlcat D_EBRE_CREU.mod | kalman > EBRE_CREU.posS

Kinematic:

Static:





4.- Plotting results:

- kinematic mode:graph.py -f EBRE_CREU.posK -x1 -y2 -s. -l "North error"

-f EBRE_CREU.posK -x1 -y3 -s. -l "East error" -f EBRE_CREU.posK -x1 -y4 -s. -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "CREU-EBRE: 288 km: Differential Positioning"

- Static mode:graph.py -f EBRE_CREU.posS -x1 -y2 -s. -l "North error"

-f EBRE_CREU.posS -x1 -y3 -s. -l "East error" -f EBRE_CREU.posS -x1 -y4 -s. -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "CREU-EBRE: 288 km: Differential Positioning"







Questions: •Looking at these results, justify intuitively why the errors are reduced in differential positioning.•Why is the error lower in static than in kinematic mode?



Analyze the effect of the differential ionosphere on the differential positioning of CREU relative to EBRE station:

Follow the next steps:1. Using file D_EBRE_CREU.obs plot the differential ionospheric

correction (from Klobuchar model) between EBRE and CREU.

2. Repeat the previous process, but without applying the ionospheric correction. Compare the results


A.1.3.2. Differential positioning.No ionospheric corrections



Plotting the Klobuchar differential ionospheric correction:

graph.py -f D_EBRE_CREU.obs -x4 -y'11' --yn -0.8 --yx 0.8 -t "CREU-EBRE: 288 km: Nominal diff Iono (Klob)"



Question: Justify the pattern seen in the nominal (Klobuchar) ionospheric corrections.




27



$4,$5-$9-$10,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'> D_EBRE_CREU.mod

Computing the differential solution, but without using ionospheric corrections:


Kinematic:

Static:

1.- Building the navigation equations system for differential positioning, but without using the ionospheric corrections:







Question: Taking into account the previous plot of the differential ionospheric corrections (slide #26), discuss the effect seen on the position domain.





Question: Discuss the pattern seen in the figure. Why is the effect of the differential ionospheric error is higher in these static positioning results?



Analyze the effect of the differential Troposphere on the differential positioning of CREU relative to EBRE station:

Follow the next steps:1. Using file D_EBRE_CREU.obs plot the differential trpospheric

correction (from nominal model) between EBRE and CREU.

2. Repeat the previous process, but without applying the tropospheric correction. Compare the results


A.1.3.3. Differential positioning.No tropospheric corrections



Plotting the nominal differential tropospheric correction:

graph.py -f D_EBRE_CREU.obs -x4 -y'10' --yn -8 --yx 8 -t "CREU-EBRE: 288 km: Nominal diff Tropo"



Question: Justify the pattern seen in the nominal tropospheric corrections.




32



$4,$5-$9-$11,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'> D_EBRE_CREU.mod

Computing the differential solution, but without using tropospheric corrections:


Kinematic:

Static:

1.- Building the navigation equations system for differential positioning, but without using the tropospheric corrections:







Questions: • Which error source has the higher impact on the position domain higher the

ionosphere or the troposphere?• Which is easier to model?





Question: • Compare the results with those of the previous case, when not considering

the ionospheric error.






OVERVIEW

35




content

36


• Run this script for GARR and MATA receivers:

ObsFile1.scr GARR0770.10o brdc0770.10nObsFile1.scr MATA0770.10o brdc0770.10n


A.2.1 Model components computation

A.2. Differential positioning of GARR_MATA receivers (Short baseline: 51 km)

Repeat the previous exercise, but using the permanent receivers GARR and MATA, with only 51 km of baseline.



Using the files GARR.obs and MATA.obs, follow the next steps:

1. Build the navigation equations system for each receiver, for absolute positioning.

2. Compute the user solutions in kinematic mode.

3. Plot the results and compare the positioning errors.






38


cat GARR.mod | kalman > GARR.pos

3.- Plotting the results:graph.py -f GARR.pos -x1 -y2 -s.- -l "North error"

-f GARR.pos -x1 -y3 -s.- -l "East error" -f GARR.pos -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "GARR: Standard Point Positioning"

1.- Building the navigation equations system for absolute positioning: cat GARR.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> GARR.mod






39


cat MATA.mod | kalman > MATA.pos

3.- Plotting the results:graph.py -f MATA.pos -x1 -y2 -s.- -l "North error"

-f MATA.pos -x1 -y3 -s.- -l "East error" -f MATA.pos -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "MATA: Standard Point Positioning"

1.- Building the navigation equations system for absolute positioning: cat MATA.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> MATA.mod




gAGE/UPC @ J. Sanz & J.M. Juan 40A.2.2. Absolute positioning


Questions: • Compare the results with the previous case with a baseline of 280 km.• Are the patterns even more similar now? Why?



Using the files GARR.obs and MATA.obs, follow the next steps:1. Compute the single differences of measurements and model


positioning of MATA receiver (user) relative to GARR (reference station).

3. Compute the user solution in kinematic mode and in static mode.

4. Plot the results and discuss the positioning error found.

A.2.3.1 Differential positioning.Full model





42

cp kalman.nml_wn kalman.nmlcat D_GARR_MATAA.mod | kalman > GARR_MATA.posK

2.- Building the navigation equations system for differential positioning: cat D_GARR_MATA.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4,$5-$9-$10-$11,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'> D_GARR_MATA.mod


Dobs.scr GARR.obs MATA.obs

cp kalman.nml_ct kalman.nmlcat D_GARR_MATA.mod | kalman > GARR_MATA.posS

Kinematic:

Static:





4.- Plotting the results:

- Kinematic mode:graph.py -f GARR_MATA.posK -x1 -y2 -s. -l "North error"

-f GARR_MATA.posK -x1 -y3 -s. -l "East error" -f GARR_MATA.posK -x1 -y4 -s. -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "GARR_MATA: 51 km: Differential Positioning"

- Static mode:graph.py -f GARR_MATA.posS -x1 -y2 -s. -l "North error"

-f GARR_MATA.posS -x1 -y3 -s. -l "East error" -f GARR_MATA.posS -x1 -y4 -s. -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "GARR_MATA: 51 km: Differential Positioning"




gAGE/UPC @ J. Sanz & J.M. Juan 44A.2.3.1 Differential positioning.

Full model


Questions: • Compare the results with the previous case with a baseline of 280 km.• Are we reaching a similar level of accuracy? Why?



Analyze the effect of the differential ionosphere on the differential positioning of MATA relative to GARR station:

Follow the next steps:1. Using file D_GARR_MATA.obs plot the differential ionospheric

correction (from Klobuchar model) between EBRE and CREU.

2. Repeat the previous process, but without applying the ionospheric correction. Compare the results





Plotting the Klobuchar differential ionospheric correction:

graph.py -f D_GARR_MATA.obs -x4 -y'11' --yn -0.8 --yx 0.8 -t "GARR-MATA: 51km: Nominal diff Iono (Klob)"



Question: Justify the pattern seen in the nominal (Klobuchar) ionospheric corrections.Compare the plot with that of the 280km baseline (slide #26). Do the results perform as expected?




47

cp kalman.nml_wn kalman.nmlcat D_GARR_MATA.mod | kalman > GARR_MATA.posK

cat D_GARR_MATA.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",

$4,$5-$9-$10,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'> D_GARR_MATA.mod

Computing the differential solution, but without using ionospheric corrections:


Kinematic:

Static:

1.- Building the navigation equations system for differential positioning, but without using the ionospheric corrections:







Question: • Do the results confirm the expected effect of neglecting the ionospheric

corrections for this baseline (using code measurements ) at the user level?


gAGE/UPC @ J. Sanz & J.M. Juan 49A.2.3.2. Differential positioning.

No ionospheric corrections


Question: • Do the results confirm the expected effect of neglecting the ionospheric




Analyze the effect of the differential Troposphere on the differential positioning of MATA relative to GARR station:

Follow the next steps:1. Using file D_GARR_MATA.obs plot the differential trpospheric

correction (from nominal model) between EBRE and CREU.

2. Repeat the previous process, but without applying the tropospheric correction. Compare the results.





Plotting the nominal differential tropospheric correction:

graph.py -f D_GARR_MATA.obs -x4 -y'10' --yn -8 --yx 8 -t "GARR_MATA: 51km: Nominal diff Tropo"



Question: Justify the pattern seen in the nominal tropospheric corrections.Compare the plot with that of the 280km baseline (slide #31). Do the results perform as expected?




52

cp kalman.nml_wn kalman.nmlcat D_GARR_MATA.mod | kalman > GARR_MATA.posK

cat D_GARR_MATA.obs | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",

$4,$5-$9-$11,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'> D_GARR_MATA.mod

Computing the differential solution, but without using tropospheric corrections:


Kinematic:

Static:

1.- Building the navigation equations system for differential positioning, but without using the tropospheric corrections:







Question: • Do the results confirm the expected effect of neglecting the tropospheric






Question: • Discuss the error found at the user level for the 50 Km of baseline. • Is the error level similar to the error seen with the 280km of baseline (slide 34#)?• Should the tropospheric corrections still be applied for these baselines?






OVERVIEW

55



Session B

Differential positioningOrbit errors



The target of this exercise is to asses the satellite orbit error on absolute and differential positioning.

This will be done by modifying the broadcast orbit parameters to generate an Along-track orbit error of about 2000m and, positioning two receivers with these corrupted orbits.

The user positioning error using the original and the corrupted orbits will be compared for absolute and differential positioning, with the receivers and baselines used in the previous session.

B. Differential positioning.Orbit error

B. Orbit error effect on Differential positioning.



True position

Reference Station

Ephemeris Errors and Geographic decorrelation

Satellite location error

Position from broadcast ephemeris

User

ref

user

user

ρε

ref

ref

ρε

user

refuser

user ref

ρρε ε

Differential range error due to satellite obit error

with a baseline 2020 1

20000 1000

b km

A conservative bound: b

sin ˆ ˆsin

ˆ ˆ

ˆ ˆˆ sin

ˆ ˆ

T T

T T

b bε u ε u

bε I ρ ρˆWhere:

is the baseline vectorbb = b




Injecting an error to broadcast orbits:Along-track Error (PRN17)

The following ephemeris block of PRN17 is modifiedIn order to simulate an Along-track error of about 2000m.The corrupted file is renamed as: brdc0770.10nERR

17 10 3 18 20 0 0.0 1.379540190101E-04 2.842170943040E-12 0.000000000000E+007.800000000000E+01-5.059375000000E+01 4.506973447820E-09-2.983492318682E+00

-9.257976353169E-05 5.277505260892E-03 8.186325430870E-06 5.153578153610E+034.176000000000E+05-5.401670932770E-08-4.040348681654E-01-7.636845111847E-089.603630515702E-01 2.215312500000E+02-2.547856603060E+00-7.964974630307E-09

-3.771585673111E-10 1.000000000000E+00 1.575000000000E+03 0.000000000000E+002.000000000000E+00 0.000000000000E+00-1.024454832077E-08 7.800000000000E+014.104180000000E+05 4.000000000000E+00

diff brdc0770.10n brdc0770.10nERR- --------------------------------------------------< -2.579763531685E-06 5.277505260892E-03 8.186325430870E-06 5.153578153610E+03> -9.257976353169E-05 5.277505260892E-03 8.186325430870E-06 5.153578153610E+03---------------------------------------------------------------------------------

B. Orbit error effect.


gAG

E/U

PC re

sear

ch g

roup

of A

stro

nom

y an

d G

eom

atic

sgAGE

Master of Science in GNSS J. Sanz Subirana, JM. Juan Zornoza, M. Hernández-Pajares,

• Errors over the hyperboloid (i.e. ) will not produce

differential range errors.• The highest error is given by the

vector , orthogonal to the hyperboloid and over the plain containing the baseline vector and the LoS vector .Note: Being the baseline b much smaller than the distance to the satellite, we can assume that the LoS vectors from A and B receives are essentially identical to .That is,

u

ρb

uB A ctt

( ) / 2 : hyperboloid semiaxis/ 2 : focal length

1 cos2

B Aab

where a b

B A

( ) 2

2 2 sin

1sin

B A aa a b

bsinb

ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ ˆ

ˆ ˆ ˆˆ ˆ ˆ ˆ

T T

T T

u ρ b ρ b ρ ρ -ρ ρ b

Ib ρ ρ b I ρ ρ b

ε

sin ˆ ˆsin

ˆ ˆ

ˆ ˆˆ sin

ˆ ˆ

T T

T T

b bε u ε u

bε I ρ ρ

Differential range error produced by anorbit error parallel to vector Let

Thence:

Note: ε ρε ρε

ˆNote: being a vector orthogonalˆ ˆ to the LoS , thence, ˆT

uρ ε u

u

ˆWhere: is the baseline vector

bb = b

ˆNote: sin u u

By Miguel Juan Zornoza

Note: in this 3D problem is NOT the elevation of ray.





Session B: Orbit error effects• B1 Differential positioning of EBRE-CREU receivers (Long baseline: 288 km)• B2 Differential positioning of GARR-MATA receivers (Short baseline: 51 km)• B3 Range domain orbit error.

OVERVIEW

61




content

62


• Run this script for EBRE and CREU receivers. Rename as STA.obsERR the output files ObsFile1.scr EBRE0770.10o brdc0770.10nERR

mv EBRE.obs EBRE.obsERRObsFile1.scr CREU0770.10o brdc0770.10nERRmv EBRE.obs EBRE.obsERR

• Generate the navigation equations system for absolute positioning for each receiver and compute the user solution (see the next two slides).

Repeat the computation of the absolute positioning of receivers EBRE and CREU, but using the corrupted ephemeris file brdc0770.10nERR.

B1. Orbit error: Differential positioning of EBRE-CREU receivers (Long baseline: 288 km)

B.1.1. Absolute positioning.Orbit error




63


cat EBRE.modERR | kalman > EBRE.posERR

3.- Plotting the results:graph.py -f EBRE.posERR -x1 -y2 -s.- -l "North error"

-f EBRE.posERR -x1 -y3 -s.- -l "East error" -f EBRE.posERR -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -300 --yx 300 -t "EBRE: SPP: 2000m Along-Track orbit error"

1.- Building the navigation equations system for absolute positioning: cat EBRE.obsERR | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> EBRE.modERR






64


cat CREU.modERR | kalman > CREU.posERR

3.- Plotting the results:graph.py -f CREU.posERR -x1 -y2 -s.- -l "North error"

-f CREU.posERR -x1 -y3 -s.- -l "East error" -f CREU.posERR -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -300 --yx 300 -t "CREU: SPP: 2000m Along-Track orbit error"

1.- Building the navigation equations system for absolute positioning: cat CREU.obsERR | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> CREU.modERR







Question: • Is the impact on user positioning error similar for both receivers?• From these plots, what is the expected level of error in differential positioning?



Using the files EBRE.obsERR and CREU.obsERR, follow next steps:1. Compute the single differences of measurements and model


positioning of CREU receiver (user) relative to EBRE (reference station).

3. Compute the user solution in kinematic mode.4. Plot the results and discuss the positioning error found.

Analyse the effect of the 2000m orbit error on the differential positioning of CREU receiver relative to EBRE, with 280km of baseline.


B.1.2. Differential positioning.Orbit error




67

cp kalman.nml_wn kalman.nmlcat D_EBRE_CREU.modERR| kalman > EBRE_CREU.posKERR

2.- Building the navigation equations system for differential positioning: cat D_EBRE_CREU.obsERR | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4,$5-$9-$10-$11,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'>D_EBRE_CREU.modERR

1.- Computing the single differences of measurements and model components. Dobs.scr EBRE.obsERR CREU.obsERR

mv D_EBRE_CREU.obs D_EBRE_CREU.obsERR

Kinematic:






graph.py -f D_EBRE_CREU.modERR -x1 -y2 -s. -l "North error" -f D_EBRE_CREU.modERR -x1 -y3 -s. -l "East error" -f D_EBRE_CREU.modERR -x1 -y4 -s. -l "UP error" --xl "time (s)" --yl "error (m)" --yn -15 --yx 15 -t "EBRE-CREU 280km: SPP: 2000m Along-Track orbit error"



Question: • Assuming an orbit error

of 2000m (see slide #87), compute a threshold for the differential error.






OVERVIEW

69




content

70


• Run this script for GARR and MATA receivers. Rename as STA.obsERR the output files ObsFile1.scr GARR0770.10o brdc0770.10nERR

mv GARR.obs GARR.obsERRObsFile1.scr MATA0770.10o brdc0770.10nERRmv MATA.obs MATA.obsERR


Repeat the computation of the absolute positioning of receivers GARR and MATA, but using the corrupted ephemeris file brdc0770.10nERR.

B2. Orbit error: Differential positioning of GARR-MATA receivers (Short baseline: 51 km)





71


cat GARR.modERR | kalman > GARR.posERR

3.- Plotting the results:graph.py -f GARR.posERR -x1 -y2 -s.- -l "North error"

-f GARR.posERR -x1 -y3 -s.- -l "East error" -f GARR.posERR -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -300 --yx 300 -t "GARR: SPP: 2000m Along-Track orbit error"

1.- Building the navigation equations system for absolute positioning: cat GARR.obsERR | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> GARR.modERR






72


cat MATA.modERR | kalman > MATA.posERR

3.- Plotting the results:graph.py -f MATA.posERR -x1 -y2 -s.- -l "North error"

-f MATA.posERR -x1 -y3 -s.- -l "East error" -f MATA.posERR -x1 -y4 -s.- -l "UP error" --xl "time (s)" --yl "error (m)" --yn -300 --yx 300 -t "MATA: SPP: 2000m Along-Track orbit error"

1.- Building the navigation equations system for absolute positioning: cat MATA.obsERR | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4, $14 ,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1 }'> MATA.modERR







Question: • Is the impact on user positioning error similar for both receivers?• From these plots, what is the expected level of error in differential positioning?



Using the files GARR.obsERR and MATA.obsERR, follow the next steps:1. Compute the single differences of measurements and model


positioning of MATA receiver (user) relative to GARR (reference station).

3. Compute the user solution in kinematic mode.4. Plot the results and discuss the positioning error found.

Analyse the effect of the 2000m orbit error on the differential positioning of MATA receiver relative to GARR, with 51km of baseline.






75

cp kalman.nml_wn kalman.nmlcat D_GARR_MATA.modERR| kalman > GARR_MATA.posKERR

2.- Building the navigation equations system for differential positioning: cat D_GARR_MATA.obsERR | gawk 'BEGIN{g2r=atan2(1,1)/45}{e=$12*g2r;a=$13*g2r;

printf "%8.2f %8.4f %8.4f %8.4f %8.4f %1i \n",$4,$5-$9-$10-$11,-cos(e)*sin(a),-cos(e)*cos(a),-sin(e),1}'>D_GARR_MATA.modERR


Dobs.scr GARR.obsERR MATA.obsERR

Kinematic:






graph.py -f D_GARR_MATA.modERR -x1 -y2 -s. -l "North error" -f D_GARR_MATA.modERR -x1 -y3 -s. -l "East error" -f D_GARR_MATA.modERR -x1 -y4 -s. -l "UP error" --xl "time (s)" --yl "error (m)" --yn -8 --yx 8 -t "GARR_MATA 51km: SPP: 2000m Along-Track orbit error"



Question: • Assuming an orbit error

of 2000m (see slide #87), compute a threshold for the differential error.






OVERVIEW

77



The following procedure is proposed:Using the files brdc0770.10n and brdc0770.10nERR, follow the next steps:1. Compute the absolute orbit for satellite PNR17 error by

comparing the corrupted orbits with the original ones.2. Compute the range error for the receivers EBRE and CREU3. Compute the differential range error between EBRE and CREU4. Compute the predicted range error between EBRE and CREU

and compare with the present one.

Analyze the orbit error of PRN17 in the Range Domain.

B.3. Differential positioning.Range Domain Orbit error

B3. Orbit error: Differential positioning Range Domain Orbit Error



B.3.1.- Absolute error computation for satellite PRN17:

gLAB_linux -input:nav brdc0770.10n -input:nav brdc0770.10nERR -pre:dec 30 |grep SATDIFF > dif.sel

B.3.1. Absolute Orbit error


graph.py -f dif.sel -x4 -y11 -so -c '($6==17)' --cl y -l "Rad" -f dif.sel -x4 -y12 -s. -c '($6==17)' --cl r -l "Alon" -f dif.sel -x4 -y13 -s. -c '($6==17)' --cl g -l "Cross"

--xn 55000 --xl "GPS seconds of day" --yl "metres" -t "PRN17: Orbit error"

Compute the discrepance between the satellite coordinates predicted from files brdc0770.10n and brdc0770.10nERR

Plot the results for satellite PRN17:


gAGE/UPC @ J. Sanz & J.M. Juan 80B.3.1. Absolute Orbit error




B.3.2.- Absolute Range error computation for satellite PRN17 from EBRE:

gLAB_linux -input:nav brdc0770.10n -pre:dec 30 | grep SATPVT | gawk '{if ($6==17) print $4,$7,$8,$9}' > xyz.brdc

B.3.2. Absolute Range Orbit error: EBRE


1. Using the original orbits brdc0770.10n, compute the geometric range between EBRE and satellite PRN17 (i.e rang.ebre file).

1.1- Compute the satellite coordinates with the original orbits and generate a file with the following content:

1 2 3 4[time X Y Z]

cat xyz.brdc | gawk 'BEGIN{x0=4833520.1197;y0=41537.2015;z0=4147461.6263}{dx=$2-x0;dy=$3-y0;dz=$4-z0;rho=sqrt(dx**2+dy**2+dz**2);

printf "%s %16.6f \n", $1,rho}' > rang.ebre

1.2.- Using the coordinates EBRE=[4833520.1197 41537.2015 4147461.6263], compute the geometric range between EBRE and satellite PRN17:



gLAB_linux -input:nav brdc0770.10nERR -pre:dec 30 | grep SATPVT |gawk '{if ($6==17) print $4,$7,$8,$9}' > xyz.brdcERR


2. Repeat the previous computation using the corrupted orbits file brdc0770.10nERR (i.e. generate the rang.ebreERR file).

2.1- Compute the satellite coordinates with the corrupted orbits and generate a file with the following content:

1 2 3 4[time X Y Z]

cat xyz.brdcERR|gawk 'BEGIN{x0=4833520.1197;y0=41537.2015;z0=4147461.6263}{dx=$2-x0;dy=$3-y0;dz=$4-z0;rho=sqrt(dx**2+dy**2+dz**2);

printf "%s %16.6f \n", $1,rho}' > rang.ebreERR

2.2.- Using the coordinates EBRE=[4833520.1197 41537.2015 4147461.6263], compute the geometric range between EBRE and satellite PRN17:




cat rang.ebre rang.ebreERR | gawk '{i=$1*1;if (length(r[i])==0) {r[i]=$2}else{print i,$2-r[i]}}' > drang.ebre


3. Calculate the discrepancy between the geometric ranges computed using the original and the corrupted orbits:

graph.py -f drang.ebre -x1 -y2 -l"EBRE" --xl "time (s)" --yl "error (m)" --yx 600 -t"PRN17: 2000m AT orbit error PRN17: EBRE: Range Error"

4.- Plot the results








Absolute Range error computation for satellite PRN17 from CREU:

a) Repeat the previous computations of section B.3.2 for the receiver CREU.

b) Compare in the same plot the results for EBRE and CREU

B.3.2. Absolute Range Orbit error: CREU









B.3.2. Absolute Range Orbit error: EBRE and CREU




B.3.3. Differential Range Orbit error: EBRE-CREU

B.3.3 Differential range Error computation

Using the previous files drang.ebre and drang.creu, compute the differential range orbit error of PRN17 between the receivers EBRE and CREU

cat drang.ebre drang.creu | gawk '{i=$1*1;if (length(r[i])==0) {r[i]=$2}else{printf "%s %16.6f \n", i,$2-r[i]}}' > ddrang.creu_ebre

graph.py -f ddrang.creu_ebre -x1 -y2 -s. --cl r --yn -10 --yx 35 --xl "time (s)" --yl "error (m)" -t"PRN17: 2000m AT orbit error PRN17: EBRE-CREU: Diff Range Error"

Plot the results









Results comparison



u

ε

B.3.4. Prediction of the differential range orbit errorVerify the next expression, which relates the orbit error with the differential range error :


B.3.4. Differential Range Orbit error: Prediction

ˆ ˆˆ ˆˆ ˆ ˆT T Tb bε u ε b -ρ ρ b

B: CREUReceiver

(user)

A: EBREReceiver

(ref station)

b B Ab r - rBaseline vector

[4833520.1197, 41537.2015, 4147461.6263][4833Ar[4715420.3054, 273177.8809, 4271946.7957][4715Br

ArBr

ε

b



The following procedure can be applied:


1.- Compute the orbit error vector from the original and corrupted orbits:gLAB_linux -input:nav brdc0770.10n -pre:dec 30 |grep SATPVT

|gawk '{if ($6==17) print $4,$7,$8,$9}' > xyz.brdc

gLAB_linux -input:nav brdc0770.10nERR -pre:dec 30 |grep SATPVT |gawk '{if ($6==17) print $4,$7,$8,$9}'> xyz.brdcERR

2.- From previous results, generate a file err.dat with the orbit error ( ) vector and the Line-Of-Sight ( ) from CREU receiver (with coordinates [4715420.3054, 273177.8809, 4271946.7957]), according to format:

cat xyz.brdc xyz.brdcERR|awk 'BEGIN{xb=4715420.3054;yb=273177.8809;zb= 4271946.7957} {i=$1*1;dx=$2-xb;dy=$3-yb;dz=$4-zb;rho=sqrt(dx**2+dy**2+dz**2); if (length(x[i])==0){x[i]=$2;y[i]=$3;z[i]=$4}

else{printf "%6i %16.6f %16.6f %16.6f %16.6f %16.6f %16.6f %16.6f \n", i,$2-x[i],$3-y[i],$4-z[i],dx,dy,dz,rho}}' |sort -n -k +1> err.dat

err.dat=[sec x y z x y z]




3.- Using the expression:



and the receivers’ coordinates:

ˆ ˆˆ ˆˆ ˆ ˆT T Tb bε u ε b -ρ ρ bB Ab r - r

Baseline vector

[4833520.1197, 41537.2015, 4147461.6263][4833Ar[4715420.3054, 273177.8809, 4271946.7957][4715Br

Compute the predicted differential orbit error d for the receiver CREU relative to EBRE station.

CREU:EBRE:

cat err.dat|gawk 'BEGIN{xa=4833520.1197;ya=41537.2015;za= 4147461.6263; xb=4715420.3054;yb=273177.8809;zb= 4271946.7957; bx=xb-xa; by=yb-ya; bz=zb-za; b=sqrt(bx*bx+by*by+bz*cz)} {rtc=($5*bx+$6*by+$7*bz)/$8/b;ux=bx/cb-$5/$8*rtc; uy=by/b-$6/$8*rtc;uz=bz/b-$7/$8*rtc;dr=-b/$8*($2*ux+$3*uy+$4*uz);

printf "%6i %16.6f \n", $1,dr}' > rang.err



Plot the results and compare with the result found in the previous exercise B.3.3 (i.e. with those of file ddrang.creu_ebre):



graph.py -f ddrang.creu_ebre -x1 -y2 -so --cl r -l "Observed" -f rang.err -x1 -y2 -l "Predicted" --xl "time (s)" --yl "error (m)" -t"PRN17: 2000m AT orbit error PRN17: EBRE-CREU: Diff Range Error" --yn -10 --yx 35










• To Institut Cartografic de Catalunya for the data files of receivers EBRE, CREU, GARR and MATA.

• To Adrià Rovira-Garcia for his contribution to the editing of this material and gLAB updating and integrating this learning material into the GLUE.

The ESA/UPC GNSS-Lab Tool suite (gLAB) has been developed under the ESA Education Office contract N. P1081434.

Acknowledgements



Tutorial 4Carrier ambiguity fixing





This tutorial is devoted to analyse and assess the ambiguity fixing and the differential positioning with carrier phase measurements (L1, L2). Two receivers UPC1 and UPC2 with a baseline of about 40 metres are considered.

This study includes ambiguity fixing using the “cascade method” (i.e., fixing one at a time) and with the LAMBDA method.

The effect of synchronization errors between the reference station and the user is and its effect on the navigation and ambiguity fixing is also analysed





Introduction: gLAB processing in command line.

Preliminary computations: Data files.

Session A: Fixing DD ambiguities one at a time: UPC1-UPC2.

Session B: Assessing the fixed ambiguities in navigation: Differential positioning of UPC1-UPC2 receivers.

Session C: Fixing DD ambiguities with LAMBDA method.

Note: UPC1-UPC2 receivers baseline: 37.95 metres.

OVERVIEW

4



Introduction: gLAB processing in command line.Preliminary computations: Data files.





OVERVIEW

5




sentences




“ paste” from


terminal.






Backup






Introduction: gLAB processing in command line.Preliminary computations: Data files.





OVERVIEW

8



Previous

Preliminary Computations



This section is devoted to prepare the data files to be used in the exercises.

These data files will include the code and carrier measurements and the model components: geometric range, nominal troposphere and ionosphere corrections, satellite elevation and azimuth from each receiver…

This data processing will be done with gLAB for each individual receiver.

This preliminary processing will provide the baseline data files to perform computations easily using basic tools (such as awk for data files handling, to compute Double Differences of measurements) or using octave (MATLAB) scripts for the LAMBDA method implementation.

Detailed guidelines for self learning students are provided in this tutorial and in its associated notepad text file.

P. Preliminary computations



P1. Model Components computation• The script "ObsFile.scr" generates a data file with the following content

11


1 2 3 4 5 6 7 8 9 10 11 12 13[sta sat DoY sec P1 L1 P2 L2 Rho Trop Ion elev azim]

• Run this script for all receivers:

ObsFile.scr UPC10770.11o brdc0770.11nObsFile.scr UPC20770.11o brdc0770.11n

• Merge all files into a single file:

cat ????.obs > ObsFile.dat

P1. Model components computation



• To simplify computations, a time interval with always the same set of satellites in view and without cycle-slips is selected.

• Moreover an elevation mask of 10 degrees will be applied.

12

P. Preliminary computationsSelecting measurements: Time interval [18000:19900]

If the satellites change or cycle-slips appear during the data processing interval, care with the associated parameters handling must be taken in the navigation filter. Set up new parameters when new satellites appear

and treat the ambiguities as constant between cycle-slips and white noise when a cycle-slip happens.




• Select the satellites in the time interval [18000:19900] with elevation over 10º

13


Confirm that the satellite PRN06 is the satellite with the highest elevation (this satellite will be used as the reference satellite)

cat ObsFile.dat|gawk '{if ($4>=18000 && $4<=19900 && $12>10) print $0}' > obs.dat

• Reference satellite (over the time interval [18000:19900])

Selecting measurements: Time interval [18000:19900]

1 2 3 4 5 6 7 8 9 10 11 12 13[sta sat DoY sec P1 L1 P2 L2 Rho Trop Ion elev azim]obs.dat




P2. Double differences between receivers and satellites computation

14

1 2 3 4 5 6 7 8 9 10 11 12 13[sta sat DoY sec P1 L1 P2 L2 rho Trop Ion elev azim]

The script "DDobs.scr" computes the double differences between receivers and satellites from file obs.dat.

For instance, the following sentence:DDobs.scr obs.dat UPC1 UPC2 06 03

------------------- DD_{sta1}_{sta2}_{sat1}_{sat2}.dat ----------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

[sta1 sta2 sat1 sat2 DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2]<---- sta2 ---->

------------------------------------------------------------------------------------

generates the file

Where the elevation (EL) and azimuth (AZ) are taken from station #2.and where (EL1, AZ1) are for satellite #1 and (EL1, AZ1) are for satellite #2.

P2. Double Differences computation




Compute the double differences between receivers UPC1 (reference) and UPC2 and satellites PRN06 (reference) and [PRN 03, 07,16, 18, 19, 21, 22, 24]

15

DDobs.scr obs.dat UPC1 UPC2 06 03DDobs.scr obs.dat UPC1 UPC2 06 07DDobs.scr obs.dat UPC1 UPC2 06 16DDobs.scr obs.dat UPC1 UPC2 06 18DDobs.scr obs.dat UPC1 UPC2 06 19DDobs.scr obs.dat UPC1 UPC2 06 21DDobs.scr obs.dat UPC1 UPC2 06 22DDobs.scr obs.dat UPC1 UPC2 06 24

Merge the files in a single file and sort by time:

cat DD_UPC1_UPC2_06_??.dat|sort -n -k +6 > DD_UPC1_UPC2_06_ALL.dat


P2. Double Differences computation









OVERVIEW

16



This exercise is devoted to study the ambiguity fixing using the cascade method, that is, fixing the ambiguities one at a time.

In the first part, we are going to assess this approach for a single frequency receiver, trying to fix DDN1 and DDN2 independently.

In the second part, we are going to assess this approach for dual frequency receivers, fixing first the wide-lane ambiguity DDNw and afterwards DDN1 and DDN2.The results (i.e. the DDN1 and DDN2 ambiguities) will be assessed in the next “Session B” by computing the navigation solution using the carrier phases repaired with the fixed DDN1 and DDN2 ambig.

Finally, in Session C, the LAMBDA method will be applied for comparison.

A. Fixing DD ambiguities one at a time: UPC1-UPC2

gAG

E/U

PC re

sear

ch g

roup

of A

stro

nom

y an

d G

eom

atic

sgAGE

Master of Science in GNSS @ J. Sanz & J.M. Juan

11ˆ

1

1 51jk jkN P

18

Resolving ambiguities one at a Time: single Freq.

A simple trial would be (for instance using L1 and P1):

To much error (5 wavelengths)!

11 1 1jk jk jk jk

LL N11

jk jk jkPP 1 1

11

ˆjk jk

jk

roundoff

L PN11 1 1 1

jk jk jk jkPL P N

1

1

1 20cm1m

1cm

20cmjk

jk

P

L

1N

1N

1/ 2N

1/ 2N

Note that, assuming a Gaussian distribution of errors, guarantee only the 68% of success 1

ˆ 1/ 2 1/ 2jkNN

As the ambiguity is constant (between cycle-slips), we would try to reduce uncertainty by averaging the estimate on time, but we will need 100 epochs to reduce noise up to ½ (but measurement errors are highly correlated on time!)

Good

Fail

Similar results with L2, P2 measurements



A1 Trying to fix ambiguities in Single frequency

A1.1 Fixing N1 and N2 independently:Estimate graphically values of DDN1 and DDN2 (i.e. try to identify the true ambiguity from the plot).

Hint:

From file DD_UPC1_UPC2_06_ALL.dat, generate the file DDN1N2.dat with the following content:

where:DDN1=[DDL1 -DDP1]/ ; DDN2=[DDL2 -DDP2]/

1 2 3 4 5 6[PRN sec DDN1 DDN2 nint(DDN1) nint(DDN2)]

Be careful: “nint" in awk:nint(x)must be generated as: int(x+0.5*sign(x))

Note:“nint” means near-integer



a) From file DD_UPC1_UPC2_06_ALL.dat, generate the file DDN1N2.dat with the following content:

gawk 'BEGIN{c=299792458;f0=10.23e+6;l1=c/(154*f0);l2=c/(120*f0)}{A1=($8-$7)/l1; A2=($10-$9)/l2;if (A1!=0){signA1=A1/sqrt(A1*A1)}else{signA1=0};

if (A2!=0) {signA2=A2/sqrt(A2*A2)}else{signA2=0};print $4,$6,A1,int(A1+0.5*signA1),A2,int(A2+0.5*signA2)}' DD_UPC1_UPC2_06_ALL.dat >

DDN1N2.dat

A1. DDN1 and DDN2 in single frequency

1 2 3 4 5 6[PRN sec DDN1 DDN2 nint(DDN1) nint(DDN2)]

Execute, for instance:

----------------------------- DD_UPC1_UPC2_06_ALL.dat ------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

[UPC1 UPC2 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2 ]<---- UPC2 ---->

------------------------------------------------------------------------------------




graph.py -f DDN1N2.dat -x2 -y3 -c '($1==16)' -s. -f DDN1N2.dat -x2 -y4 -c '($1==16)' -sx --cl r --yn -4 --yx 10 --xl "time (s)" --yl "cycles L1" -t "DDN1 ambiguity: PRN16"

b1) DDN1 plot:


b2) DDN2 plot:

b) Plot DDN1 and DDN2 for the different satellites and discuss if the ambiguity DDN1 and DDN2 can be fixed: 1 2 3 4 5 6

[PRN sec DDN1 DDN2 nint(DDN1) nint(DDN2)]





b1) DDN1 plot:


Questions:1.- Explain what is the meaning

of this plot.2.- Is it possible to identify the

integer ambiguity?3.- How reliability can be

improved?





b2) DDN2 plot:



of this plot.2.- Is it possible to identify the

integer ambiguity?3.- How reliability can be

improved?





c) Make plots to analyze the DDP1 and DDP2 code noise.Hint:From file DD_UPC1_UPC2_06_ALL.dat, generate the file P1P2noise.dat with the following content:

gawk '{print $4,$6,$7-$11,$9-$11}' DD_UPC1_UPC2_06_ALL.dat > P1P2noise.dat

----------------------------- DD_UPC1_UPC2_06_ALL.dat ------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

[UPC1 UPC2 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2 ]------------------------------------------------------------------------------------


1 2 3 4 5[PRN sec DDP1-DDRho DDP2-DDRho]





c1 ) Depict the DDP1 code noise:

graph.py -f P1P2noise.dat -x2 -y3 -c '($1==16)' -so --yn -2 --yx 1.5 --xl "time (s)" --yl "metres" -t "DDP1 noise: PRN16"

Questions:

Discuss why the ambiguities cannot be fixed by rounding-off the expression DDN1=[DDL1 -DDP1]/





c2 ) Depict the DDP2 code noise:

graph.py -f P1P2noise.dat -x2 -y4 -c '($1==16)' -so --yn -2 --yx 1.5 --xl "time (s)" --yl "metres" -t "DDP2 noise: PRN16"



Questions:

Discuss why the ambiguities cannot be fixed by rounding-off the expression DDN2=[DDL2 –DDP2]/



d) Make plots to analyze the DDL1 and DDL2 carrier noise.Hint:From file DD_UPC1_UPC2_06_ALL.dat, generate the file L1L2noise.dat with the following content:

gawk '{print $4,$6,$8-$11,$10-$11}' DD_UPC1_UPC2_06_ALL.dat > L1L2noise.dat

----------------------------- DD_UPC1_UPC2_06_ALL.dat ------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17



1 2 3 4 5[PRN sec DDL1-DDRho DDL2-DDRho]





d1) Depict the DDL1 code noise:

graph.py -f L1L2noise.dat -x2 -y3 -c '($1==16)' -so --yn 0.38 --yx 0.40 --xl "time (s)" --yl "metres" -t "DDL1 noise: PRN16"

Questions:

Discuss the plot.What is the level of noise?

Compare the noise with the wavelength =19.0cm





d2) Depict the DDL2 code noise:

graph.py –f L1L2noise.dat -x2 -y4 -c'($1==16)' -so --yn -0.24 --yx -0.22 --xl "time (s)" --yl "metres" -t "DDL2 noise: PRN16"

Questions:

Discuss the plot.What is the level of noise?

Compare the noise with the wavelength =24.4cm



gAG

E/U

PC re

sear

ch g

roup

of A

stro

nom

y an

d G

eom

atic

sgAGE

Master of Science in GNSS @ J. Sanz & J.M. Juan30

Resolving ambiguities one at a Time: Dual Freq. Dual frequency measurements: wide-laning with the Melbourne-Wübbenacombination

1

2

1 1 1

2 2 2

jk jk jk jkL

jk jk jk jkL

L N

L N

1

2

1

2

jk jk jkP

jk jk jkP

P

P

ˆjk jk

jk W NW

W roundoff

L PN

1 1 2 2

1 2

1 1 2 2

1 2

N

W

jk jkjk jk jk

N P

jk jkjk jk jk jkW W W L

f P f PPf f

f L f LL Nf f

1 2

1 2

86.2 m86.2 m

W

W

N N Nc c

f f

Now, with uncorrelated measurements from 10 epochs will reduce noise up to about ¼.

ˆ1 71 0.8

86.271 0.8

86 2jk jkNW

N PW

cmcm

N

jk jk jk jkW N W W PL P N

1 2

1 2

1 2 1 1 2 2

1 2 1 2

jk jk jk jk jkL L

jk jk jkW L L

L L N N

N N

1

1

/ 2 71 m

6 6cm

jk jkN

jk jkW

P P

L L

c

1 2 21

1 2

ˆˆjk jk jk

jk W

roundoff

L L NN

Fixing N1 (after fixing NW)

1 1ˆ

1 2

1 1.42 1/ 45.41.4 1/ 41.45 4jk jk

LN

cmcm

2 1ˆ ˆ ˆjk jk jk

WN N N

1

1

2

2 1

19.0cm24.4cm

5.4cm1cmjkL



A2 Dual Frequency Ambiguity Fixing

A2.1 Fixing Wide-lane ambiguity (Nw):Estimate graphically values of DDNw (i.e. try to identify the true ambiguity from the plot).

Hint:

From file DD_UPC1_UPC2_06_ALL.dat, generate the file DDNw.dat with the following content:

where: DDNw=[DDLW-DDPN]/ W1 2 3 4

[PRN sec DDNw nint(DDNw)]

1 2 1 2 1

2 1 2

154; ; ; 86.21 1 120W N W

L L P P f cL P cmf f f

Note:

A2. 1 Fixing Wide-lane ambiguity DDNw



a) From file DD_UPC1_UPC2_06_ALL.dat, generate the file DDNw.dat with the following content: where: DDNw=[DDLW-DDPN]/ W

cat DD_UPC1_UPC2_06_ALL.dat| gawk 'BEGIN{s12=154/120} {mw=(s12*$8-$10)/(s12-1)-(s12*$7+$9)/(s12+1);if(mw!=0){sign=mw/sqrt(mw*mw)} else{sign=0};printf "%02i %i %14.4f %i \n", $4,$6, mw/0.862,int(mw/0.862+0.5*sign)}'>

DDNw.dat


----------------------------- DD_UPC1_UPC2_06_ALL.dat ------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


1 2 3 4[PRN sec DDNw nint(DDNw)]





graph.py -f DDNw.dat -x2 -y3 -c '($1==03)' -s. -f DDNw.dat -x2 -y4 -c '($1==03)' -sx --cl r --yn -1 --yx 7 --xl "time (s)" --yl "cycles Lw" -t "DDNw ambiguity: PRN03"

b) Plot DDNw for the different satellites and discuss if the ambiguity DDNw can be fixed: 1 2 3 4

[PRN sec DDNw nint(DDNw)]


- Example PRN03 plot:

- Example PRN07 plot:






PRN03 plot:

DDNw= 3 ?





PRN07 plot:

DDNw= 0 ?







graph.py -f DDNw.dat -x2 -y3 -c '($1==21)' -s. -f DDNw.dat -x2 -y4 -c '($1==21)' -sx --cl r --yn 4 --yx 12 --xl "time (s)" --yl "cycles Lw" -t "DDNw ambiguity: PRN21"


graph.py -f DDNw.dat -x2 -y3 -c '($1==24)' -s. -f DDNw.dat -x2 -y4 -c '($1==24)' -sx --cl r --yn 0 --yx 8 --xl "time (s)" --yl "cycles Lw" -t "DDNw ambiguity: PRN24"



The remaining plots:







PRN16 PRN18 PRN19

PRN21 PRN22 PRN24



Hint: From file DD_UPC1_UPC2_06_ALL.dat, generate the file DDNws.dat with the content:

cat DDNw.dat|gawk '{dt=300;for (j=0;j<dt;j++) {t=j+dt/2+int(($2-j)/dt)*dt;ind=$1" "t; n[ind]++;v[ind]=$3;m[ind]=m[ind]+$3}}

END{for (i in n) {if (n[i]!=0) {;if(n[i]>1) {val=v[i];mean=m[i]/n[i]; print i,val,mean}}}}' | sort -n -k+1 > DDNws.tmp

Execute, for instance (to smooth the DDNw):

1 2 3 4 5 6 [PRN sec DDNw DDNws nint(DDNw) nint(DDNws)]

A.2.2 Smoothing the DDNw:Smooth the DDNw with a 300 seconds sliding window, in order to improve the ambiguity fixing.

cat DDNws.tmp | gawk '{sign3=$3/sqrt($3*$3);sign4=$4/sqrt($4*$4);print $1,$2,$3,$4,int($3+0.5*sign3),int($4+0.5*sign4)}' > DDNws.dat

Estimate again the ambiguity from the raw DDNw and smoothed DDNws:


A2. 2 Fixing Wide-lane ambiguity DDNw after smoothing



graph.py -f DDNws.dat -x2 -y3 -c '($1==03)' -s. -f DDNws.dat -x2 -y5 -c '($1==03)' -sx --cl r -f DDNws.dat -x2 -y4 -c '($1==03)' -s. --cl g -f DDNws.dat -x2 -y6 -c '($1==03)' -sx --cl m --yn 0 --yx 6 --xl "time (s)" --yl "cycles Lw" -t "DDNw ambig. PRN03"

b) Plot DDNw and DDNws for the different satellites and discuss if the ambiguity DDNw can be fixed:

- Example: PRN03 plot:

1 2 3 4 5 6 [PRN sec DDNw DDNws nint(DDNw) nint(DDNws)]






PRN03 plot:

DDNw=3





graph.py -f DDNws.dat -x2 -y3 -c '($1==07)' -s. -f DDNws.dat -x2 -y5 -c '($1==07)' -sx --cl r -f DDNws.dat -x2 -y4 -c '($1==07)' -s. --cl g -f DDNws.dat -x2 -y6 -c '($1==07)' -sx --cl m --yn -3 --yx 3 --xl "time (s)" --yl "cycles Lw" -t "DDNw ambig. PRN07"

PRN07 plot:

DDNw=0






PRN16 plot:

DDNw=3






PRN18 plot:

DDNw=-3






PRN19 plot:

DDNw=2






PRN21 plot:

DDNw=8






PRN22 plot:

DDNw=0





PRN24 plot:

DDNw=4







A2.2 Fixing DDN1 from DDNw and DDL1, DDL2Using the previous DDNw fixed values, estimate graphically the DDN1 ambiguity (i.e. try to identify the true ambiguity from the plot).

Hint:

From file DD_UPC1_UPC2_06_ALL.dat, and using the fixed DDNw, generate the file DDN1.dat with the following content:

where:DDN1=(DDL1 DDL2 2 DDNw)/( 1 2)

1 2 3 4[PRN sec DDN1 nint(DDN1)]

PRN = [ 03 07 16 18 19 21 22 24]DDNw= [ 3 0 3 -3 2 8 0 4]

A2. 2 Fixing DDN1 after fixing DDNw



gawk 'BEGIN{c=299792458;f0=10.23e+6;f1=154*f0;f2=120*f0;l1=c/f1;l2=c/f2}{Nw=4;if ($4==24) {amb=($8-$10-l2*Nw)/(l1-l2);

print $4,$6,amb,int(amb+0.5*amb/sqrt(amb*amb))}}' DD_UPC1_UPC2_06_ALL.dat > DDN1_PRN24

Execute, for instance for PRN24 (with DDNw=4):

----------------------------- DD_UPC1_UPC2_06_ALL.dat ------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


From file DD_UPC1_UPC2_06_ALL.dat, and using the fixed DDNw, generate the file DDN1.dat with the following content:

where:DDN1=(DDL1 DDL2 2 DDNw)/( 1 2)

1 2 3 4[PRN sec DDN1 nint(DDN1)]





graph.py -f DDN1_PRN24 -x2 -y3 -c '($1==24)' -s. -f DDN1_PRN24 -x2 -y4 -c '($1==24)' -sx --cl r --yn 1 --yx 6 --xl "time (s)" --yl "cycles L1" -t "DDN1 ambiguity: PRN24"



PRN24 plot:

DDN1=4



gawk 'BEGIN{for (i=0;i<100;i++) {getline <"sat.ambNw";Nw[$1*1]=$2}} {c=299792458;f0=10.23e+6;f1=154*f0;f2=120*f0;l1=c/f1;l2=c/f2}{amb=($8-$10-l2*Nw[$4*1])/(l1-l2);if (amb!=0){sign=amb/sqrt(amb*amb)} else{sign=0};

print $4,$6,amb,int(amb+0.5*sign)}' DD_UPC1_UPC2_06_ALL.dat > DDN1.dat

Other possibility is to execute the following sentence to generate the file for all satellites:

----------------------------- DD_UPC1_UPC2_06_ALL.dat ------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


From file DD_UPC1_UPC2_06_ALL.dat, and using the fixed DDNw, generate the file DDN1.dat with the following content: 1 2 3 4

[PRN sec DDN1 nint(DDN1)]

Where sat.ambNw is a file containing the DDNw ambiguities:

03 307 016 318 -319 2 21 822 024 4





graph.py -f DDN1_PRN24 -x2 -y3 -c '($1==03)' -s. -f DDN1_PRN24 -x2 -y4 -c '($1==03)' -sx --cl r --yn -1 --yx 4 --xl "time (s)" --yl "cycles L1" -t "DDN1 ambiguity: PRN03"



PRN03 plot:

DDN1=2



PRN07 plot:

DDN1=1

graph.py -f DDN1_PRN24 -x2 -y3 -c '($1==07)' -s. -f DDN1_PRN24 -x2 -y4 -c '($1==07)' -sx --cl r --yn -2 --yx 3 --xl "time (s)" --yl "cycles L1" -t "DDN1 ambiguity: PRN07"







PRN16DDN1=2

PRN18DDN1=-1

PRN19DDN1=4

PRN21DDN1=7

PRN22DDN1=1

PRN24DDN1=4




A2.3 Fixing DDN2Using the previous DDNw and DDN1 ambiguities fixed, fix the DDN2 ambiguity:

Hint: The DDN2 can be easily computed by: DDN2=DDN1-DDNw

Then:

PRN = [ 03 07 16 18 19 21 22 24]DDNw= [ 3 0 3 -3 2 8 0 4]DDN1= [ 2 1 2 -1 4 7 1 4]

DDN2= [-1 1 -1 2 2 -1 1 0]

A2. 3 Fixing DDN2 after fixing DDNw and DDN1









OVERVIEW

56



Session B

Assessing the fixed ambiguities in navigation: Differential positioning of UPC1-UPC2 receivers

(baseline: 37.95 metres)



The DDN1 and DDN2 ambiguities have been fixed in the previous Session A using the “cascade method”.

The obtained results (i.e. the DDN1 and DDN2 ambiguities) will be assessed in this Session B by computing the navigation solution using the carrier phases repaired with the fixed DDN1 and DDN2 ambiguities

Finally, in next Session C, the ambiguities will be fixed using the LAMBDA method and the performance with the cascade method will be compared.

B. Assessing the fixed ambiguities in navigation

B1. Repairing DDL1 and DDL2 carriers



After repairing the carrier ambiguities, these measurements will be used to navigate.

Indeed, once the integer ambiguities are known, the carrier phase measurements become like “unambiguous pseudoranges”, accurate at the centimetre level or better.

Thence, the positioning is straightforward following the same procedure as with pseudoranges.

Nevertheless, a wrong ambiguity fix can degrade the position solution significantly.

B. Assessing the fixed ambiguities in navigation



B1. Repair the DDL1 and DDL2 carrier measurements with the DDN1 and DDN2 ambiguities FIXED and plot results to analyze the data.

03 2 -107 1 116 2 -118 -1 219 4 2 21 7 -122 1 124 4 0

Using the previous file N1N2.dat and "DD_UPC1_UPC2_06_ALL.dat",generate a file with the following content:

----------------------------- DD_UPC1_UPC2_06_ALL.fixL1L2 -------------------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

[UPC1 UPC2 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2 DDN1 DDN2]<---- UPC2 ---->

------------------------------------------------------------------------------------------------

Note: This file is identical to file "DD_UPC1_UPC2_06_ALL.dat", but with the ambiguities added in the last fields #18 and #19.

B. Repairing the DDL1 and DDL2 with the ambiguities fixed


Write in it the DDN1 and DDN2 ambiguities fixed in previous exercise in file N1N2.dat



gawk 'BEGIN{c=299792458;f0=10.23e+6;l1=c/(154*f0);l2=c/(120*f0)}{printf "%02i %3i %3i %14.4f %14.4f \n", $1,$2,$3,$2*l1,$3*l2}' N1N2.dat >

sat.ambL1L2

a) From previous file, generate a the file "sat.ambL1L2" with the following content:

cat DD_UPC1_UPC2_06_ALL.dat|gawk 'BEGIN{for (i=1;i<1000;i++) {getline <"sat.ambL1L2";A1[$1]=$4;A2[$1]=$5}}

{printf "%s %02i %02i %s %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f\n",

$1,$2,$3,$4,$5,$6,$7,$8,$9,$10,$11,$12,$13,$14,$15,$16,$17,A1[$4], A2[$5]}' > DD_UPC1_UPC2_06_ALL.fixL1L2

b) Generate the "DD_UPC1_UPC2_06_30.fixL1L2" file:


1 2 3 4 5[PRN DDN1 DDN2 DDN1 DDN2]




graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL1-lambda1*DDN1)-DDrho" --xl "time (s)" --yl "m"

c) Make and discuss the following plots for DDL1

graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($8-$11)' -so --yn -5 --yx 5 -l "(DDL1)-DDrho" --xl "time (s)" --yl "metres"

graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -20 --yx 20 -l "(DDL1-lambda1*DDN1)" --xl "time (s)" --yl "metres"


B1. Plotting the repaired DDL1



------------------------------------------------------------------------------------------------



graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL1- DDN1)-DDrho" --xl "time (s)" --yl "m"

Questions:Explain what is the meaning of this plot.



------------------------------------------------------------------------------------------------





graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($8-$11)' -so --yn -5 --yx 5 -l "DDL1-DDrho" --xl "time (s)" --yl "m"




------------------------------------------------------------------------------------------------





graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -20 --yx 20 -l "(DDL1- DDN1)" --xl "time (s)" --yl "m"


of this plot.2.- Why a trend and a

discontinuity appears?



------------------------------------------------------------------------------------------------





graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($10-$19-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL2-lambda2*DDN2)-DDrho" --xl "time (s)" --yl "m"

d) Make and discuss the following plots for DDL2

graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($10-$11)' -so --yn -5 --yx 5 -l "(DDL2)-DDrho" --xl "time (s)" --yl "metres"

graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($10-$19)' -so --yn -20 --yx 20 -l "(DDL2-lambda2*DDN2)" --xl "time (s)" --yl "metres"





------------------------------------------------------------------------------------------------



graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($9-$19-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL2- DDN2)-DDrho" --xl "time (s)" --yl "m"




------------------------------------------------------------------------------------------------





graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($9-$11)' -so --yn -5 --yx 5 -l "DDL2-DDrho" --xl "time (s)" --yl "m"




------------------------------------------------------------------------------------------------





graph.py -f DD_UPC1_UPC2_06_ALL.fixL1 -x6 -y'($9-$198)' -so --yn -20 --yx 20 -l "(DDL2- DDN2)" --xl "time (s)" --yl "m"



------------------------------------------------------------------------------------------------




of this plot.2.- Why a trend and a

discontinuity appears?



After repairing the carrier ambiguities, these measurements will be used to navigate.

Indeed, once the integer ambiguities are known, the carrier phase measurements become like “unambiguous pseudoranges”, accurate at the centimetre level or better.

Thence, the positioning is straightforward following the same procedure as with pseudoranges.

Nevertheless, a wrong ambiguity fix can degrade the position solution significantly.

B2 Assessing the fixed ambiguities in navigation



In this exercise we will considerer an implementation of differential positioning where the user estimates the baseline vector using the time-tagged measurements of the reference station.

This approach is usually referred to as relative positioning and can be applied in some applications where the coordinates of the reference station are not accurately known and where the relative position vector between the reference station and the user is the main interest. Examples are formation flying, automatic landing on ships…

Of course, the knowledge of the reference receiver location would allow the user to compute its absolute coordinates.

This is a simple approach, where synchronism delays between the time tag measurements of the reference station and the user must be taken into account for real-time positioning.

B2.1 UPC1-UPC2 Baseline vector estimation with DDL1 carrier(using the time-tagged reference station measurements)



Where the elevation (EL) and azimuth (AZ) are taken from station UPC2 (the user)

and where, (EL1, AZ1) are for satellite PNR06 (reference) and (EL1, AZ1) are for satellite PRNXX




------------------------------------------------------------------------------------------------

IND3 (user)IND2 (ref)

PRN06 (ref) PRNXX

UPC1 (ref) UPC2 (user)

Data file

Measurements broadcast by the reference station.1,

jrefL

1,jrefL

Baseline vectorr

B2.1 Baseline vector estimation with DDL1 (single epoch LS, whole interval)



1 DDL1(involving satellites and )k jDDL j k

1 1, 1,

1, 1, 1, 1,

k j k j k jusr ref

j k j kusr usr ref ref

DDL DL DL

L L L L

1,jrefL Measurements broadcast

by the reference station.

[DDL1- DDN1 ]=[Los_k - Los_06]*[baseline]

3 66,03 6,031 1 16,07 6,07 7 61 1 1

6,24 6,2424 61 1 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDL DDNDDL DDN

DDL DDN

ρ ρ

ρ ρ r

ρ ρ

Notation

Estimate the baseline vector between UPC1 and UPC2 receivers using the code measurements of file (DD_UPC1_UPC2_06_ALL.dat). Note: Use the entire file (i.e. time interval [18000:19900]).





Estimate the baseline vector between UPC1 and UPC2 receivers using the code measurements of file (DD_UPC1_UPC2_06_ALL.dat). Note: Use the entire file (i.e. time interval [18000:19900]).

74

[DDL1- DDN1 ]=[Los_k - Los_06]*[baseline]

3 66,03 6,031 1 16,07 6,07 7 61 1 1

6,24 6,2424 61 1 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDL DDNDDL DDN

DDL DDN

ρ ρ

ρ ρ r

ρ ρ


ˆ Line-Of-Sight unit vector to satelite k kρ


Baseline vectorrNotation





Using the DDL1 carrier with the ambiguities FIXED, compute the LS single epoch solution for the whole interval 180000< t <199000 with the program LS.f

Note: The program LS.f computes the Least Square solution for eachmeasurement epoch of the input file (see the FORTRAN code LS.f)

The following procedure can be applied:a) generate a file with the following content;

[Time], [DDL1- DDN1], [ Los_k - Los_06]

where:Time= seconds of day DDL1- DDN1= Prefit residulas (i.e., "y" values in program LS.f)Los_k-Los_06 = The three components of the geometry matrix

(i.e., matrix "a" in program LS.f)





cat DD_UPC1_UPC2_06_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;

printf "%s %14.4f %8.4f %8.4f %8.4f \n",$6, $8-$18, -cos(e2)*sin(a2)+cos(e1)*sin(a1),

-cos(e2)*cos(a2)+cos(e1)*cos(a1), -sin(e2)+sin(e1)}' > M.dat

Justify that the next sentence builds the navigation equations system

[DDL1- DDN1]=[Los_k - Los_06]*[baseline]

[DDL1- DDN1] [ Los_k - Los_06] ------------ ---------------------3.3762 0.3398 -0.1028 0.0714-7.1131 0.1725 0.5972 0.0691 4.3881 -0.6374 0.0227 0.2725

3 66,03 6,031 1 16,07 6,07 7 61 1 1

6,24 6,2424 61 1 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDL DDNDDL DDN

DDL DDN

ρ ρ

ρ ρ r

ρ ρ



See file content in slide #31

Time



The following sentence can be used:

cat DD_UPC1_UPC2_06_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$8-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),

-cos(e2)*cos(a2)+cos(e1)*cos(a1),-sin(e2)+sin(e1)}' > L1model.dat

[Time], [DDL1- DDN1], [Los_k - Los_06]

b) Compute the Least Squares solution:

cat L1model.dat |LS > L1fix.pos





------------------------------------------------------------------------------------------------



Plot the baseline estimation error:

graph.py -f L1fix.pos -x1 -y'($2+27.4170)' -s.- -l "North error" -f L1fix.pos -x1 -y'($3+26.2341)' -s.- -l "East error" -f L1fix.pos -x1 -y'($4+ 0.0304)' -s.- -l "UP error"

--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "Baseline error”

Note: An accurate estimate of baseline is:bsl_enu =[-27.4170 -26.2341 -0.0304]

Use this determination to assess the baseline vector estimation error.





L1 Baseline estimation error

after fixing ambiguities



Questions:1.- What is the expected

accuracy when positioning with carrier after fixing ambiguities?

2.- Discuss why a trend and a discontinuity appears?



In the previous exercise we have considered an implementation of differential positioning where the user estimates the baseline vector from the time-tagged measurements of the reference station.

In the next exercises, we will consider the common implementation of Differential positioning, where the reference receiver coordinates are accurately known and used to compute range corrections for each tracked satellite in view. Then, the user applies these corrections to improve the positioning.

Unlike in the previous implementation, the synchronism errors between the time-tagged measurements will be not critical in this approach, as the differential corrections vary slowly.

B2.2. UPC1-UPC2 differential positioning with DDL1 carrier(using the computed differential corrections)

B2.2. Differential positioning with DDL1 (using computed dif. corrections)



Using code DDL1 measurements, estimate the coordinates of receiver UPC2 taking UPC1 as a reference receiver.

Justify that the associated equations system is given by:

81

1 DDL1(involving satellites and )k jDDL j kˆ Line-Of-Sight unit vector to satelite k kρ

ˆ cos( )sin( ) cos( )cos( ) sin( )kk k k k kEl Az El Az Elρ

3 0, 3-IND INDdr r rNotation

[DDL1- DDRho- DDN1]=[Los_k - Los_06]*[dr]

3 66,03 6,031 1 16,07 6,07 7 61 1 1

6,24 6,3024 61 1 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDL DD DDNDDL DD DDN

DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ







82


Notation

1,1 1,j j j

L ref refPRC LComputed corrections broadcast by the reference station.

3 66,03 6,031 1 16,07 6,07 7 61 1 1

6,24 6,3024 61 1 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ

1 1, 1,

1, 1, 1, 1,

k j k j k j k j k j k jusr usr ref ref

j j k k j j k kusr usr usr usr ref ref ref ref

DDL DD D L D L

L L L L







PRN06 (ref) PRN j

83

[DDL1- DDRho- DDN1]=[Los_k-Los_06]*[dr]

6ρ ˆ jρ

UPC2 0,UPC2-dr r rˆ cos( )sin( ), cos( )cos( ), sin( )j

j j j j jEl Az El Az Elρ

3 66,03 6,031 1 16,07 6,07 7 61 1 1

6,24 6,3024 61 1 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ

UPC1 (ref) UPC2 (user)







cat DD_UPC1_UPC2_06_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;

printf "%s %14.4f %8.4f %8.4f %8.4f \n",$6, $8-$11-$18, -cos(e2)*sin(a2)+cos(e1)*sin(a1),

-cos(e2)*cos(a2)+cos(e1)*cos(a1),-sin(e2)+sin(e1)}'> M.dat



[DDL1-DDRho- DDN1] [Los_k - Los_06] ----------- -------------------3.3762 0.3398 -0.1028 0.0714-7.1131 0.1725 0.5972 0.0691 4.3881 -0.6374 0.0227 0.2725

3 66,03 6,03 6,031 1 16,07 6,07 6,07 7 61 1 1

6,24 6,24 6,2424 61 1 1

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ r

ρ ρ



Time




The following sentence can be used

cat DD_UPC1_UPC2_06_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$8-$11-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),


[Time], [DDL1- DDRho - DDN1], [Los_k - Los_06]

b) Compute the Least Squares solution




------------------------------------------------------------------------------------------------





Plot the absolute positioning error:

graph.py -f L1fix.pos -x1 –y2- s.- -l "North error" -f L1fix.pos -x1 –y3 -s.- -l "East error" -f L1fix.pos -x1 –y4 -s.- -l "UP error" --yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "Absolute positioning error with DDL1"





L1 Differential positioning after fixing ambiguities

Questions:Discuss why the results have improved, achieving centimetre level navigation.






cat DD_UPC1_UPC2_06_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$9-$11-$19,-cos(e2)*sin(a2)+cos(e1)*sin(a1),


[Time], [DDL2- DDRho – DDN2], [Los_k - Los_06]

Compute the Least Squares solution




------------------------------------------------------------------------------------------------



Repeat the previous positioning, but with the DDL2 carrier




graph.py -f L2fix.pos -x1 –y2- s.- -l "North error" -f L2fix.pos -x1 –y3 -s.- -l "East error" -f L2fix.pos -x1 –y4 -s.- -l "UP error" --yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "Absolute positioning error with DDL2"





L2 Differential positioning after fixing ambiguities

Questions:Compare the results with the previous ones computed from DDL1.






cat DD_UPC1_UPC2_06_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45; {if ($4==07){$18=$18+0.19029};}

{e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$8-$11-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),


Compute the Least Squares solution


B2.4. Differential positioning with DDL1 Effect of wrong ambiguity fix.


Analyze the effect of a wrong ambiguity fix over a single satellite (e.g. PRN07)

Simulate an error of 1 cycle in DDN1 for satellite PRN07 and compute the navigation solution: 1 cycle is added to the

DDN1 of satellite PRN07




graph.py -f L1fix.pos -x1 –y2- s.- -l "North error" -f L1fix.pos -x1 –y3 -s.- -l "East error" -f L1fix.pos -x1 –y4 -s.- -l "UP error" --yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "Absolute positioning error with a wrong ambiguity fix"





L1 Differential positioning with a wrong ambiguity fix on a single satellite

Questions:Discuss the results. What is the effect of the wrong fix?











OVERVIEW

94



Session C

Fixing DD ambiguities with LAMBDA method

(baseline: 37.95 metres)



Apply the LAMBDA method to fix the ambiguities.

Consider only the two epochs: t1=18000 and t2=18015.

Note: To avoid the synchronization issues, consider the Differential Positioning using the computed differential corrections, instead of the time-tagged measurements.

That is, we are going to solve the following navigation equations systems:

1. Navigating with L1 carrier, to fix DDN1:[DDL1-DDRho]=[Los_k-Los_06]*dr + [ A ]*[ *DDN1]

2. Navigating with L2 carrier, to fix DDN2:

[DDL2-DDRho]=[Los_k-Los_06]*dr + [ A ]*[ *DDN2]

C Fixing the DDN1 and DDN2 ambiguities with LAMBDA Method

C. Fixing DDN1 and DDN2 ambiguities with LAMBDA

gAG

E/U

PC re

sear

ch g

roup

of A

stro

nom

y an

d G

eom

atic

s

gAGE

Master of Science in GNSS @ J. Sanz & J.M. Juan97

Consider again the previous problem of estimating , a 3-vector of real numbers , and a (K-1)-vector of integers, which are solution of

rN

y G r AN νThe solution comprises the following steps:

1. Obtain the float solution and its covariance matrix:

2. Find the integer vector N which minimizes the cost function

a) Decorrelation: Using the Z transform, the ambiguity search space is re-parametrized to decorrelate the float ambiguities.

b) Integer ambiguities estimation (e.g. by rounding or by using sequential conditional least-squares adjustment, together with a discrete search strategy).

c) Using the Z-1 transform, the ambiguities are transformed to the original ambiguity space.

3. Obtain the ‘fixed’ solution r, from the fixed ambiguities N.

ˆ;ˆ

rN

ˆ ˆˆ ,

ˆ ˆˆ ,

r r N

r N N

P P

P P

1ˆ ˆN NW P

ˆ

2

ˆˆ ˆ ˆ( )

Tc

NNW

N N N N N W N N

y AN G r ν



C1. DDN1 ambiguity fixing: Differential positioning using computed differential corrections from a reference receiver.


The following procedure can be applied:1. Build-up the navigation system.

2. Compute the FLOATED solution, solving the equations system with octave. Assess the accuracy of the floated solution.

3. Apply the LAMBDA method to FIX the ambiguities. Compare the results with the solution obtained by rounding directly the floated solution and by rounding the solution after decorrelation.

C1. Fixing DDN1 ambiguities with LAMBDA




1. Building-up the navigation system

99

[DDL1-DDRho]= [Los_k - Los_06]*[dr] + [ A ]*[lambda1*DDN1]

3 66,03 6,03 6,031 1 16,07 6,07 6,077 61 1 1

6,24 6,24 6,2424 61 1 1

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ

1110 111

11110

Notation

Where the vector of unknowns x includes the user coordinates and ambiguities

y =G x

C1 Fixing the DDN1 ambiguities with LAMBDA Method



gAGE/UPC @ J. Sanz & J.M. Juan 100[DDL1-DDRho]=[Los_k - Los_06]*[dr] + [ A ]*[lambda1*DDN1]

3 66,03 6,03 6,031 11 1 1 1 16,07 6,07 7 61 1 1 11 1

6,24 6,2430 61 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T

t tDDL t DD t DDNDDL t DD t t t

DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

11110

1110000 6,071

6,241 1

DDN

DDN

3 66,03 6,03 6,032 21 2 2 1 16,07 6,07 7 61 2 2 12 2

6,24 6,2430 61 2 2

2 2

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

11110

1110000 6,071

6,241 1

DDN

DDN

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]

The receiver was not moving (static) during the data collection. Thence, for each epoch we have the equations system:




In the previous computation we have not taken into account thecorrelations between the double differences of measurements. Thismatrix will be used now, as the LAMBDA method will be applied toFIX the carrier ambiguities.

a) Show that the covariance matrix of DDL1 is given by Py

2

2 1 11 2 1

2

1 1 1 2

1111

yP

b) Given the measurement vectors (y) and Geometry matrices (G) for two epochsy1:=y[t1] ; G1:=G[t1] ; Pyy2:=y[t2] ; G2:=G[t2] ; Py

show that the user solution and covariance matrix can be computed as:P=inv(G1'*W*G1+G2'*W*G2);

where: W=inv(Py)x=P*(G1'*W*y1+G2'*W*y2) ;

; -1yy = G x W = P

T -1 Tx = (G WG) G WyT -1P = (G WG)





The script MakeL1DifMat.scr builds the equations system

The OUTPUTare the files M1.dat and M2.dat associated with each epoch.

for the two epochs required t1=18000 and t2=18015, using the input file DD_UPC1_UPC2_06_ALL.dat generated before.

[DDL1-DDRho]=[ Los_k- Los_06]*[dr] + [ A ]*[ 1*DDN1]

MakeL1DifMat.scr DD_UPC1_UPC2_06_ALL.dat 18000 18015

Execute:

Where: the columns of files M.dat are the vector y (first column) and Matrix G (next columns)





2. Compute the FLOATED solution (solving the equations system).

The following procedure can be applied

octave

load M1.datload M2.dat

y1=M1(:,1);G1=M1(:,2:12);

y2=M2(:,1);G2=M2(:,2:12);Py=(diag(ones(1,8))+ones(8))*2e-4;W=inv(Py);

P=inv(G1'*W*G1+G2'*W*G2);x=P*(G1'*W*y1+G2'*W*y2);

Solutionx(1:3)'1.4216 -0.6058 0.4035





3. Applying the LAMBDA method to FIX the ambiguities. Compare the results with the solution obtained by rounding the floated solution. The following procedure can be applied (justify the computations done)

octave

c=299792458;f0=10.23e+6;f1=154*f0;lambda1=c/f1a=x(4:11)/lambda1;Q=P(4:11,4:11); [Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);

[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 3.10696822814451afixed(:,1)'2 1 2 -1 4 7 1 4

round(a)'0 6 -6 6 6 -1 8 9

1. Rounding directly the floated solution

3.- Decorrelation and integer LS search solution

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);afix=iZ*round(az);2 1 2 -1 4 7 1 4

2.- Rounding the decorrelated floated solution





Questions: 1. Can the ambiguities be well fixed?2. Is the test resolutive?3. Compare the fixed ambiguities with those obtained

in the previous exercises when fixing the ambiguities one at a time. Are the same results found?

4. What is the elapsed time to needed fix the ambiguities? And in the previous exercise when fixing the ambiguities one at a time?

5. The values found for the ambiguities are the same than in the previous case?





C2 Checking the Z-transform matrix

C2. Checking the Z-transform Matrix

a. Using the Octave/MATLAB program sentence imagesc display the covariance matrix of ambiguities before and after the decorrelation with the Z-matrix.

imagesc(Q) imagesc(Qz)





b.- Show the content of the integer matrix Z

Note: The previous routines computes its transpose (Zt). Then: Z=Zt'.

Z =Zt’3 -5 -4 -5 6 7 4 -23 2 -7 -6 -5 -4 9 3

-4 -0 -5 8 3 -4 1 -31 -5 1 -8 4 -1 1 8

-0 1 2 7 -1 -8 -4 38 -3 -1 4 2 -6 -1 4

-5 -1 1 -6 1 0 1 4-5 -3 -0 -0 5 -2 -1 3





c.- Compute by hand the transformed covariance matrix Qz:

d.- Compute the decorrelated ambiguities az:

Z * Q * Z'

Z*a67.19877600816902

-27.00815309344809-52.8079252234807449.18410614456196

-53.87737144457776-11.7073003521210018.080818807498264.09968790147667





e.- Round-off the decorrelated ambiguities:

f.- Apply the inverse transform to these values:

g. - Compare the previous results with the direct rounding of initial ambiguities “a”:

Nz=round(Z*a)

67 -27 -53 49 -54 -12 18 4

format short

inv(Z)*Nz2.00000 1.00000 2.00000 -1.00000 4.00000 7.00000 1.00000 4.00000

round(a)

0 -6 6 6 -1 12 8 9



C3. DDN2 ambiguity fixing: Differential positioning using computed differential corrections from a reference receiver.


The following procedure can be applied, as in the previous case:1. Build-up the navigation system.







1. Building-up the navigation system

111


3 66,03 6,03 6,032 2 26,07 6,07 6,077 62 2 2

6,24 6,24 6,2424 62 2 2

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ

2220 222

22220

Notation


y =G x





3 66,03 6,03 6,031 12 1 1 2 26,07 6,07 7 62 1 1 21 1

6,24 6,2430 62 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

22220

2220000 6,072

6,242 2

DDN

DDN

3 66,03 6,03 6,032 22 2 2 2 26,07 6,07 7 62 2 2 22 2

6,24 6,2430 62 2 2

2 2

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

22220

2220000 6,072

6,242 2

DDN

DDN

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]





In the previous sessions A and B we have not taken into account thecorrelations between the double differences of measurements. Thismatrix will be used now, as the LAMBDA method will be applied toFIX the carrier ambiguities.


2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P










MakeL2DifMat.scr DD_UPC1_UPC2_06_ALL.dat 18000 18015Execute:






2. Computing the FLOATED solution (solving the equations system).


octave


y1=M1(:,1);G1=M1(:,2:12);



Solutionx(1:3)'

0.1442 -0.5154 0.5568






octave


[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 3.54056715815950afixed(:,1)'-1 1 -1 2 2 -1 1 0

round(a)'-1 -2 1 2 1 -2 3 -1



[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);afix=iZ*round(az);-1 1 -1 2 2 -1 1 0














C4. Estimate the baseline vector between UPC1 and UPC2 receivers using the L1 carrier measurements of file (DD_UPC1_UPC2_06_ALL.dat).

Consider only the two epochs used in the previous exercise: t1=14500 and t2=14515

C4. Baseline vector estimation with DDL1

C4. UPC1-UPC2 Baseline vector estimation with L1 carrier(using the time-tagged reference station measurements)






C4.1 Estimate the baseline vector between UPC1 and UPC2 receivers using the L1 carrier measurements of file (DD_UPC1_UPC2_06_ALL.dat).

119

[DDL1]= [Los_k - Los_06]*[baseline] + [ A ]*[lambda1*DDN1]

3 66,03 6,031 1 16,07 6,077 61 1 1

6,24 6,2424 61 1 1

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

T

T

T

DDL DDNDDL DDN

DDL DDN

ρ ρ

ρ ρ r

ρ ρ

1110 111

11110

Notation (for each epoch t)


y =G x




gAGE/UPC @ J. Sanz & J.M. Juan 120[DDL1]=[Los_k - Los_06]*[baseline] + [ A ]*[lambda1*DDN1]

3 66,03 6,031 11 1 1 16,07 6,077 61 1 1 11 1

6,24 6,2424 61 1 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

T

T

T

t tDDL t DDNDDL t DDNt t

DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

1110 111

11110

3 66,03 6,032 21 2 1 16,07 6,077 61 2 1 12 2

6,24 6,2424 61 2 1 1

2 2

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

T

T

T


DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

1110 111

11110

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]

The receiver was not moving (static) during the data collection. Therefore, for each epoch we have the equations system:



gAGE/UPC @ J. Sanz & J.M. JuanC4. Baseline vector estimation with DDL1 121



2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P





The script MakeL1BslMat.scr builds the equations system



[DDL1]=[ Los_k- Los_06]*[baseline] + [ A ]*[ 1*DDN1]

MakeL1BslMat.scr DD_UPC1_UPC2_06_ALL.dat 18000 18015Execute:








octave


y1=M1(:,1);G1=M1(:,2:12);



x(1:3)'-24.5735 -27.1121 3.0021bsl_enu =[-27.4170 -26.2341 -0.0304]

x(1:3)'-bsl_enuans= 2.84348 -0.87798 3.03248






octave


[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 1.22717645070483afixed(:,1)'-1 -12 18 2 -4 8 9 4

round(a)'-4 -20 13 11 -14 19 10 16



[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);afix=iZ*round(az);-1 -12 18 2 -4 8 9 4














C5. Estimate the baseline vector between UPC1 and UPC2 receivers using the L2 carrier measurements of file (DD_UPC1_UPC2_06_ALL.dat).









C5.1 Estimate the baseline vector between UPC1 and UPC2 receivers using the L2 carrier measurements of file (DD_UPC1_UPC2_06_ALL.dat).

127


3 66,03 6,032 2 26,07 6,077 62 2 2

6,24 6,2424 62 2 2

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

T

T

T

DDL DDNDDL DDN

DDL DDN

ρ ρ

ρ ρ r

ρ ρ

2220 222

22220



y =G x





3 66,03 6,031 12 1 2 26,07 6,077 62 1 2 21 1

6,24 6,2424 62 1 2 2

1 1

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

T

T

T


DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

2220 222

22220

3 66,03 6,032 22 2 2 26,07 6,077 62 2 2 22 2

6,24 6,2424 62 2 2 2

2 2

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

T

T

T


DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

2220 222

22220

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]




gAGE/UPC @ J. Sanz & J.M. JuanC5. Baseline vector estimation with DDL2 129



2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P









MakeL2BslMat.scr DD_UPC1_UPC2_06_ALL.dat 18000 18015

Execute:








octave


y1=M1(:,1);G1=M1(:,2:12);



x(1:3)'-25.85097 -27.02162 3.15538 bsl_enu =[-27.4170 -26.2341 -0.0304]

x(1:3)'-bsl_enuans= 1.5660 -0.7875 3.18578






octave


[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 1.00508811343751afixed(:,1)'-3 7 -6 13 -3 19 -3 24

round(a)'-5 -13 6 7 -9 4 4 4



[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);afix=iZ*round(az);3 2 9 -27 13 -32 -13 -35

















• To the University of Delft for the MATLAB files of LAMBDA method.• To Adrià Rovira-Garcia for his contribution to the editing of this material

and gLAB updating and integrating this learning material into the GLUE.

The ESA/UPC GNSS-Lab Tool suite (gLAB) has been developed under theESA Education Office contract N. P1081434.

Acknowledgements



Tutorial 5Analysis of propagation effects from

GNSS observables based on laboratory exercises







These slides can be obtained either from the server http://www.gage.upc.edu,or [email protected]. Any partial reproduction should be previously authorized by the authors, clearly referring to the slides used.


2



IntroductionThe gLAB tool suiteExamples of GNSS Data Processing using gLABLaboratory session organization

LABORATORY SessionStarting up your laptopBasic: Introductory lab exercises: Iono & Posit, SF, storm,TIDs

Medium: Laboratory Work Projects: LWP1 to LWP4Advanced: Homework

OVERVIEW

3



This tutorial is devoted to analysing and assessing different issues associated with GNSS signal propagation effects in the atmosphere. The laboratory exercises will be developed with actual GPS measurements, and processed with the ESA/UPC GNSS-Lab Tool suite (gLAB), which is an interactive software package for GNSS data processing and analysis. All software tools (including gLAB) and associated files for the laboratory session are included in the USB stick delivered to those who attend the lecture.The laboratory session will consist of a set of exercises organized in three different levels of difficulty (Basic, Medium and Advanced). A set of introductory examples range from a first glance assessment of the ionosphere effects on single frequency positioning, and Zenith Tropospheric Delays estimate to showing different perturbation effects in the ionosphere (Solar Flair, Halloween storm, TIDs). Electron density profiles (Ne) retrieval, bending effects analysis (phase excess rate depicture), as well as in-depth analysis of the code-carrier ionosphere divergence on single-frequency smoothed codes and the second order ionospheric effects are analysed in detail in four Laboratory Work Projects. Other topics are given as homework.The target is to provide the participants with a wide range of selected exercises to choose from, according their interests and their level of knowledge of these topics.

Introduction



IntroductionThe gLAB tool suiteExamples of GNSS Data Processing using gLABLaboratory session organization



OVERVIEW

5



gLAB has been developed under the ESA Education Office contract N. P1081434.

The gLAB Tool suite

Main features:• High Accuracy Positioning

capability.• Fully configurable.• Easy to use.• Access to internal computations.

The GNSS-Lab Tool suite (gLAB) is an interactive multipurpose educational and professional package for GNSS Data Processing and Analysis.



Students/Newcomers:• Easy to use: Intuitive GUI.• Explanations: Tooltips over the different GUI options.• Guidelines: Several error and warning messages.

Templates for pre-configured processing.

Professionals/Experts:• Powerful tool with High Accuracy Positioning capability.• Fast to configure and use: Templates and carefully chosen defaults.• Can be executed in command-line and included in batch processing.

The gLAB Tool suite



In order to widen the tool availability, gLAB Software has been designed to work in both Windows and Linux environments.

The package contains:• Windows binaries (with an installable file).• Linux .tgz file.• Source code (to compile it in both Linux and Windows OS)

under an Apache 2.0 license.• Example data files.• Software User Manual.• HTML files describing the standard formats.

hh group o

gA

The gLAB Tool suite



Modelling module:• Fully configurable model.• Satellite positions.• Satellite clock error correction.• Satellite movement during signal flight

time.• Earth rotation during signal flight time.• Satellite phase center correction.• Receiver phase center correction.

(frequency dependent).• Relativistic clock correction.• Relativistic path range correction.• Ionospheric correction (Klobuchar).• Tropospheric correction

- Simple and Niell mappings.- Simple and UNB-3 nominals.

• Differential Code Bias corrections.• Wind up correction.• Solid tides correction (up to 2nd

degree).

9

Read files capability:• RINEX observation v2.11 & v3.00• RINEX navigation message.• SP3 precise satellite clocks and orbits files• ANTEX Antenna information files.• Constellation status.• DCBs files.• GPS_Receiver_Type files.• SINEX position files.

Pre-processing module:• Carrier-phase pre-alignment.• Carrier-phase / pseudo-range consistency

check.• Cycle-slip detection (customizable parameters)

- Melbourne-Wübbena.- Geometry-free CP combination.- L1-C1 difference (single frequency).

• Pseudo-range smoothing.• Decimation capability.• On demand satellite enable/disable.• Elevation mask.• Frequency selection.• Discard eclipsed satellites.

The gLAB Tool suite

Backup



Filtering module:

• Able to chose different measurements to process (1 or more), with different weights. This design could be useful in future Galileo processing, where processing with different measurements may be desired.

• Fixed or elevation-dependent weights per observation.

• Troposphere estimation on/off.• Carrier-Phase or Pseudo-range

positioning.• Static/Kinematic positioning (full

Q/Phi/P0 customization).• Able to do a forward/backward

processing.• Able to compute trajectories (no need

for a priori position).

Output module:• Cartesian / NEU coordinates.• Configurable message output.

Other functionalities:• Computation of satellite coordinates

and clocks from RINEX and SP3 files.• Satellite coordinates comparison

mode. For instance RINEX navigation vs. SP3, or SP3 vs. SP3 (along-track, cross-track and radial orbit errors, clock errors, SISRE).

• Show input mode. No processing, only parsing RINEX observation files.

• Current version allows full GPS data processing, and partial handling of Galileo and GLONASS data.

• Future updates may include full GNSS data processing.

The gLAB Tool suite

Backup



GNSS learning material package

• GNSS Book: Complete book with theory, practical examples, and with a Laboratory course on GNSS Data Processing & Analysis [R-1].

• gLAB tool suite: Source code and binary software files, plus configuration files, allowing processing GNSS data from standard formats. The options are fully configurable through a GUI.

• gAGE-GLUE: Bootable USB stick with a full environment ready to use; based on LINUX (Ubuntu) OS.

Image courtesy of USAF Research Laboratory

GPS Data Processing: Code and PhaseAlgorithms, Techniques and Recipes

Research group of Astronomy & GeomaticsSatellite Navigation, LLC

http://www.gage.es

gAGE-NAV Manuel Hernández PajaresJosé Miguel Juan Zornoza

Jaume Sanz Subirana

11

Includes three different parts, allowing participants to follow either a guided or a self-learning GNSS course:



IntroductionThe gLAB tool suiteExamples of GNSS processing using gLABLaboratory session organization



OVERVIEW

12



Example 1: Ionospheric effects on single frequency positioning.

• This exercise is devoted to analysing the effect of the ionospheric error in single frequency positioning. This is done both in the Signal-In-Space (SIS) and User Domains.

• A receiver will be positioned in Standard Point Positioning (SPP) mode: a) with full modelling, b) neglecting the ionospheric correction.

13

Examples of GNSS Data Processing using gLAB



May 4, 2000

Data set: 24h data collected by the IGS permanent receiver “ramo” (Lon,Lat ) on May 4th 2000.

Example 1: Iono effects on single freq. Posit.

14



1. Compute SPP using files: ramo1250.00o,brdc1250.00n

15

1

2

3

4

5gLAB.out

ecTechn caical U eUnive yyys yrsity oof Ca aCatalo aoniaRR


Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_Full.cfg -input:obs ramo1250.00o -input:nav brdc1250.00n




Example 1. NEU Position Error plot from gLAB.out

North East Up

FULL SPP model


Equivalent command line sentence:

graph.py -f gLAB.out -x4 -y18 -s.- -c '($1=="OUTPUT")' -l "North error" -f gLAB.out -x4 -y19 -s.- -c '($1=="OUTPUT")' -l "East error"

-f gLAB.out -x4 -y20 -s.- -c '($1=="OUTPUT")' -l "UP error“ --yn -20 --yx 50 --xl "time (s)" --yl "error (m)" -t "NEU positioning error [SPP]: Full model"

gLAB.out



The different model terms can be analyzed with gLAB:

•Using the previous data file, the impact of neglecting the ionospheric correction is evaluated in the Range and Position domains.

•This is a baseline example of this analysis procedure. The same scheme must be applied for all model terms (troposphere, relativistic correction...). A full analysis of the different model components can be found in [R-2].)

The modeling options set in this panel are applied by default to the

SPP solution.

17

Example 1. gLAB Modeling panel



Example 1. Model component analysis: IONO.

Default configuration

for SPP

In the Default configuration the

output file was gLAB.out

icsics

C

Set output file as

gLAB1.out

z &

Disable Ionosphericcorrection

The procedure explained here is applicable for all model terms: iono, tropo…1.In Modeling panel, disable the model component to analyze.

(in this example: disable

Ionospheric correction)

2.Save as gLAB1.out the associated output file.Notice that the gLAB.outfile contains the processing results with the FULLmodel, as was set in the default configuration.

1

2

3Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_NoIono.cfg -input:obs ramo1250.00o -input:nav brdc1250.00n

18



Example 1. NEU Position Error plot from gLAB1.out

North East Up

No Iono. correction


Equivalent command line sentence:

graph.py -f gLAB1.out -x4 -y18 -s.- -c '($1=="OUTPUT")' -l "North error" -f gLAB1.out -x4 -y19 -s.- -c '($1=="OUTPUT")' -l "East error"

-f gLAB1.out -x4 -y20 -s.- -c '($1=="OUTPUT")' -l "UP error“ --yn -20 --yx 50 --xl "time (s)" --yl "error (m)" -t "NEU positioning error [SPP]: No Iono. Corr."

gLAB1.out



gLAB1.out gLAB.out Time (sec) Vertical

Y-min, Y-max

Example 1. VPE plot from gLAB.out,gLAB1.out


2 3



Example 1. HPE plot: gLAB.out, gLAB1.out

gLAB.out East: 19North: 18

X-min, Y-min, Y-max


2 3gLAB1.out



Example 1. Klobuchar iono. corr. plot: gLAB.out

gLAB.out SelectIONO


Code delay

Ionosphere delays code and advances carrier measurements.

Carrier advance


gAGE/UPC @ J. Sanz & J.M. Juan@@@@@@@@@@@@@@@@ JJJ... SanSannSannnnnnnzzz &&&&&&&&&&&&&&&& JJJJJJJJJJJJJJJJJJJJJJJJJJ...MMMMMMMMMMMMMMMM... JuaJuaaJuaaaaaaaaJJJJJJ nnn 23

Example 1. Measur. (P2-P1) v.s. Model (Klobuchar)

gLAB.out

Y-min=0 Y-max=40

P2-P1=STEC+Krec+Ksat



Example 1. Summary: Klobuchar model performance

gLAB.out

gLAB1.out

gLAB.out

Code delay

gLAB.out

gLAB1.out

Ionospheric correction (broadcast Klobuchar )Ionospheric delays are larger at noon due to the higher illumination. Large positioning errors (mainly in vertical) appear when neglecting ionosphericcorrections.



From previous configuration set following options

25

Disable Iono correct.

and (P1-P2) TGDs

1Iono-free (PC)

2-frequencies

2

3After running gLAB, plot results as in previous cases

Equivalent command line sentence:gLAB_linux -input:cfg gLAB_pc_IFree.cfg -input:obs ramo1250.00o -input:nav brdc1250.00n

gLAB2.out

Example 1. 2-frequency Ionosphere-free solution

25



2-freq.: Iono-free


ramo station location

Plot gLAB2.out results as in previous cases

May 4, 2000

gLAB.out gLAB.out

gLAB2.out gLAB2.out

Example 1. Single-frequency vs. Dual-frequency





• Two-frequency receivers can remove this error source (up to 99.9%) using ionosphere-free combination of pseudo-ranges (PC) or carriers (LC).

• Single-frequency users can remove about a 50-70% of the ionospheric delay using the Klobuchar model, whose parameters are broadcast in the GPS navigation message.

27

eSTEC N ds

2 21 2

2 21 2

1 2f P f PPCf f

1I

Ionospheric delayThe ionosphere extends from about 60 km over the Earth’s surface until more than 2000 km, with a sharp electron density maximum at around 350 km. The ionospheric refraction depends, among other things, on the location, local time and solar cycle (11 years).

Backup

240.31I STECf




Annex: gLAB processing in command line




Execute in a single line: (gnuplot can also be used )



graph.py -f gLAB.out -x4 -y25 -s. -c '($1=="MODEL")' -f gLAB.out -x4 -y'($10-$9)' -s. -c '($1=="INPUT")‘ --cl r --xl "time (s)" --yl "meters" --yn -0 --yx 40 -t "Ionospheric Combination"


Example 1: gLAB processing in command line

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ........... SanSannSanSanSanSanSaSanaSanSanaaaaSanSanSanSanSanSananSannnSanaSanaanaaaaaSanSanSSSSSanSanSanSannaaaaSaSSSSSannSanaaSaaSSSSSanSanSanSannaanaaSSSSaSSSSSSannnaaanSSSSSanSSaSSSSSSaSannanSSSSSannSanaannaSaSannanannaSSSSSSS naSSSSaSaS nnaaSSSaSanaaSSaaSaSSSSSSS zzzzz &&& JJJ.MMM. uaJuaJuaJuaJuauaaaJuaJuauauauuuauJuauuJuuaJuaaJuaaaJuauuuJuauauauJuuJuauaauuJuuuauaaaaaJuauuuauauuJuuaaauaaaaauauauuJuuuuuuaauaaaaaaJuauuuuuaaauaauuuuJuJuaJuaJuaJ auuJJuauauauJuaJJJuaaaauuJJJuJuaaaaauuJJJ aaJJJJJJJJJ nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 22929292929299292929292929999292922229999299929222999992999929222222999999292222292999999929299292999922229292922229999999299999922222222222999999292999292929222929292999299292929292929929992929292992999999929292929929292929299229999999929292992222229999999992922222229999929222222299222299922922292929299222299999922222999999292929922999992222222229222222929292922992922229229922222 29




sentences


A “notepad”with the



“ paste” from


terminal.





Backup






Example 2: Depict the ionospheric delays for the different satellites in view from station amc2

• This is a simple exercise aimed to illustrate how to use gLAB to easily analyze GNSS measurements and their combinations.

• gLAB will used to read the RINEX measurements file and to generate a “text” with the measurements provided in a columnar format (more suitable to make plots).

Example 2: Ionospheric delay analysis

• From “text” file, compute and plot the Ionosphericdelay for a given satellite, by using code and carrier measurements at f1, f2:

2 1 21

1 2

I

I


1 1 1

2 2 2

2 12 2

P L I ambiguityP L I ambiguity

32




The target is to generate this plot to depict the

ionospheric delay from code & carrier data

2 1 21

1 2

I

I



1 2 121

2 221 1 2

1 1.546 ; 11

/ (154 /120)f f


Carrier Phase L1-L2 (ambiguous but precise)

Code P2-P1 (unambiguous but noisier)

Ambiguity= P L

Iono

sphe

ric c

ombi

natio

n (m

eter

s)



Example2: GPS measurements content

1 1 21 1

2 2 21 2

P I K

P I K1 1 1 1

2 2 2 2

L I BL I B

, is in sat

erecSTEC N dl STEC TECUs

16 21 10 / 0.10 of 1- 2 delayTECU e m m L L

2 21 2 16

1 22 21 2

40.310 ; ( is in of delay)

f fI STEC I m L L

f f

21 21, 21sat

recK K K

As the satellite clocks are referred to the ionosphere-free combination of codes (PC), the cancels in such combination. Note: is broadcast in GPS nav. Message.1 21

satTGD K

Refers to all non dispersive terms: geometric range, clocks, tropo. delay… (see [R-1]).

Ionospheric delay

Interfrequency bias21satK 2 2

1 1 2 22 2

1 2C

f P f PPf f

i i i iB N bCarrier ambiguities

Ni is an integer number. bi is a real number (fractional part of ambiguity)

2 1

121

221 1 2

11 1.546

1

/f f

Code measurement content Carrier measurement content

Backup



1.- Read RINEX file with gLAB and generate a “measurements file” in a columnar format (the easiest to manipulate and plot content):

Using the configuration file meas.cfg, READ the RINEX and generate the MEAS file:

35

[Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 xx xx 14 15 16 ]



-pre:dec 1 -print:none -print:meas

--model:satphasecenter --model:recphasecenter --model:satclocks --pre:cs:li --pre:cs:bw

gLAB configuration fileRINEX

Measurementfile

RINEX Navigation

file

OUTPUT: measurement file in columnar format



2.- Manipulate the file with the easy & powerful awk (or gawk) programming language (to compute the combinations of measurements):

From coco.meas file:

Compute different ionospheric combination of codes and carriers, and generate the obs.txt file containing the fields: [PRN,sec, P2-P1, (P2-L2)/5.09, (P1-L1)/3.09, L1-L2, Elev/10]

36

gawk '{print $6,$4,$15-$11,($15-$16)/5.09,($11-$14)/3.09,$14-$16,$7/10}' coco.meas > obs.txt


PRN#6

sec#4

(P2-P1)

#15 -- #11

(P2-L2)/5.09

#15 -- #16

(P1-L1)/3.09

#11-- #14

(L1-L2)

#14 -- #16

Elev/10#7

P1 L1 P2 L2 ] [Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 xx xx 14 15 16



3.-Plot results with “graph.py” (you can use the gnuplot as well)

From obs.txt file:

Show in the same plot the following iono. delays for satellite PRN01: P2-P1, (P2-L2)/5.09, (P1-L1)/3.09, L1-L2, Elev./10

37

graph.py -f obs.txt -c'($1==01)' -x2 -y3 --l "P2-P1" -f obs.txt -c'($1==01)' -x2 –y4 --l "(P2-L2)/5.09" -f obs.txt -c'($1==01)' -x2 -y5 --l "(P1-L1)/3.09" -f obs.txt -c'($1==01)' -x2 –y6 --l "L1-L2" -f obs.txt -c'($1==01)' -x2 –y7 --l "Elev/10" --yn -10 --yx 15 --xl "time (s)" --yl "meters of L1-L2 delay"


[PRN, sec, P2-P1, (P2-L2)/5.09, (P1-L1)/3.09, L1-L2, Elev/10] 1 2 3 4 5 6 7

File to plot

Condition:Select PRN01

(from 1-st field)

Fields to plot:#2 (x-axis)

versus#3 (y-axis)

Label:P2-P1




zoom

2 1 21

1 2

I

I



1 2 121

2 221 1 2

1 1.546 ; 11

/ (154 /120)f f




cocoPRN01

Sky plots at different latitudes

Example 2: Sky plots

=90º

=40º

=0º





-Measurement : roap1810.09o - ANTEX: igs05_1525.atx - Orbits & clocks: igs15382.sp3 - SINEX: igs09P1538.snx

3. RUN gLAB

Default output file:gLAB.out1

2

3

Example 3: Zenith Troposphere Delay estimation

40



Plotting Results• Coordinates are taken as

constants in nav. filter.• Dual frequency Code and

Carrier measurements.• Precise orbits and clocks.• Measurements modellingat the centimetrelevel.

Centimetre level accuracyover 24h data is achieved

in PPP static mode


41




The ZTD in this file is given in mm of delay. Thus, it is converted to m to compare with gLAB resultsgrep ROAP roap1810.09zpd | gawk -F\: '{print $3} ' | gawk '{print $1,$2/1000}' > roap_igs.trp

ftp://cddis.gsfc.nasa.gov/pub/gps/products/troposphere/new/2009/181/roap1810.09zpd.gz

1 2

The troposphere is estimated as a Random Walk process in the Kalman Filter. A process noise of 1cm/sqrt(h) has been taken.

42



Tropospheric delayThe troposphere is the atmospheric layer situated between the Earth’s surface and an

altitude of about 50 km. The effect of the troposphere on GNSS signals appears as an extra delay in the

measurement of the signal travelling from satellite to receiver.

The tropospheric delay does not depend on frequency and affects both the pseudo-range (code) and carrier phases in the same way. It can be modeled by:

• A hydrostatic component, composed of dry gases (mainly nitrogen and oxygen) in hydrostatic equilibrium. This component can be treated as an ideal gas. Its effects vary with the temperature and atmospheric pressure in a reasonably predictable manner, and it is responsible for about 90% of the delay.

• A wet component caused by the water vapor condensed in the form of clouds. It depends on the weather conditions and varies faster than the hydrostatic component and in a totally random way. For high accuracy positioning, this component must be estimated together with the coordinates and other parameters in the navigation filter.

Backup


43






OVERVIEW

44



The laboratory session is organized as an assisted activity where a set of exercises must be developed individually or in groups of two.

As they are conceived as self-learning work, a detailed guide is provided in the slides (pdf file) to carry out the exercises.

A notepad file with the command line instructions is also provided to help the sentence writing (doing copy & paste).

A set of questions is presented, and the answers are also included in the slides.Teachers will attend individual (or collective) questions that could arise during exercise resolution.


45



The exercises are organized at three different levels of difficulty.The student can choose the level of exercises to do, although at least one introductory exercise is recommended to learn basic gLAB usage.

1. Basic: Introductory exercises. From 1 to 6.They consist of simple exercises to: 1) Study the Ionosphere effects on single frequency positioning. 2) To depict the STEC on a Radio occulation 3) Solar Flare effect on TEC, 4,5) TEC evolution during the Halloween Storm, 6) To depict a TID propagaction.


G Pa

46



G Pa

A minimum knowledge of UNIX (e.g., awk) would be desirable

2. Medium: Laboratory Work Projects (LWP).

Four different LWP are proposed (to choose from):

• LWP1: To show a simple numerical method to estimate electron density profiles (Ne(h)) from RO data.

• LWP2: To analyse the phase excess rate from GPS to LEO due to atmospheric (ionosphere & troposphere) bending.


G Pa

Ne

LWP1 LWP2

Actual measurements from FORMOSAT-3/COSMIC

LEOs will be used

aa

47



A minimum knowledge of UNIX (e.g., awk) would be desirable

Given that session time is limited to 3h, students who feel comfortable using gLAB, can

skip part of the previous basic exercises (Ex1, Ex2,.. ) and

jump to the Lab. Work Project.

2. Medium: Laboratory Work Projects (LWP).

Four different LWP are proposed (to choose from):

• LWP3: To study the code-carrier ionosphere divergence effect on single-frequency carrier smoother code.

• LWP4: To analyse if second-order ionospheric effects can be depicted from three-frequency GNSS measurements.


f f

48



3 . Advanced: Labeled as “Homework exercises”

A set of additional exercises addressed to those students that already have a solid background in GPS data processing.These exercises are beyond the scope of this 3h laboratory session, and are given for a possible further discussion…As in the previous cases, the answers to the questions are also included as BACKUP slides.

gawk 'BEGIN{g=(77/60)^2}{print $6, $4, (g*($13-$14)-($15-$16))/(g-1)}' meas.txt > PC.txt

A minimum knowledge of UNIX (e.g., awk) is desirable for these homework exercises.


APC correction term

sinUPk k k k

k kL bias

01 3 3

1 1

7427 cos72572 cos2 2

sat

L erec

cBcI N B ds STECf f

49






OVERVIEW

50



1. Plug the stick into an USB port and boot your laptop from the stick.

2. Access the Boot Device Menu when starting up the laptop.

Note: The way to do it depends on your computer:Usually, you should press [ESC] or [F4], [F10], [F12]....

hh group o

gA

Starting up your laptop



3. The following screen will appear after about 2 minutes:

52

The US keyboard is set by default.

You can change it by clicking on the upper right corner.

Click on the gLAB icon to start-up gLAB

Click on this icon to open a console




Now, the system is ready to

start working!


sentences




Copy and paste the sentences

from notepad

to consoleConsole to execute “command line”

sentences





LABORATORY SessionStarting up your laptopBasic: Introductory lab exercises: Iono & Posit, Solar Flair, Halloween storm,TIDs


OVERVIEW

55



A severe ionospheric storm was experienced on October 29-31,2003 producing and increase of the electron density which led to large ionospheric refraction values on the GPS signals. Such conditions were beyond the capability of the GPS Klobuchar model broadcast for single frequency users, producing large errors in the SPS (see details in [R-3]).

56

EX. 1 Halloween storm: October 2003

Dual frequency users, navigating with the ionospheric-free combination of GPS signals were not affected by such ionospheric errors, as the ionospheric refraction can be removed up to 99:9% using dual-frequency signals.

.

Backup



Exercise: Repeat the previous study of Example 1 to analyze the single freq. solution, but for the Halloween storm.

The following steps are recommended:1. Using files amc23020.03o,brdc3030.03n compute with gLAB

the following solutions:1. Solution with full SPS modeling. Name output file as: gLAB.out2. Solution with the ionospheric corrections disabled gLAB1.out3. Solution with the 2-freq. Ionosphere-free code (PC) gLAB2.out

2. Plot results

57

Ex. 1: Assessing Iono effects on single freq. pos.

Note: The gLAB GUI or the command line sentences can also be used . A “notepad” with the command line sentence is provided to facilitate the sentence writing: just “copy” and “paste” from notepad to the working terminal



1. Compute SPP using files: amc23020.03o,brdc3030.03n

1

2

3

Technical Unive yyrsity of CataloniaRR


Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_Full.cfg -input:obs amc3030.03o -input:nav brdc3030.03n

By default, the output file name is gLAB.out

Ex. 1: Full processing gLAB.out



Ex. 1: Iono. Disabled gLAB1.out

Change output file name to gLAB1.out

Disable Ionospheric corrections

31

2

2. Reprocess the same files, with the iono. corrections disabled

ecTechn caical U eUnive yyys yrsity oof Ca aCatalo aoniaRR


Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_NoIono.cfg -input:obs amc3030.03o -input:nav brdc3030.03n


gAGE/UPC @ J. Sanz & J.M. Juan 60@@@@@@@@@ JJJ... SanSanSanzz & J.M. JuaJuaJuaJ nnn 60

3. Reprocess the same files, but with 2-frequency ionosphere-free (PC)

Ex. 1: Processing with PC gLAB2.out

Disable Ionospheric corrections and P1-

P2 corrections

1Select Dual Frequency

2

Change output file name to gLAB2.out 3

4Technical Unive yyrsity of Catalonia

RRRTechnTechnicalicalTechnical UniveUniversityrsityUniversity ofofof CatalCataloniaoniaCatalonia

Equivalent command line sentence:gLAB_linux -input:cfg gLAB_p1_IFree.cfg -input:obs amc3030.03o -input:nav brdc3030.03n

60




61

Execute in a single line: (or use the gLAB GUI)



graph.py -f gLAB.out -x4 -y'($10-$9+4)' -s. -c '($1=="INPUT")' -f gLAB.out -x4 -y25 -s. -c '($1=="MODEL")' --cl r --xl "time (s)" --yl "meters" --yn -5 --yx 80 -t "Ionospheric Combination"

@@@@@ JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ... nnSannSananSaaaaSaSaSSSSannnSaSSanSanSSSanSSSSSanSSanSSSSanSSaSSaSSSanSSSaSSanSanSannSannSananSannnSanSaanSaSSSannSanSanSSaanSaSSaaSanSSSSSS nnnSaaanSSSSSS nnSanSSaanaaaaSSSSSanSannnnnanaaaaaSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS zzzzzzzzzzzzzzzzzzzzzzzzzzzz &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ..................MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM..... JuauJuaJuaJuaJuaJuaJuaJuaJuJuJuJ aJJ n 616161616161616161616161616161616161616161661616161661616166161666166611111161111111111116

P2-P1 shifted +4 m

r


61



gLAB.out

gLAB1.out

gLAB.out

Code delay

gLAB.out

gLAB1.out

Ionospheric correction (broadcast Klobuchar )Ionospheric delays are larger at noon due to the higher insulation. Klobuchar model is unable to mitigate the large ionospheric errors during the storm. Position domain errors reach up to 40 meters with Klobuchar corrections used.




2-freq.: Iono-free



October 30, 2003

Ionospheric correction(broadcast Klobuchar )•The ionosphere-free combination (PC) of P1 and P2 codes is immune to the ionospheric storm. • Although PC is three-times noisier than P1 or P2, it provides positioning accurate at the level of a few meters during the storm.


2 21 1 2 2

2 21 2

Cf P f PP

f f



Radio Occultation (RO) commonly refers to a sounding technique in which a radio signal from a transmitting satellite (e.g., GPS) passes through a planetary atmosphere before arriving at a receiver on board a Low Earth Orbiter (LEO) satellite.

Along the ray path, the phase of the radio signal is perturbed in a manner related to the refractivity.RO measurements can reveal the refractivity, from which one can then derive atmospheric quantities such as Pressure, Temperature and the partial pressure of water vapor; and electron density, among others.

Ex. 2: STEC in a Radio Occultation (RO)

This is a simple exercise where the STEC variation along a radio occultation will be depicted using GPS L1, L2 measurements from a receiver on board a LEO of COSMIC constellation.

In the LWP1, Electron Density Profiles will be retrieved from this data using an algorithm equivalent to the Abel Transform.

G Pa

64



FORMOSAT-3/COSMIC mission

65

Constellation Observing System for Meteorology Ionosphere and Climate: 6 microsatellites; orbit altitude ~ 800km

• Three instruments:GPS receiver. 4 antennas: 2 for POD, 2 for RO. TIP, Tri-band beacon

• Weather + Space Weather data. Global observations of:

Pressure, Temperature, HumidityRefractivityIonospheric Electron DensityIonospheric Scintillation

• Demonstrate quasi-operational GPS limb sounding with global coverage in near-real time

• Climate Monitoring Information available at www.cosmic.ucar.edu



Exercise: The file “RO.obs” contains the following fields [*]: | ------ LEO ------>|<------- GPS ------->| YY DoY HH.HH CODE PRN elev r_LEO AR_LEO DEC_LEO r_GPS AR_GPS DEC_GPS L1 L2 L1-L2 arc (deg) (km) (Deg) (Deg) (km) (Deg) (Deg) (cycles) (m) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Plot the L1-L2 measurement in function of time to depict the variation of STEC along the occultation: Select for instance : PRN=02 and “CODE=l241”, that corresponds to LEO=4 and Antenna 1 - Selecting: CODE=l241 and PRN=02 grep l241 RO.obs|gawk '{if ($5==02) print $3,$15}'> ro.dat - Ploting L1-L2 graph.py -f ro.dat --xl "time (H)" --yl "meters of L1-L2" -t"RO: L1-L2: COSMIC #4 Antenna #1"


p

[*] This file has been generated from files (http://cosmic-io.cosmic.ucar.edu/cdaac): podObs_2006.253.004.01.01_rnx, leoOrb_2006.253.004.01_2009.2650_sp3, igs13920.sp3



The previous plot shows only the variation of the Integrated Electron Content along the ray path (STEC).

More information can be retrieved from occultation measurements. For instance:

• Electron Density Profile of the Ionosphere (LWP1).

• Phase excess rate, which is related to the bending of ray (LWP2).

G Pa

NeG P

a




Given that session time is limited to 2h, participants who feel comfortable using gLAB, can skip part of the next basic exercises (Ex3..., Ex6) and jump to the

Laboratory Work Projects (LWP).

There, if you prefer, you can jump to slide #87 and choose one from the four

LWPs



On October 28, 2003, an intense solar eruption (a Solar Flare) was detected around 11h UT in an active region which had grown one of the largest sunspots ever seen by the SOlar Helioscopic Observatory (SOHO). It appeared as a bright spike in the SOHO ultraviolet images.

69

This sudden enhancement of the solar radiation in the X-ray and extreme ultra-violet band produced a sudden increase in the ionospheric electron density on the daylight hemisphere, (see [R-3]).

Ex. 3: Solar Flare October 28, 2003



Exercise: Analyze the effect of the Solar Flare on the Slant Total Electron Content (STEC) measurements of four permanent IGS receivers ankr, asc1, kour and qaq1, covering a wide range of longitude and latitude.

Data sets: ankr3010.03o, asc13010.03o,kour3010.03o, qaq13010.03o

70


ankr

qaq1

kour

asc1



Execute:

gLAB_linux -input:cfg meas.cfg -input:obs ankr3010.03o > ankr3010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs asc13010.03o > asc13010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs kour3010.03o > kour3010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs qaq13010.03o > qaq13010.03.meas

graph.py -f ankr3010.03.meas -x4 -y'($14-$16)' --l "ankr" -f asc13010.03.meas -x4 -y'($14-$16)' --l "asc1" -f kour3010.03.meas -x4 -y'($14-$16)' --l "kour" -f qaq13010.03.meas -x4 -y'($14-$16)' --l "qaq1" --xl "time (s)" --yl "meters of L1-L2" --xn 38500 --xx 40500 --yn -20 --yx 20 -t "28 Oct 2003 Solar flare"

ankr

qaq1

kour

asc1



71



ankr

qaq1

kour

asc1




Associated with the Solar Flare analysed in the previous exercise, a Coronal Mass Ejection occurred, which sent a large particle cloud impacting the Earth's magnetosphere about 19 hours later, on October 29.

Subsequent impacts were still occurring several hours later. This material interacted with the Earth's magnetosphere and a Storm Enhancement Density (SED) appeared in North America and affected later the northern

latitudes in Europe. Extra large gradients of TEC associated with this phenomenon were also produced, degrading the GPS positioning performance.

The TEC evolution in October 30, 2003 (i.e., Day 303 of year 2003) can be seen in the movie TEC 2003oct30 anim.gif.

Ex. 4: Halloween storm: P2-P1 analysis



The measurement files garl3010.03o, garl3020.03o, garl3030.03o, garl3040.03o, garl3050.03o, garl3060.03o were collected by the permanent receiver garl in Empire, Nevada, USA ( = 40.42 deg

=-119:36 deg) from October 28 to November 2, 2003.

Using these files, plot the STEC for all satellites in view and discuss the range of such variations. Analyse, in particular, the satellite PRN 04 and calculate the maximum rate of STEC variation in mm=s of L1 delay. Add the elevation of satellite PRN 04 in the plot.

The associated broadcast navigation les are brdc3010.03n, brdc3020.03n, brdc3030.03n, brdc3040.03n, brdc3050.03n, brdc3060.03n.




Exercise: Depict the ionospheric delays for the different satellites in view from station amc2

• This is a simple exercise aimed to illustrate how to use gLAB to easily analyze GNSS measurements and their combinations.

• gLAB will used to read the RINEX measurements file and to generate a “text” with the measurements provided in a columnar format (more suitable to make plots).

• Using such “text” file, the STEC pattern for the different satellites in view during the storm is depicted from the geometry-free combination of codes P2-P1.

Note:

75


2 1 21P P I K



The next commands read a RINEX file and generate a text file (in columnar format) that allows to easily plot the measurements and their combinations:

1. Using the configuration file meas.cfg, READ the RINEX and generate the MEAS message with data format:

Execute:

2. From meas.txt file, Compute the ionospheric combination of codes: PI=P2-P1.

Generate the file PI.txt with the following content: [PRN, hour, PI, elevation]

3. From PI.txt file,Plot the PI=P2-P1 for time interval [15 to 24].hours. Show in the same graph: 1) ALL satellites, 2) PRN 13, 28 and 29, and 3) The elevation of each satellite.(13, 28 and 29)

76


gawk '{print $6, $4/3600, $15-$13, $7}' amc23030.03.meas > PI.txt

Backup

gLAB_linux -input:cfg meas.cfg -input:obs amc23030.03o -input:nav brdc3030.03n > amc23030.03.meas

graph.py -f PI.txt -x2 -y3 --l "ALL" -f PI.txt -c'($1==28)' -x2 -y3 -so --l "28:P2-P1" -f PI.txt -c'($1==28)' -x2 -y4 --l "29:ELEV" -f PI.txt -c'($1==29)' -x2 -y3 -so --l "29:P2-P1" -f PI.txt -c'($1==29)' -x2 -y4 --l "13:ELEV" -f PI.txt -c'($1==13)' -x2 -y3 -so --l "13:P2-P1" -f PI.txt -c'($1==13)' -x2 -y4 --l "13:ELEV" --xn 15 --xx 25 --yn 0 --yx 85 --xl "time (s)" --yl "meters of L1-L2 delay"


76





October 30, 2003



Exercise: Analyze the ionospheric delays for 6 consecutive days including the Halloween storm

• This is a simple exercise aimed to illustrate the ionospheric delays variation during the Halloween storm. A period of 6 consecutive days (from October 28 to November 2, 2003) are analyzed using measurements collected in the “garl” station in North America.

• The STEC variations are depicted from the geometry-free combination of codes P2-P1.

Note:

78

Ex. 5: Halloween storm evolution

2 1 21P P I K



gLAB_linux -input:cfg meas.cfg -input:obs garl3010.03o -input:nav brdc3010.03n > garl3010.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3020.03o -input:nav brdc3020.03n > garl3020.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3030.03o -input:nav brdc3030.03n > garl3030.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3040.03o -input:nav brdc3040.03n > garl3040.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3050.03o -input:nav brdc3050.03n > garl3050.03.meas gLAB_linux -input:cfg meas.cfg -input:obs garl3060.03o -input:nav brdc3060.03n > garl3060.03.meas

graph.py -f PI.txt –x2 –y3 --l "ALL P2-P1" -f PI.txt -c'($1==04)' –x2 –y4 --l "PRN04: ELEV" -f PI.txt -c'($1==04)' –x2 –y3 –so --l "PRN04: P2-P1" --xn 0 --xx 144

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ JJJJ. SanSanSannSannnnnnnnnnnzzzzzzzzzzzzzzzzzzzzz &&&& JJJJ.MMMMMMMMMMMMMMMM....... JuaJJJJJJJJJJJJJJJJJJJJJJJJuaJuauaauJ aaaaannnnnnnnnnn

cat garl30?0.03.meas |gawk '{d=($3-301)*86400;$4=$4+d; print $6, $4/3600, $15-$13, $7}' > PI.txt

2.- Merge files and refer all the data to 0h of October 28th: Doy0301:

3.- Plot results:

1.- Read RINEX file: [Id YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2P L2P] 1 2 3 4 5 6 7 8 9 10 11 xx 13 14 15 16 ]


79



Zoom at time interval: 70 to 78 h graph.py -f PI.txt –x2 –y3 --l "ALL P2-P1" -f PI.txt -c'($1==04)' –x2 –y4 --l “04: EL" -f PI.txt -c'($1==04)' –x2 –y3 –so --l “04" --xn 0 --xx 144

graph.py -f PI.txt –x2 –y3 --l "ALL P2-P1" -f PI.txt -c'($1==04)' –x2 –y4 --l “04: EL" -f PI.txt -c'($1==04)' –x2 –y3 –so --l “04" --xn 70 --xx 78


80



Travelling Ionospheric Disturbances (TIDs) are understood as plasma density fluctuations that propagate through the ionosphere at an open range of velocities and frequencies. The trend of such fluctuations can be seen from the geometry free combination of GPS carrier measurements .

Some authors distinguish between Large-Scale TIDs (LSTIDs) with a period greater than 1 hour and moving faster than 0,3 km/s, and Medium- Scale TIDs (MSTIDs) with shorter periods (from 10 minutes to 1 hour) and moving slower (0.05-0.3 km/s). The LSTIDs seem to be related to geomagnetic disturbances (i.e., aurora, ionospheric storms, etc.). The origin of MSTIDs seems to be more related to meteorological phenomena such as neutral winds, eclipses, or solar terminator that produces Atmospheric Gravity Waves (AGW) being manifested as TIDs at ionospheric heights, due to the collision between neutral and ionised molecules.

Ex. 6: Travelling Ionospheric Disturb.

1 2IL L L



In [R4, 2006] a simple method to detect MSTIDs is proposed. It consists of detrending the geometry free combination of GPS carrier measurements from the diurnal variation and elevation angle dependences, applying the following equation:

where a value of 300sec is suitable to keep enough variation of LI (i.e., STEC).

Using the previous equation, the detrending is done simply by subtracting from each value an average value of the previous and posterior measurements (i.e., the curvature of the LI temporal dependency). It must be pointed out that that this detrending procedure can be used in real time with a single receiver, so it is suitable for identifying these ionospheric perturbations in navigation applications.


( ) ( ) ( ) ( ) / 2I I I IL t L t L t L t



An example of MSTID propagation can be depicted as follows using the measurements of three stations SODB, MHCB and MONB, which are separated by a few tens of kilometres.

The target is to reproduce the figure 10 of the above mentioned paper [R4, 2006].


[R4, 2006] Hernández-Pajares, M; Juan, M.; Sanz, J., 2006].

sodb

mhcb

monb



Exercise: Execute in a single line:# a) Reading RINEX files: gLAB_linux -input:cfg meas.cfg -input:obs mhcb2910.01o > mhcb.meas gLAB_linux -input:cfg meas.cfg -input:obs monb2910.01o > monb.meas gLAB_linux -input:cfg meas.cfg -input:obs sodb2910.01o > sodb.meas

# b) Selecting satellite PRN16: gawk '{if ($6==14) print $0}' mhcb.meas > mhcb_14.meas gawk '{if ($6==14) print $0}' monb.meas > monb_14.meas gawk '{if ($6==14) print $0}' sodb.meas > sodb_14.meas

# c) Detrending on the geometry-free combination L1-L2: gawk '{for (i=0;i<21;i++) {t[i]=t[i+1];l[i]=l[i+1]};t[21]=$4;l[21]=$14-$16; if (NR>21){tt=t[0]*t[10]*t[20];if (tt!=0) print t[10],(l[10]-(l[0]+l[20])/2)}}' mhcb_14.meas > mhcb_dLi.meas gawk '{for (i=0;i<21;i++) {t[i]=t[i+1];l[i]=l[i+1]};t[21]=$4;l[21]=$14-$16; if (NR>21){tt=t[0]*t[10]*t[20];if (tt!=0) print t[10],(l[10]-(l[0]+l[20])/2)}}' monb_14.meas > monb_dLi.meas gawk '{for (i=0;i<21;i++) {t[i]=t[i+1];l[i]=l[i+1]};t[21]=$4;l[21]=$14-$16;if (NR>21){tt=t[0]*t[10]*t[20]; if (tt!=0) print t[10],(l[10]-(l[0]+l[20])/2)}}' sodb_14.meas > sodb_dLi.meas

sodb

mhcb

monb


84



Execute in a single line:graph.py -f sodb_dLi.meas -s.- --l "sodb: PRN14" -f mhcb_dLi.meas -s.- --l "mhcb: PRN14" -f monb_dLi.meas -s.- --l "monb: PRN14" --xn 55500 --xx 57000 --yn -0.05 --yx 0.07 --xl "time (s)" --yl "Detrended STEC (meters of L1-L2 delay)" -t "MS Travelling Ionospheric Disturbance (MSTID) propagation"

ResearchResearch group fof A tAstronomy && GeomaticsGeomaticsTechnicalTechnical UniversityUniversity ofof CataloniaCatalonia

gggggggggggggggggggggAAAAAAAAAAAAAAAAAAGGGGGEEEEEEEEEEEEE//////////////UUUUPPPPCCCCCCCCCCCCCCCCCC sodb

mhcb

monb


85




LABORATORY SessionStarting up your laptopBasic: Introductory lab exercises: Iono & Posit, SF, storm,TIDsMedium: Laboratory Work Projects: LWP1 to LWP4Advanced: Homework

OVERVIEW

86



In the previous Exercise #2 the variation of the Integrated Electron Content along the ray path (STEC) has been shown. From these integrated measurements during an occultation it is possible to retrieve the electron density profile (i.e., Ne(h)) of the ionosphere.

LWP1: Electron Density Profile from ROG P

aNe

LWP1: TargetIn this LWP we will retrieve the Ne(h) using a simple numerical algorithm which is equivalent to the Abel transform (see [R-6]).



• The basic observable of this technique is the additional delay, due to the refractivity index, of a radio signal when passing through the atmosphere.

• This additional delay is proportional to the integrated refractivity, in such a way that we can obtain an estimation of the vertical refractivity profiles using observations at different elevation angles by solving an inverse problem.

• Traditionally, the solution of this inverse problem is obtained by using the Abel inversion algorithm assuming a refractivity index that only depends on the altitude (see [RD-6])

LWP1: Electron Density Profile from RO

G Pa

Ne

An equivalent expression, assuming spherical symmetry

where p stands for the impact parameter (the closest point to the Earth centre along the optical ray path).

As it is know, STEC and Ne are related by:

( )LEO

eGPSSTEC p N dl

,1( ) 2 ( )n

n e i i niSTEC p N p l




where p stands for the impact parameter (the closest point to the Earth centre along the optical ray path).

Thence, starting from the outer ray (p1=rLEO), for a given ray i, where i=1,…, with impact parameter pi, its STEC can be written in a discrete representation as:

where lii is the fraction of ith ray within the spherical layer ith (see [R-6]).

The previous equation defines a triangular linear equations system that can be solved recursively for the electron density Ne(p).

As measurements we use L1-L2 carrier phases that are related with the STEC by:

where the bias term b is eliminated making differences to a reference in the arch data.

1

, ,1

( ) 2 ( ) ( )j i

i e i i i e j i jj

STEC p N p l N p l

1 2L L STEC b

1 2L L STEC b



The program “abel.perl” implements the previous algorithm to estimate the Ne(p) profile from GPS L1-L2 carrier measurements.• The input data is [p(n),L1-L2(n)], with p in km and L1-L2 in meters (of L1-L2 delay)

where the impact parameter must be sorted from larger to lower value.Only measurements with negative elevation must be given (i.e., occultation).

• The output data is: [n,p(n),L1-L2(n),Ne(n)], where Ne is given in e-/m3.


Note: the Impact parameters can be computed from the LEO elevation (elev) and its distance to Earth’s centre (rLEO) by (see figure):

cos( )LEOp r elev



- Selecting: CODE=l241 and PRN=02 and negative elevations (ocult) grep l241 RO.obs|gawk '{if ($5==02 && $6<0) print $0}'> ro.tmp

- Generating the input file gawk '{printf "%9.5f %7.5f \n",$7*cos($6*3.14/180),$15}' ro.tmp > abl.tmp

- Sort the file by impact parameter: sort –nr –k+1 abl.tmp > abl.dat


1.- Using the file RO.obs, select the measurements with negative elevations for GPS satellite PRN02, the LEO #4 and antenna #1, and generate the input file [p(n),L1-L2(n)] for program “abel.perl”

Exercise: The file “RO.obs” contains the following fields (see Ex.5): | ------ LEO ------>|<------- GPS ------->| YY DoY HH.HH CODE PRN elev r_LEO AR_LEO DEC_LEO r_GPS AR_GPS DEC_GPS L1 L2 L1-L2 arc (deg) (km) (Deg) (Deg) (km) (Deg) (Deg) (cycles) (m) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16



- Sort the file by impact parameter: cat abl.dat| abel.perl > Ne.dat

LWP1: Electron Density Profile from RO2.- Run the program “abel.perl” over the generated file “abl.dat“ to compute the electron density profile Ne(p):

3.- The output file “abl.dat“ contains the fields [n,p(n),L1-L2(n),Ne(n)] Plot the electron density profile Ne as a function the impact parameter p and as a function of height above Earth‘s

- Plot1: As a function of “p”

graph.py -f Ne.dat -x4 -y2 --xl "Ne(e-/m3)" --yl "p (km)"

- Plot2: As a function of “height”

graph.py -f Ne.dat -x4 –y’($2-6370)’ --xl "Ne(e-/m3)" --yl “h (km)"




1. Taking into account the relationship between the electron density (Ne) and the critical frequency (fp), i.e., minimum frequency for a signal not being reflected, [R-1]:

Compute the minimum frequency of a signal to cross through the ionosphere.

Answer: From previous plot, the Ne of the maximum is 3.7E+11 e-/m3. Thence

2. Calculate the height where a signal with frequency f=4 MHz will be reflected, according to the previous plot of Ne profile.Answer:

38.98 ( in e /m , in Hz)p e e pf N N f

Questions

118.98 3.7 10 5.46pf MHz

2 6 2 11( / 8.98) (4 10 / 8.98) 1.98 10 150 kmeN f



LWP2: Atmospheric Bending in ROLWP2: TargetThis LWP is focused in depicting and analysing the effect of the atmospheric bending in Radio Occultation measurements.

A simple procedure will be given to depict the phase excess rate due to the troposphere and ionosphere over L1, L2 and LC measurements.

2 21 2

2 21 2

1 2f L f LLCf f

Note: LC is the Ionosphere Free combination of carriers L1 and L2 is given by:

G Pa



LWP2: Atmospheric Bending in RO

being the Euclidean distance between GPS and LEO and B a constant bias along continuous phase arc

• The bias B cancels, taking time differences of L1.Thence, from previous equation, it follows

Let L1 be the carrier measurement at frequency f1.A procedure to depict the L1 bending is given next:

G Pa

G Pa

No bending

Bending

Ref. GPS

Ref. LEO

Ref Ref

Ref Ref( ) ( ) ( ) ( ) ( )GPS GPSGPS GPS

LEO LEO LEO LEODD

Reference satellites (GPS, LEO) are taken in NON-OCULTATION .

*jL

DD DDt t

* *1 1 1;sat

recL cdt B T I

• And clocks cancel taking Double-Differences between pairs of LEO and GPS satellites:

*1

satreccdtL

t t t

Note: LEO and GPS orbits are known at the level of few cm (~5cm), thus the Euclidean range can be calculated accurately and, thus, the range rate

t

*

0occult occult jLDD DD

t t t t




* *satj jrec

satC rec C

L Lcdt DD DDt t t t t

L cdt LDD DDt t t t t

*

*

0 ; 1, 2

0

occult occult

occult occult

j

C

LDD DD j

t t t tLDD DD

t t t t

G Pa

G Pa

No bending

Bending

Ref. GPS

Ref. LEO

Ref Ref

Ref Ref( ) ( ) ( ) ( ) ( )GPS GPSGPS GPS

LEO LEO LEO LEODD

And the clock term cancels taking Double Differences between LEO and GPS satellites

Reference satellites (GPS, LEO) are taken in NON-OCULTATION .Bending is assumed only for the GPS-LEO ray in occultation.

* *; ; 1, 2

;

satj rec j j

satC rec C

L cdt B T I j

L cdt B T

Next expressions generalize previous results for L1, L2 and Lc measurements:

The differences in time to depict the bending

Carrier Excess Rate



LWP2: Atmospheric Bending in ROAnother possibility to remove the clock term, could be to subtract the LC combination

from L1 (or L2). The result will provide the “discrepancy between L1 (or L2) and LC excess ray path.

That is:

Notice that the Euclidian range rate is not needed to subtract as in the previous case, because it is cancelled when taking the difference between L1 (or L2) and Lc. Other delays can also be cancelled...

*

*; 1, 2; 1, 2

occult

occult occult

occult

satj rec

j Csat

C rec

L cdt j L Lt t t jt t t tL cdt

t t t

In the following exercises, we will plot the previous combinations and discuss the different contribution of the ionosphere and troposphere to the phase excess rate.



The program “RO.perl” uses the “RO.obs” as input data and computes the following combinations of RO measurements:

The output file:

where • Rho is the Euclidean Distance between GPS and LEO • d: means differences in time • DD: means Double Differences between GPS and LEOs satellites.

Note: the GPS PRN13 and LEO “l252” are used as reference satellites. (the rays between these satellites are not in occultation).

The results are computed for the RO between GPS PRN02and LEO “l241” (the same occultation as in previous cases)

The aim of this exercise is to analyse the phase excess ratein the different combinations due to the bending of the ray.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 sec CODE PRN p dRho dL1 dL2 dLc d(L1-Lc) d(L2-Lc) DDdRho DDdL1 DDdL2 DDLc

(units m/s)

G Pa

G Pa

No bending

Bending

Ref. GPS

Ref. LEO

Exercise:



1.- Run the program “RO.perl” over the file “RO.obs” and generate the combinations of measurements indicated in the previous table.

Note: the results are provided for the occultation associate to PRN=02 and “CODE=l241”, that corresponds to LEO=4 and Antenna 1. This is hard code in the program, but can be changed, as well.

- Execute (the file RO.obs, must be available in the directory)

RO.perl > bending.dat


2.- Discuss next plots:



graph.py -f bending.dat -x'($12-$11)' -y4 -l "DDdL1-DDdRho" -f bending.dat -x'($13-$11)' -y4 -l "DDdL2-DDdRho" --xn -0.4 --xx 4

LWP2: Atmospheric Bending in ROP1.- Plot “DDdL1-DDdRho” and DDdL2-DDdRho as a function of time and

discuss the results found

Q1: Justify the discrepancy between the two plots. Answer 1: • The curves in the plot show phase

excess rate due the effect of both ionosphere and troposphere.

• As the bending in the ionosphere is a frequency dependent effect, the contribution is different for each signal (L1 and L2).



graph.py -f bending.dat -x'($14-$11)' -y4 --xn -0.1 --xx 0.3 --xl "m_Lc/s" --yl "p (km)" -t"DDdLc-DDdRho: COSMIC #4 Antenna #1, PRN02"

LWP2: Atmospheric Bending in ROP2.- Plot DDdLc-DDdRho as a function of time. Discuss results.

Q2: Why there is no excess ray path for p> 6420 km?Answerer 2: • The ionospheric bending effect on L1

and L2 is proportional to the inverse of squared frequencies and cancels in the ionosphere-free combination of carriers Lc.

• There is only bending effect in Lc dueto the troposphere, which produces the path at the bottom of the figure.



LWP2: Atmospheric Bending in ROP3.- Plot “dL1-dLc” and DDdL1-DDdRho as a function of time. Discuss results.

graph.py -f bending.dat –x9 -y4 -l "dL1-dLc" -f bending.dat -x'($12-$11)' –y4 -l "DDdL1-DDdRho" --xl "m_L1/s" --yl "p (km)" --xn -0.4 --xx 4 -y4

Q3: Justify the discrepancy between the two plots. Answer 3: • DDdL1-DDdRho accounts for the

contribution of ionosphere and troposphere. The troposphere produces the large drift at the bottom.

• dL1-dLc cancels common effects in both signals, like troposphere and ionosphere. But, as there is no bending effect due to the ionosphere on Lc (see previous plot P2) , thence, the curves match for p> 6420 km.




graph.py -f bending.dat –x10 -y4 -l "dL2-dLc" -f bending.dat -x'($13-$11)' –y4 -l "DDdL1-DDdRho" --xl "m_L2/s" --yl "p (km)" --xn -0.4 --xx 4 -y4

Q4: Justify the discrepancy between the two plots. Answer 4:• The same answer as in previous plot.

P4.- Plot “dL2-dLc” and DDdL2-DDdRho as a function of time. Discuss results.




graph.py -f bending.dat -x'($6-$5)' -y4 -l "dL1-dRho" -f bending.dat –x9 -y4 -l "dL1-dLc" --xl "m_L1/s" --yl "p (km)" -t"COSMIC #4 Antenna #1, PRN02"

P5.- Plot “dL1-dRho” and dL1-dLc as a function of time. Discuss results.

Q5: Justify the discrepancy between the two plots. Answer 5: • The large drift in dL1-dRho curve is

due to the satellites (GPS and LEO) clock drift.

• These large clock variations do not allow to see the atmospheric bending effect.




graph.py -f bending.dat -x'($7-$5)' -y4 -l "dL2-dRho" -f bending.dat –x10 -y4 -l "dL2-dLc" --xl "m_L2/s" --yl "p (km)" -t"COSMIC #4 Antenna #1, PRN02"

P6.- Plot “dL2-dRho” and dL2-dLc as a function of time. Discuss results.

Q6: Justify the discrepancy between the two plots. Answer 6: • The same answer as in previous plot.



vGPS vLEOGPS LEOG P

a LLLLLLEEEEEEEEEOOOOOOGPPPPPPPPPPPSSSSSS OGPS

LEO

Bending Angle ( )

rGPS

rLEO


Backup

GPS VGPS LEO VLEO GPS

GPS

LEOLEO

*occult occult jL

f DD DDt t t t

Derivation of bending angle a from Excess Phase Rate (or Atmospheric Doppler Shift )

( )occult

GPS LEOtv v

*occult

GPS GPS LEO LEOtv k v k

sin( ) sin( )GPS GPS GPS GPS LEO LEO LEO LEOn r n r a

GPS GPS LEO LEOf v k

GPS LEO

( )aThe Bending Angle can be derived iteratively from this equations system (see, [R-7])

f

106




Comments:From phase excess rate measurements the bending angle can be estimated.From the bending angle, the variations of the refractivity can be computed, and from these one can then derive atmospheric quantities such as Pressure, Temperature and the partial pressure of water vapor, and electron density, among others.

Backup



The target of LWP3 is to analyze the error induced by the divergence of the ionosphere (between code and carrier) into the Single-Frequency (SF) carrier smoothed code.

LWP3: Iono. Divergence on Smoothing

This effect will be analyzed analytically and tested with single and double frequency GPS measurements under large ionospheric gradients.

The Divergence Free (Dfree) and the Ionosphere Free (IFree) smoothed codes will be compared with the SF one.



The noisy code can be smoothed with the precise (but ambiguous) carrier measurements. This carrier smoothing can be done in real-time applying the Hatch filter.

The smoothing depends on the time smoothing constant or filter length. The more the filter length is used, the more smoothed the code is, but (with single frequency measurements) a higher code-carrier divergence error is induced by the ionosphere.

This is because the ionospheric refraction has opposite sign on code and carrier, being its effect twice on the difference of code and carrier. This double ionospheric refraction is propagated forward through the filter, producing a bias.

The error induced by the code-carrier divergence of the ionosphere on thesingle frequency smoothed codes is assessed in this exercise for different filter

lengths.




The noisy code P can be smoothed with the precise (but ambiguous) carrier Lmeasurements. This carrier smoothing can be done in real-time applying the Hatch filter.

The previous algorithm can be interpreted as real-time alignment of carrier with code:

where


where [ if ], and [ if ].

1 1ˆ( ) ( ) ( 1) ( ) ( 1)

ˆThe algorithm is initialised with: (1) (1).

n k k N n N k N

nP k P k P k L k L kn n

P P

( )

1 1ˆ( ) ( ) ( 1) ( ) ( 1)

( )k

nP k P k P k L k L kn nL k P L

( ) ( 1)

1 1 1( ) ( ) ( ) ( )k k

nP L P k L k P L P k L kn n n

Carrier Phase L (ambiguous but precise)

Code P (unambiguous but noisier)

Ambiguity= P L

Iono

sphe

ricco

mbi

natio

n(m

eter

s)



Time varying ionosphere induces a bias in the single frequency smoothed code when it is averaged in the smoothing filter. This effect is analysed as follows:

Let:


1 1 1

1 1 1 1

P IL I B

thence,

1 1 1 12P L I B 12 : Code-carrier divergenceI

Substituting in Hatch filter equation (see the previous slide #110):1 1P L

1 1 1ˆ

IP I bias

where, being the ambiguity term a constant bias, thence , and cancels in the previous expression

1B1 1B B

1 1 1 1( ) ( )

1 1 1( )

ˆ ( ) ( ) ( ) ( ) 2

( ) ( ) 2 ( )

I

k k

k

bias

P k L k P L k I k B I B

k I k I I k

where is the noise term after smoothing

1

Note: the carrier noise is neglected against code noise .1

1

1I1B

1 1,

Where includes all non dispersive terms (geometric range, clock offsets, troposphere) and represents the frequency dependent terms (ionosphere and DCBs). Is the carrier ambiguity, which is constant along continuous carrier phase arcs and account for code and carrier multipath and thermal noise.



Raw assessment of the induced bias on P1 smoothed code by ionosphere:

• Let assume a simple model where the STEC vary linearly with time:

where is the Hatch filter smoothing time constant (i.e., in previous eq.).

Exercise: Proof the previous statement.Solution: Let be and . The averaging in the Hatch filter can be implemented as:

Thence:


01 1 1 1 1 1( )( ) 2 ( ) 2I kI t I I t bias I I k I

N

( ) ( )f t I t ( )( )t

y t I

( ) ( ) ( )T Ty t T y t f t T 0( ) ( ) 1 1 1 1( ) ( ) ' ( )T

y t T y t y t f t T y y f tT

0

/1 1 1 1 1 1 1 1 1( ) ( )( ) ( ) 1 2 ( ) 2t

I tt tI t I I t I I t I e bias I I t I



• Divergence Free smoothing (DFree):With 2-frequency measurements, the ionosphere can be removed from a combination of two carriers:


1 1 1 2 12 1 1 1 12ˆ2 ( )P L L L B P I

22

2 21 2

ff f

12 1 1 22 ( )B B B B

• Ionosphere Free smoothing (IFree):Using both, code and carrier 2-frequency measurements, it is possible to remove the frequency dependent effects using the ionosphere-free combination :

C C

C C C

PL B

2 21 1 1 2

2 21 2

2 21 1 1 2

2 21 2

C

C

f P f PPf f

f L f LLf f

,C CP L

C CP

DFree smoothed code is not affected by iono. temporal gradients, being the ionospheric delay the same as in the original code .1P

IFree smoothed code is not affected by either spatial or temporal gradients,but is 3-times noisier than the DFree, or the in the Single Freq. smoothed code.



114

LWP3: Iono. Divergence on Smoothing 1.- Multipath and measurement noise assessment on raw code measurements:


a) Generate the “meas” file for PRN03:

1 1 1 1 22 ( )CM C L L L



c) Plot the raw (unsmoothed) measurements for PRN03:

222

2 21 2

1 771.545 ;1 60

ff f




b) Using previous expression, compute the C1 multipath and code noise: :




2. Apply the Hatch filter to smooth the code using a filter length of N =100 sample (as the measurements are at 1Hz,this means 100 seconds smoothing). Then, as in the previous case, depict the multipath and noise of the smoothed code.

a) Smoothing code (T=100sec):

b) Plotting results and compare with the row C1.

gawk 'BEGIN{Ts=100}{if (NR>Ts){n=Ts}else{n=NR}; C1s=$11/n+(n-1)/n*(C1s+($14-L1p));L1p=$14; print $4,C1s-$14-3.09*($14-$16)-21.3}' upc3.meas > upc3.C1s100

graph.py -f upc3.C1 -s- --l "C1 Raw" -f upc3.C1s100 -s.- --cl r --l "C1 SF smoothed" --xn 35000 --xx 40000 --yn -5 --yx 5 --xl "time (s)" --yl "meters" -t "PRN03: C1 100s smoothing and iono div."



LWP3: Iono. Divergence on Smoothing 3 . . Using 2-frequency carriers it is possible to generate a combination with the

same ionospheric delay (the same sign) as the code to avoid the code-carrier divergence:

a) Apply the Hatch filter to compute the DFree smoothed code

b) Plot results and compare with the row C1 code:

gawk 'BEGIN{Ts=100}{if (NR>Ts){n=Ts}else{n=NR}; C1f=$11; L1f=$14+2*1.55*($14-$16); C1fs=C1f/n+(n-1)/n*(C1fs+(L1f-L1p));L1p=L1f; print $4,C1fs-L1f-21.3}' upc3.meas > upc3.C1DFs100

222

2 21 2

1 771.545 ;1 60

ff f

graph.py -f upc3.C1 -s- --l "C1 Raw" -f upc3.C1s100 -s.- --cl r --l "C1 SF smoothed (100s)" -f upc3.C1DFs100 –s.- --cl g --l "C1 DFree smooth(100s)" --xn 35000 --xx 40000 --yn -5 --yx 5 --xl "time (s)" --yl "meters"

1 1 1 2 12 ( )DFreeL L L L I B



LWP3: Iono. Divergence on Smoothing 4 . Generate the ionosphere-free combinations of code and carrier measurements

to compute the Ionosphere Free (IFree) smoothed code:

• Apply the Hatch filter to compute the IFree smoothed code

• Plot results and compare with the unsmoothed PC:

gawk 'BEGIN{g=(77/60)**2}{pc=(g*$13-$15)/(g-1); lc=(g*$14-$16)/(g-1); print $4,pc-lc-3.5}' upc3.meas > upc3.PC

27760

1 2 1 2;1 1IFree C IFree C

P P L LC P L L

gawk 'BEGIN{g=(77/60)**2}{pc=(g*$13-$15)/(g-1); lc=(g*$14-$16)/(g-1); if (NR>100){n=100}else{n=NR}; ps=1/n*pc+((n-1)/n*(ps+lc-lcp)); lcp=lc; print $4,ps-lc-3.5}' upc3.meas > upc3.PCs100

graph.py -f upc3.PC -s- --l "IFree raw" -f upc3.PCs100 -s.- --cl black --l "Ifree(100s)" --xn 35000 --xx 40000 --yn -5 --yx 5 --xl "time (s)" --yl "meters"



LWP3: Iono. Divergence on Smoothing 5 . Repeat previous plots but using: N=360, N=3600 and compare results. Plot also

the ionospheric delay (from L1-L2) (see more details in [R-1]):

STEC

Note that the y-range in bottom row

plots is 3 times larger than in

top plots

T=100s T=360s T=3600s

C1

PC

C1

PC

C1

PC



Repeat the previous exercise using the RINEX file amc23030.03o_1Hz collected for the station amc2 during the Halloween storm. Take N=100(i.e, filter smoothing time constant =100 sec).




The aim of LWP4 is to build a combination of carriers measurements at three different frequencies to remove the geometry and the first order ionosphere effects.

Once this combination is obtained, its suitability to depict the second order ionospheric effects will be analyzed.

LWP4: Second order Ionospheric Effect

The assessment will be based on actual GPS measurements at frequencies L1, L2 and L5



As commented before, about the 99.9% of the ionospheric delay depends on the inverse of squared frequency:


Its effect on code and carrier is equal but with opposed sign:

121

240.31I STECf

eSTEC N ds1I

First order Ionospheric delay

1 1carr codeI I

Second order Ionospheric delayPrevious expression comes from a simplification of the ionospheric delay derivation, where the

dependence of the refraction index with the magnetic field B is neglected. If such dependence is taken into account, higher order terms appears (but, they represent less than 0.1% of total effect)

The second order ionospheric term is given by:

In global geodetic computations, I2 mainly affects to the satellite clock estimates (cm level) and orbits (few mm), but the impact on receiver positions is smaller than1mm, (see [R-5] and [R-1]).

372572 coscode e

cI N B dsf

1; 2 22carr codeI I




122

, ,i j kf f f

/ij i jf fwith

Question 1: Show that there is a unique linear combination of three carriers cancelling both geometry and (first order) ionospheric refraction. a) Apply results to GPS L1, L2 and L5 signals. b) Using file l5dt1260.09o depict such combination of carriers.

i i j j k ka L a L a L, ,i j ka a a

2 2

3 3

0 geometry-free0 1st-oder iono-free

2nd-order iono1

i j k

i ij j ik k

i ij j ik k

a a a

a a a

a a a

Note: The first equation cancels all non-frequency dependent effects (geometric range, clocks, troposphere…)The second equation cancels all effects that depends of inverse squared frequency (1st-order: ionosphere and instrumental delays).The last equation is to normalize the coefficients giving the combination in delay units at frequency .if

Second order Ionospheric delay combination

Hint:Let be a linear combination of three carrier measurements at frequencies .The coefficients , shall verify the conditions:


estiooth g



123

12

15

154 /120154 /115

with1 2 52 2

1 12 2 15 53 3

1 12 15 5

001j

a a aa a aa a a

Thence, the combination is: (in delay units at frequency).

Answer to question 1a:Show that there is a unique linear combination of three carriers cancelling both the geometry and the (first order) ionospheric refraction. Apply results to the L1, L2 and L5 signals.

1 0 2 0 5 0154 , 120 , 115 .f f f f f fApplying previous equations system to GPS signals

1

2

3

6.28734.084

27.797

aaa

1 2 5LI2 6.287 34.084 27.797L L L

LI2 44.4 L

1f

On the other hand, assuming the carriers uncorrelated and with the same , the noise associated to this combination is given by:

iL L

Note: As , the combination of codes is given by:

1 2 5 PI2PI2 3.144 17.042 13.899 ; 22.2 CC C C

12 22code carrI I


theL2



gLAB_linux -input:cfg meas.cfg -input:obs l5dt1260.09o -input:nav l5dt1260.09n -pre:dec 0| grep GPS > l5dt.meas

[MEAS YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2C L2C C2P L2P C5X L5X ] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1. Using the configuration file meas.cfg, READ the RINEX and generate the MEAS file with content:

gawk '{if ($6==01) {print $4,6.287*$14-34.084*$18+27.797*$20,$7}}' l5dt.meas > LI2.dat

2. From l5dt9.meas file, generate a file with the following content: [sec LI2 elev] 1 2 3

Answer to question 1b:Make a plot to depict the geometry-free and first-order ionosphere-free combination of GPS carrier phase measurements [L1,L2,L5].

Use files l5dt1260.09o, l5dt1260.09n [*] (and satellite PRN01).

[*] Note, although the elevation is not needed for this exercise (and thence the broadcast orbit file l5dt1260.09n, it is computed because it will be useful for a further study).




graph.py -f LI2.dat -x1 -y2--l "LI2[125]" --xn 29700 --xx 49200 --yn 5128 --yx 5134 --xl "time (s)" --yl "meters of L1 delay"


Discussion:1. What is the order of magnitude of the second

order ionospheric effect?2. Is the pattern seen in the figure due to the

2nd order ionospheric effect or it is related to other phenomena?

Hint:Add the elevation in the previous plot and explore if the pattern could be related to the antenna phase centers of the different signals.




graph.py -f LI2.dat -x1 -y'($2-5133)' –s- --l "LI2[125]" -f LI2.dat -x1 -y'($3/10)' –s- --l "Elev/10" –s- --xn 29700 --xx 49200 --yn -7 --yx 7 --xl "time (s)" --yl "meters of L1 delay"

3.- Plotting results with the elevation added:

Note: The figure is shifted (by 5133m) to align with the x-axis.This bias is due to the carrier ambiguity(see HW1).




Answers to the previous discussion:

1. What is the order of magnitude of the second order ionospheric effect?2. Is the pattern seen in the figure due to the 2nd order ionospheric effect

or it is related to other phenomena?

The I2 effect on ground measurements is typically less than 2cm of L1 delay(see HW3 or [R-5]). Thence, the pattern must be related to another phenomena, as explained as follows:• In the derivation of previous combination LI2, the antenna phase center (APC) correction

for the GPS signals has not been taken into account. Indeed, as L1, L2 and L5 have different APCs, the geometric range for such signals is slightly different, producing an elevation dependent error if it is not modelled.

• In HW1 it is shown that, assuming only APC correction in the UP component, the APC effect can be removed from LI2 as:

LI2+ sinUP UP UPi i j j k ka a a

where are the combination coefficients, are the antenna phase centres for the different signals and is the elevation of ray

, ,i j ka a a, ,

UP UP UPi j k




Question 2: Using the following values for the APCs (in meters, see HW1) plot the previous expression and discuss results.

Now the combination to plot is:

1 2 50.09, 0.12, 0.28UP UP UP

1 2 5LI2_corr 6.287( 0.09sin ) 34.084( 0.12sin ) 27.797( 0.28sin )L L L

gawk '{if ($6==01) {s=sin($7*3.14/180); print $4,6.287*($14+0.09*s)- 34.084*($18+0.12*s)+27.797*($20+0.28*s),$7}}' l5dt.meas > LI2corr.dat

1.- Using previous file l5dt.meas, generate a file content: [sec LI2corr elev] 1 2 3

raph.py -f LI2corr.dat -x1 -y'($2-5133)' -s- --l "LI2[125]" -f LI2.dat -x1 -y'($3/10)' --l "Elev/10" -s- --xn 29700 --xx 49200 --yn -7 --yx 7 --xl "time (s)" --yl “L1 meters"

2.- Plot results:




Final questions:1. Discuss if the second-order

ionospheric effect can be depicted from GPS data.Hint:1. The expected I2 effect on a

ground receiver is less than 2cm in L1 delay (see HW3)

2. The estimation noise of LI2 is . .Thence even in an ideal case without APC errors and no carrier multipath (take for instance ), the noise will be over the phenomena threshold. 2.- The same question for Galileo

data (see HW2).

LI2 44.4 L

2L mm







OVERVIEW

130



Aim

Different complementary questions (theoretical and experimental) related to the LW4 are asked in this homework section.

The aim is to analyze in depth the combinations of three frequency signals.

Home Work

The assessment will be based in actual GPS measurements at frequencies L1, L2 and L5, as well as Galileo at E1, E5 and E5b frequencies



Question 1: Study the effect of the Antenna Phase Centre (APC) on the LI2 combination in order to analyze the elevation dependent pattern seen in previous of LWP2 and HW1 plots for the GPS signals (see [R-1]).

Answer :GNSS signals at different frequencies (e.g., L1, L2, L5) have, in general, different APCs and they can produce an elevation dependent effect in the LI2 combination. Indeed, referring the geometric range to a common reference (the Antenna Reference Point [ARP]) and assuming only APC in the UP component, it follows (see figure):

k k sinUPk kk

where:

k

k

UPk

APC( )kLThence, the APC correction to apply to LI2 combination is given by:

APC correction term

sinUPk k k k

k kL bias

where the bias term is due to the carrier ambiguities.

Note: the satellite APC is not considered as the deviation angle from the direction pointing to the Earth centre is less than 14º.

HW1: APC effect on the LI2 combination.



Question 2: Knowing the L1 and L2 signals APCs, estimate the L5 APC.

a) The file l5dt1260.09o has been collected by a TRIMBLE NETR8 receiver with TRM59800.00 antenna. According the ANTEX file igs05_1525.atx the antenna phase centers of L1 and L2 are given by:

Taking into account previous results, estimate the APC of L5 signal.

Note: Neglect the North/East components against the UP component. According previous table

# TRM59800.00 NONE TYPE / SERIAL NO # G01 START OF FREQUENCY # 0.37 0.86 90.02 NORTH / EAST / UP # G02 START OF FREQUENCY # 0.09 0.01 119.89 NORTH / EAST / UP


1 20.09002 , 0.11989UP UP

m m



Answer to Question 2: (Knowing the L1 and L2 APCs, estimate the L5 APC.)

The APC of L5 signal, together with the carrier ambiguity (bias), can be estimated from carrier measurements along a continuous data arch (for the three carriers) as follows:

1 1 2 2 5 5 1 1 2 2 5 5( ) ( ) ( ) ( )sin ( ) sin ( )

( )UP UP UP

L t L t L t t bias t

y t

1 5 1

55

( ) 1 sin ( )

( ) 1 sin ( ) UPn n

y t tbias

y t t

y A

1

5UP

bias TA A y

sinUPk k k

kL bias




Numerical application to L1, L2 and L5 signals:

Applying the valuesto previous equation, it follows:

1 2 5 56.287 ( ) 34.084 ( ) 27.797 ( ) 43.505sin ( ) 27.797sin ( )( )

UPL t L t L t t bias t

y t

1 1

5

( ) 1 27.797sin ( )

( ) 1 27.797sin ( ) UPn n

y t tbias

y t t

y A

1

5UP

bias TA A y 5 0.2835133.1

UPm

bias m

Using the L1, L2, L5 values of file l5dt1260.09o in the time interval 30000<t <49000 sec.(see details in the notepad).

1 2 3 1 26.287, 34.084, 27.797, 0.09002, 0.11989UP UP

a a a




b) Plot the LI2 combination corrected by the antenna phase center values: (in meters)

Now the combination to plot is:1 2 50.09, 0.12, 0.28

UP UP UP

1 2 5LI2_corr 6.287( 0.09sin ) 34.084( 0.12sin ) 27.797( 0.28sin )L L L

gawk '{if ($6==01) {s=sin($7*3.14/180); print $4,6.287*($14+0.09*s)- 34.084*($18+0.12*s)+27.797*($20+0.28*s)-5133,$7}}' l5dt.meas > LI2c.dat

1.- Using previous file l5dt.meas, generate a file content: [sec LI2corr elev] 1 2 3

graph.py -f LI2c.dat -x1 -y2 -s- --l "LI2[125]" -f LI2c.dat -x1 -y'($3/10)' -s- --l "Elev/10" --xn 29700 --xx 49200 --yn -7 --yx 7 --xl "time (s)" --yl "L1 meters"

2.- Plot results:







This HP2 is an extension of previous LWP2 and it is devoted to analysing the three different combinations of three frequency signals (see [R-1]):

1.The first and second order ionosphere-free combination (LC2, PC2).2.The geometry-free and second-order ionosphere-free combination (LI1, PI1).3.The geometry-free and first-order ionosphere-free combination (LI2, PI2).

HW2: Combinations of three-frequency measur.

The target is to analyze the suitability (or not) of such combinations to provide:• [LC2, PC2]: A measurement free from 1st and 2nd order ionospheric effects.• [LI1, PI1]: A direct measurement of the 1st order ionosphere (free from 2nd order). • [LI2, PI2]: A direct measurement of the 2nd order ionospheric effect.

The last case, i.e. LI2, PI2, has been already studied in the previous LWP2 for the GPS signals L1,L2,L5. This study will be extended here to the Galileo signals.



139

Let the carrier measurements at frequencies , and the first and second order ionospheric effects at the frequency (including instrumental delay terms). Show the following expressions, where is the geometrical range plus all other non dispersive terms and the carrier ambiguity:

, ,i j kL L L , ,i j kf f f 1 , 2i iI Iif

3/2

3/2

1 21 2

1 2

i i i

j ij i ij i

k ik i ij i

L I IL I I

L I I

2/ij i jf fwith

Consider the GPS carriers (L1, L2, L5). Show that

1 2 5 LC2

1 2 5 LI1

1 2 5 LI2

LC2 7.08 26.130 20.050 ; 33.7LI1 12.368 60.215 47.847 ; 77.9LI2 6.287 34.084 27.797 ; 44.4

L

L

L

L L LL L L

L L L

being . The carriers are assumed uncorrelated and with the same iLLC2 ; LI1 1 ; LI2 2i iI I L

Note:

1 0 2 0 5 0154 , 120 , 115 .f f f f f f

HW2: Combinations of three-frequency measur.Preliminar: Combinations of three-frequency signals derivation:

et secoShow



140

Note: The previous expressions correspond to: First order and Second order Ionosphere Free combination. Geometry-free and Second order Ionosphere Free combination. Geometry-free and First order Ionosphere Free combination.

Hint:Let the previous equations system, where , and is the

associated matrix, evaluated at the given frequencies. Thence, the coefficients of are given by . The sigmas are the square-root of diagonal elements of matrix .

[LC2,LI1, LI2]

[ ] : LC2 :[ 1 ] : LI1 :iI[ 2 ] : LI2 :iI

y Ax [ , , ]Ti j kL L Ly [ , 1 , 2 ]T

i iI Ix A

-1A -1( )TA A

1 2 5 PC2

1 2 5 PI1

1 2 5 PI2

PC2 7.081 26.130 20.050 ; 33.7PI1 12.368 60.215 47.847 ; 77.9PI2 3.144 17.042 13.899 ; 22.2

C

C

C

C C CC C C

C C C

The same question for GPS codes (C1, C2, C5). Show that:

1 1 13/2

2 12 1 12 13/2

5 15 1 15 1

1 2 21 2 21 2 2

C I IC I IC I I


[ ] : [ 1 ] i[



141

1 7 8 PC2

1 7 8 PI1

1 7 8 PI2

PC2 6.964 78.318 72.354 ; 106.8PI1 12.110 182.385 170.275 ; 249.8PI2 3.073 52.033 48.960 ; 71.5

C

C

C

C C CC C C

C C C

The same question for Galileo carriers (E1, E7, E8) and codes (C1, C7, C8). Show that:

1 1 13/2

7 17 1 17 13/2

8 18 1 18 1

1 2 21 2 21 2 2

C I IC I IC I I

1 2 5 LC2

1 2 5 LI1

1 2 5 LI2

LC2 6.694 78.318 72.354 ; 106.8LI1 12.110 182.385 170.275 ; 249.8LI2 6.146 104.067 97.921 ; 143.0

L

L

L

L L LL L L

L L L

1 1 13/2

7 17 1 17 13/2

8 18 1 18 1

1 21 21 2

L I IL I IL I I

Note:

1 1 0 7 5 0 8 5 0154 , 118 , 116.5 .E E b Ef f f f f f f f f




Questions: analyse the suitability of the combinations PC2 and LC2, obtained in the previous exercises, to navigate:

1. Calculate the theoretical noise of the (first order)-ionosphere-free combinations PC and LC and compare with the noise of first-order and second-order ionosphere- free combinations (LC2 and PC2) found in the previous exercise. Consider the Galileo signals [E1,E7] and [E1,E7,E8]. Which combinations are more suitable to navigate, the PC/LC or PC2/LC2?

2. Using files gien327sw.09o and orb15591.sp3, make a plot to compare the code noise of the first-order-ionosphere free combination of Galileo signals [E1,E7] and the first-order and second-order iono-free combination of signals [E1,E7,E8].

3. The same questions using files l5dt1260.09o, l5dt1260.09n for the GPS signals L1, L2, L5.


A) First order and Second order Iono-Free combination analysis



Answer to question A.1:Calculate the theoretical noise of the (first-order) ionosphere-free combinations PC and LC and compare with the noise of first-order and second-order ionosphere- free combinations (LC2 and PC2)?

Assuming uncorrelated and with the same or :

P L

2

[ ] [ ]

11 1

ijijij PC ij P

ij ij

Pi PjPC 2

/ij i jf f.Idem :

Thence, for the Galileo signals [C1,C7] and [C1,C7,C8], it follows:

[17]

[17]

2.812.81

PC P

LC L

PC2[178]

LC2[178]

106.8106.8

C

L

Results show that the LC2 and PC2 are two orders of magnitude noisier than the original measurements. Thus, they are not suitable to navigate.

2

[ ] [ ]

11 1

ijijij LC ij L

ij ij

Li LjLC

2 217 1 7/ 154 /118 1.703f f




Answer to question A.2:Make a plot to compare the code noise of the first-order ionosphere-free combination of Galileo signals [E1,E7] and the first-order and second-order ionosphere-free combination of Galileo signals [E1,E7,E8].

1. Using the configuration file meas.cfg, READ the RINEX and generate the MEAS message with content:

Execute:

2. From gien327.09.meas file, generate a file with the following content: (select the Galileo satellite PRN16, as well):

Note: The following expressions have been used to compute PC and LC

144

[MEAS YY Doy sec GAL PRN el Az N. list C1B L1B C1C L1C C7Q L7Q C8Q L8Q] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

gawk '{if ($5=="GAL" && $6==16){print $4,$11-1.42*($15-$11)-($12+1.42*($12-$16)), 6.96*($11-$12)-78.32*($15-$16)+72.35*($17-$18)}}' gien.meas > gienPc2Lc2.dat

Backup

gLAB_linux -input:cfg meas.cfg -input:obs gien327sw.09o -input:sp3 orb15591.sp3> gien.meas

[sec PC-LC PC2-LC2] 1 2 3

[ ] [17] 1 7 1 [ ] [17] 1 1 71 11.42 ; 1.42

1 1 1 1ij ij

ij i j i ij i i jij ij ij ij

Pi Pj Li LjPC P P P PC P P P LC P L L LC L L L




graph.py -f gienPc2Lc2.dat -x1 -y3 --l "PC2-LC2[178]" -f gienPc2Lc2.dat -x1 -y2 --l "PC-LC[17]" --cl r --yn -100 --yx 100 --xl "time (s)" --yl "meters"


[17] PC2[178]2.81 ; 106.8PC C C

As expected from the theoretical results, the measurement noise and mutipath are strongly amplified in the PC2 combination. Thence, it makes no sense to remove the second-order ionospheric effect (which is at the level of few centimetres) using this noisier combination.Note: The theoretical noise values found are:




Answer to Question A.3:Repeat the previous exercise, for the GPS signals L1, L2, L5, using the filesl5dt1260.09o, l5dt1260.09n (and satellite PRN01).

gLAB_linux -input:cfg meas.cfg -input:obs l5dt1260.09o -input:nav l5dt1260.09n -pre:dec 0| grep GPS > l5dt.meas

gawk '{if ($6==01) {print $4,$13-1.55*($17-$13)-($14+1.55*($14-$18)),7.08*($13-$14)- 26.13*($17-$18)+20.05*($19-$20)}}' l5dt.meas > l5dtPc2Lc2.dat

[MEAS YY Doy sec GPS PRN el Az N. list C1C L1C C1P L1P C2C L2C C2P L2P C5X L5X ] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1. Using the configuration file meas.cfg, READ the RINEX and generate the MEAS file with content:

2.From l5dt126.09.meas file, generate a file with the following content: [sec PC-LC PC2-LC2] 1 2 3

Resolution:




graph.py -f l5dtPc2Lc2.dat -x1 -y'($3+5140)' --l "PC2-LC2[125]" -f l5dtPc2Lc2.dat -x1 -y2 --l "PC-LC[12] " --cl r --xn 29700 --xx 49200 --yn -100 --yx 100 --xl "time(s)" --yl "m"


[12] PC2[125]2.98 ; 33.7PC C C

Although the noise is lower than in previous case with the Galileo C1, C7 and C8 signals, it does not make sense to use the PC2 combination to navigate.


Note: The theoretical noise values found are:



Questions: analyse the suitability of the combinations PI1 and LI1, obtained in the previous exercises, to estimate the STEC:

1. Calculate the theoretical noise of the geometry-free combinations PI=P2-P1 and LI=L1-L2 and compare with the noise PI1 and LI1 combinations found in the previous exercise. Consider the Galileo signals [E1,E7] and [E1,E7,E8]. Which combinations are more suitable to navigate, the PI/LI or PI1/LI1?

2. Using files gien327sw.09o and orb15591.sp3, make a plot to compare the code noise of the geometry-free combination of Galileo signals [E1,E7] and the geometry-free and first-order ionosphere-free combination of signals [E1,E7,E8].

3. The same questions using files l5dt1260.09o, l5dt1260.09n for the GPS signals L1, L2, L5.


B) Geometry-free & Second-order Iono-Free combination analysis



Answer to questions:

Question B.1: Measurement noise:

Thence, the measurement noise is strongly amplified in these combinations as in the previous case.

[ ] [ ]

[ ] [ ]

2

2ij j i PI ij P

ij i j LI ij L

PI P P

LI P L

[178]

[178]

PI1

LI1

249.8

249.8C

L

[17 ]

[17 ]

2

2

PI C

LI L

[12]

[12]

2

2

PI C

LI L

[125]

[125]

PI1

LI1

77.9

77.9C

L

GAL: E1, E7, E8 GPS: L1, L2, L5

From previous results, seen at the beginning of this exercise.




Question B.2: LI1, PI1 Plots: Following a similar procedure as in previous cases (see detailed instructions in the notepad):

Carriers

Galileo: E1, E7, E8 signals


Codes



Question B.3: LI1, PI1 Plots: Following a similar procedure as in previous cases (see detailed instructions in the notepad): :

GPS: L1, L2, L5 signals

Why does this pattern appear in LI1/PI1? (see exercise HW1)


CarriersCodes



Questions: analyse the suitability of the combinations PI2 and LI2, obtained in the previous exercises, to estimate the second-order ionosphere effect.

1. Make a plot to show the “geometry-free and first-order ionosphere-free combination (LI2) of Galileo carrier phase measurements [E1,E7,E8]. Use the files gien327sw.09o and orb15591.sp3 (and satellite PRN16). Discuss the results taking into account the theoretical noise figures found at the beginning of this exercise.

2. The same question for GPS carrier phase measurements [L1,L2,L5]. Use the files l5dt1260.09o, l5dt1260.09n (and satellite PRN01).

3. Discuss if the second-order ionospheric effect can be depicted from Galileo or GPS data.


C) Geometry-Free & First-order Iono-Free combination analysis



Answer to questions:

Question C.1: Measurement noise:

Thence, the measurement noise is strongly amplified in these combinations as in the previous case.

[178]

[178]

PI2

LI2

71.5

143.0C

L

[125]

[125]

PI2

LI2

22.2

44.4C

L

GAL: E1, E7, E8 GPS: L1, L2, L5

From previous results, seen at the beginning of this exercise.




Questions C.2 and C3 : LI2 Plots: Following a similar procedure as in previous cases (see detailed instructions in the notepad):

Galileo: E1, E7, E8 signals


Carriers

GPS: L1, L2, L5 signals

CarriersCCCCCCCCCCCCCCCCCarriiiiiiiiers

g

Carrieeeeeeeeeeeeeeers



Comment 1:In previous plot of GPS LI2 combination a clear pattern of about 2m appears (see this plot generation in LWP2).


This pattern is an elevation dependent effect due to the different Antenna Phase Centres (APC) of the L1, L2, L5 signals.

The study of this effect was done in the previous Home Work exercise (HW1).



Comment 2:After removing the error due to the APCs, the following plot is found (see this plot generation in exercise LWP2).


Nevertheless, the noise in the combination (in both cases, GPS and Galileo) is over the expected value for the 2nd order ionospheric effect (which is less than 2cm, see HW3 or [R-5]).



Question 1:

Show that the second-order ionospheric delay on the L1 carrier produced by 10 TECU of STEC is less than 2 millimetres. Which values would reach I2 in the Halloween Ionospheric Storm (October 30, 2003) analyzed in exercise 3?.

Hint:Consider the next expression where a single thin ionospheric layer approximation has been taken for the second term:

Where c is the light speed, B is the module of the earth magnetic field and o is the angle between B and the propagation direction. Units are in the International System (SI).The value can be taken for magnetic field module at the pierce point of the satellite-receiver ray with the ionospheric layer, the Ionospheric Pierce Point (IPP), (assumed at about 400 km in height). Note:

HW3: Theoretical exercises on 2nd order iono

01 3 3

1 1

7427 cos72572 cos2 2

sat

L erec

cBcI N B ds STECf f

6 8 16 21 1575.420 10 ; 2.99792458 10 / , 1 10 /f Hz c m s TECU e m

50 4 10B Tesla



Question 2:

Assuming that the STEC can be estimated from smoothed code PI, after removing the DCBs [1], with an accuracy better than 5 TECUs, and assuming a negligible error in the magnetic field B value [2], show that the second order I2 effect can be calculated from the expression given in previous question 1 with an error less than 1 millimetre of delay in the L1 carrier.

Note:[1] The DCBs can be obtained from the IONEX files available at the IGS site

ftp://cddis.gsfc.nasa.gov/gps/products/ionex/[2] The subroutines International Geomagnetic Reference Field (IGRF) could be used as well to compute the magnetic field.




Question 3:

Taking into account the previous results of HW2 and HW3, and thinking ofhigh accuracy geodetic positioning, discuss what is more suitable to remove this effect on the (first-order) ionosphere-free combination LC: To use a model or to remove this effect from a linear combination of three frequency signals?


Question 4:

The previous expressions give the I2 effect in L1 delay units. Show the following relation between the I2 delay in the L1 carrier and in the (first order) ionosphere-free combination LC[12] :

[12]

121

12

2 21LC LI I

2/ij i jf f



Thank you for your attention



R-1: J. Sanz-Subirana, J.M. Jaun-Zoroza, M. Hernández-Pajares. GNSS Data processing. Volume-I and Volume-II. ESA Publications Division, 2012.R-2: J. Sanz-Subirana, J.M. Jaun-Zoroza, M. Hernández-Pajares. Tutorial on GNSS Data Processing Laboratory Exercises. ESAInternational Summer School on GNSS, 2010.R-3: Hernández-Pajares M., J.M. Juan, J. Sanz, "EGNOS Test Bed Ionospheric Corrections Under the October and November 2003 Storms", IEEE Transactions on Geoscience and Remote Sensing, Vol.43(10), pp.2283-2293, 2005.R-4: Hernández-Pajares M., J.M. Juan, J. Sanz, "Medium Scale Traveling Disturbances Affecting GPS Measurements: Spatial and Temporal Analysis", Journal of Geophysical Research, Space Physics, Vol.111, A07-S11, 2006, (doi:10.1029/2005JA011471).R-5: Hernández-Pajares M., J.M. Juan, J. Sanz, "Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates", Journal of Geophysical Research, Solid Earth, Vol.112, pp.1-16, 2007, (doi:10.1029/2006JB004707).R-6: Hernández-Pajares M., J.M. Juan, J. Sanz, "Improving the Abel inversion by adding ground data LEO to radio occultations in the ionospheric sounding", Geophysical Research Letters Vol. 27(16), pp. 2743-2746, 2000.R-7: Hajj GA, Kursinsky ER, Romans, LJ, Bertier WI, Leroy SS. “ A technical description of atmospheric sounding by GPS occultation”. JASTP, Vo.l 64, pp 451-469, 2002.

RRese

Bibliography



The ESA/UPC GNSS-Lab Tool suite (gLAB) has been developed under the ESA Education Office contract N. P1081434.The other data files used in this study were acquired as part of NASA's Earth Science Data Systems and archived and distributed by the Crustal Dynamics Data Information System (CDDIS). To the NSPO/UCAR Agency for the FORMOSAT-3/COSMIC data.To Adrià Rovira-Garcia for his contribution to the editing of this material and gLAB updating and integrating this learning material into the GLUE.

162

Acknowledgements



Tutorial 6Differential Positioning and

carrier ambiguity fixingContact: [email protected]

Web site: http://www.gage.upc.edu






These slides can be obtained either from the server http://www.gage.upc.edu, or [email protected]. Any partial reproduction should be previously authorized by the authors, clearly referring to the slides used.


5 March 2017



This tutorial is devoted to analysing and assessing the differential positioning with carrier phase measurements (L1, L2 and LC). Five different receivers and three baselines (of 7m, 18m and 15km) are considered.

This study includes ambiguity fixing with the LAMBDA method and the analysis of different effects such as the geometry diversity and atmospheric propagation errors (troposphere and ionosphere).

Two different implementations of differential positioning are considered:• Using time-tagged measurements the baseline vector is directly estimated.• Using computed differential corrections a user receiver is positioned. The effect of synchronization errors between the reference station and the user is

also analysed for both implementations.






Preliminary computations: data files & reference values

Session A: Differential positioning of IND2-IND3 receivers (baseline: 18 metres)

Session B: Differential positioning of IND1-IND2 receivers (baseline: 7 metres, but synchronization errors)

Session C: Differential positioning of PLAN-GARR receivers(baseline: 15 km, Night time): tropospheric effects

Session D: Differential positioning of PLAN-GARR receivers(baseline: 15 km, Day time): tropospheric and Ionospheric effects

OVERVIEW

4



Introduction: gLAB processing in command linePreliminary computations: data files & reference values





OVERVIEW

5




sentences




“ paste” from


terminal.






Backup












OVERVIEW

8



Previous

Preliminary Computations



This section is devoted to computing the reference values (receivers coordinates) and to preparing the data files to be used in the exercises.

These data files will include the code and carrier measurements and the model components: geometric range, nominal troposphere and ionosphere corrections, satellite elevation and azimuth from each receiver…

This data processing will be done with gLAB for each individual receiver.

This preliminary processing will provide the baseline data files to perform computations easily using basic tools (such as awk for data files handling, to compute Double Differences of measurements) or using octave (MATLAB) scripts for the LAMBDA method implementation.

Detailed guidelines for self learning students are provided in this tutorial and in its associated notepad text file.




P.1. Computation of reference values of receiver coordinatesUsing gLAB and precise orbits and clocks, compute the PPP solution:Note: the receivers were not moving (static receivers) during the data collection.

• Data files: - Measurements: PLAN0540.13O, GARR0540.13O, IND10540.13O, IND20540.13IO, IND30540.13O.- Orbits and clocks: brdc0540.13n, igs17286.sp3, igs17286.clk - ANTEX: igs08_1719.atx.- Configuration file (to compute LC APC coordinates): gLAB_2files_APC.cfg

• Computation example:

11


gLAB_linux -input:cfg gLAB_2files_APC.cfg -input:obs PLAN0540.13O-input:orb igs17286.sp3 -input:clk igs17286.clk -input:ant igs08_1719.atx

grep OUTPUT gLAB.out | tail -1|gawk '{print "PLAN",$6,$7,$8,$15,$16,$17}' >> sta.pos

P.1. Computation of reference values of receiver coordinates


gAGE/UPC @ J. Sanz & J.M. Juan 12P.1. Computation of reference

values of receiver coordinates


@@@@@@@@@@ JJJJJJJ. nannananaaaaSaSaSaSaSaSaSaSaSSaaSSSanaaaSanaSanaaaaSaSSaSaaaaanaaaaaSSaanaannanaSSSSS zzzzzzzz &&&&&&&&&& JJJJJJJ..MM. uaJuaannnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 2222222212221211111112222221121121221212212112221112122122212121222121222112211222222222222122222222222222121212121222212222222222222222222122122222222212222122

PLAN

GARR

INDx

IND1

IND2

IND3

IND1-IND2: 7.197 mIND2-IND3: 18.380 m PLAN-GARR: 15.228 km

Barcelona

Toulouse




P.1. Computation of reference values of receiver coordinatesPlotting results:

13


graph.py -f gLAB.out -x4 -y18 -s.- -c '($1=="OUTPUT")' -l "North error" -f gLAB.out -x4 -y19 -s.- -c '($1=="OUTPUT")' -l "East error" -f gLAB.out -x4 -y20 -s.- -c '($1=="OUTPUT")' -l "UP error" --yn -.5 --yx .5 --xl "time (s)" --yl "error (m)" -t "PPP"

Note: the values of "APPROXIMATE COORDINATES written in RINEX files correspond to the precise APC of LC coordinates.

As a starting point, assume the same APC for L1 and LC



P.1. Computation of reference values of receiver coordinatesPlotting results:

14


more sta.pos

PLAN 4787328.7916 166086.0719 4197602.8893 41.418528940 1.986956885 320.0721GARR 4796983.5170 160309.1774 4187340.3887 41.292941948 1.914040816 634.5682IND1 4787678.1496 183409.7131 4196172.3056 41.403026173 2.193853893 109.5681IND2 4787678.9809 183402.5915 4196171.6833 41.403018646 2.193768411 109.5751IND3 4787689.5146 183392.8859 4196160.1653 41.402880392 2.193647610 109.5743

Question: What is the expected accuracy of the computed coordinates?




P.1. Computation of reference values of receiver coordinatesUsing octave (or MATLAB), compute the baseline length between the different

receivers:

• Computation example:

15


octave

IND1=[ 4787678.1496 183409.7131 4196172.3056 ]IND2=[ 4787678.9809 183402.5915 4196171.6833]

norm(IND1-IND2,2)ans = 7.1969

exit

Results:

IND1-IND2: 7.197 mIND2-IND3: 18.380 m IND1-IND3: 23.658 m PLAN-GARR: 15.228 kmPLAN-IND1: 17.386 kmIND1-GARR: 26.424 km




P.2. Model Components computation• The script "ObsFile.scr" generates a data file with the following content

16



• Run this script for all receivers:

ObsFile.scr PLAN0540.13O brdc0540.13nObsFile.scr GARR0540.13O brdc0540.13nObsFile.scr IND10540.13O brdc0540.13nObsFile.scr IND20540.13O brdc0540.13nObsFile.scr IND30540.13O brdc0540.13n

• Merge all files into a single file:cat ????.obs > ObsFile.dat

P.2. Model components computation



• To simplify computations, a time interval with always the same set of satellites in view and without cycle-slips is selected.

• Moreover an elevation mask of 10 degrees will be applied.

17

P. Preliminary computationsSelecting measurements: Time interval [14500:16500]


If the satellites change or cycle-slips appear during the data processing interval, care with the associated parameters handling must be taken in the navigation filter. Set up new parameters when new satellites appear

and treat the ambiguities as constant between cycle-slips and white noise when a cycle-slip happens.



• Select the satellites with elevation over 10º in the time interval [14500:16500]

18



cat ObsFile.dat|gawk '{if ($4>=14500 && $4<=16500 && $12>10) print $0}' > obs.dat













OVERVIEW

19



Session A

Differential positioning of IND2- IND3 receivers

(baseline: 18 metres)



A.1. Double differences between receivers and satellites computation

21

A. IND2- IND3 Differential positioning


DDobs.scr obs.dat IND2 IND3 06 03



------------------------------------------------------------------------------------

generates the file


A.1. Double Differences computation


For instance, the following sentence:



Compute the double differences between receivers IND2 (reference) and IND3 and satellites PRN06 (reference) and [PRN 03, 07,11, 16, 18, 19, 21, 22, 30]

22


DDobs.scr obs.dat IND2 IND3 06 03DDobs.scr obs.dat IND2 IND3 06 07DDobs.scr obs.dat IND2 IND3 06 11DDobs.scr obs.dat IND2 IND3 06 16DDobs.scr obs.dat IND2 IND3 06 18DDobs.scr obs.dat IND2 IND3 06 19DDobs.scr obs.dat IND2 IND3 06 21DDobs.scr obs.dat IND2 IND3 06 22DDobs.scr obs.dat IND2 IND3 06 30


cat DD_IND2_IND3_06_??.dat|sort -n -k +6 > DD_IND2_IND3_06_ALL.dat




----------------------------- DD_IND2_IND3_06_ALL.dat --------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

[IND2 IND3 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2]<---- IND3 ---->

---------------------------------------------------------------------------------

OUTPUT file

Where the elevation (EL) and azimuth (AZ) are taken from station IND3 (the user)

and where, (EL1, AZ1) are for satellite PNR06 (reference) and (EL1, AZ1) are for satellite PRNXX


PRN06 (ref) PRNXX





In this exercise we will considerer an implementation of differential positioning where the user estimates the baseline vector using the time-tagged measurements of the reference station.

This approach is usually referred to as relative positioning and can be applied in some applications where the coordinates of the reference station are not accurately known and where the relative position vector between the reference station and the user is the main interest. Examples are formation flying, automatic shipboard landing…

Of course, the knowledge of the reference receiver location would allow the user to compute its absolute coordinates.

A.2. IND2-IND3 Baseline vector estimation with P1 code(using the time-tagged reference station measurements)



This is a simple approach, but synchronism delays between the time tag measurements of the reference station and the user must be taken into account for real-time positioning.

We will start positioning with the code C1 measurements, which is the simplest approach. Afterwards we will focus on positioning with L1 carrier by floating and fixing ambiguities.

As the target is to perform differential positioning with carrier and carrier ambiguity fixing, we will work with double differences of measurements from the beginning (to have integer ambiguities), although these are not needed for code positioning.




Preliminary: Using octave (or MATLAB), and the receiver coordinates estimated before, compute the baseline vector between IND2-IND3. Give the results in the ENU local system (at IND3).

26

IND2=[4787678.9809 183402.5915 4196171.6833]IND3=[4787689.5146 183392.8859 4196160.1653]

IND3-IND2ans= 10.5337 -9.7056 -11.5180 (XYZ)

R=[ -sin(l) cos(l) 0 ; -cos(l)*sin(f) -sin(l)*sin(f) cos(f); cos(l)*cos(f) sin(l)*cos(f) sin(f)]

bsl_enu=R*(IND3-IND2)' ans -10.1017 -15.3551 -0.0008 (ENU)

IND3 (lat and long):

l=2.193647610*pi/180f=41.402880392*pi/180




From ECEF (x,y,z) to Local (e,n,u) coordinates

Backup



A.2.1 Estimate the baseline vector between IND2 and IND3 receivers using the code measurements of file (DD_IND2_IND3_06_ALL.dat). Note: Use the entire file (i.e. time interval [14500:16500]).

28

[DDP1]=[Los_k - Los_06]*[baseline]

3 663

167 7 6

1

63030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDPDDP

DDP

ρ ρ

ρ ρ r

ρ ρ

1 DDP1(involving satellites and )k jDDP j k

ˆ Line-Of-Sight unit vector to satelite k kρ


Baseline vectorrNotation

A.2.1. Baseline vector estimation with DDP1 (using with all epochs)





29


3 663

167 7 6

1

63030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDPDDP

DDP

ρ ρ

ρ ρ r

ρ ρ

1 DDP1(involving satellites and )k jDDP j kNotation



1 1, 1,

1, 1, 1, 1,

k j k j k jusr ref

j k j kusr usr ref ref

DDP DP DP

P P P P

1,jrefP Measurements broadcast

by the reference station.




PRN06 (ref) PRN j


30

3 663

167 7 6

1

63030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDPDDP

DDP

ρ ρ

ρ ρ r

ρ ρ

6ρ ˆ jρr



[DDP1]=[Los_k-Los_06]*[baseline]

ˆ cos( )sin( ), cos( )cos( ), sin( )jj j j j jEl Az El Az Elρ



cat DD_IND2_IND3_06_ALL.dat | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;

printf "%14.4f %8.4f %8.4f %8.4f \n",$7, -cos(e2)*sin(a2)+cos(e1)*sin(a1),




[DDP1] [ Los_k - Los_06] ------ ---------------------3.3762 0.3398 -0.1028 0.0714-7.1131 0.1725 0.5972 0.0691 4.3881 -0.6374 0.0227 0.2725

3 663

167 7 6

1

63030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDPDDP

DDP

ρ ρ

ρ ρ r

ρ ρ





gAGE/UPC @ J. Sanz & J.M. Juan 32[DDP1]=[Los_k - Los_06]*[baseline]

3 61 1

6,31 1 7 6

1 16,71 1

30 66,301 11 1

6,3 3 616,7

1 7 6

6,301

30

ˆ ˆ( ) ( )( ) ˆ ˆ( ) ( )( )

ˆ ˆ( ) ( )( )

( ) ˆ ˆ( ) ( )( )

ˆ ˆ( ) ( )

( )ˆ ( )

T

T

T

Tn n n

Tnn n

n

n

t tDDP t

t tDDP t

t tDDP t

DDP t t tDDP t

t t

DDP tt

ρ ρ

ρ ρ

ρ ρ

ρ ρ

ρ ρ

ρ 6ˆ ( )T

nt

r

ρ

The receiver was not moving (static) during the data collection. Thence, we can merge all the epochs in a single system to compute the static LS solution:

y =G x

T -1 Tx = (G G) G yT -1P = (G G)

Least Squares Solution




Solve the equations system using octave (or MATLAB) and assess the estimation error:

33

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx(1:3)'-10.2909 -15.3856 -0.6511

bsl_enu =[-10.1017 -15.3551 -0.0008]

Estimation error:

x(1:3)-bsl_enu'-0.1891639885218108-0.0304617199913011-0.6502684114849081


A.2.1. Baseline vector estimation with DDP1 (using all epochs)



A.2.2. Repeat the previous computation, but using just the two epochs: t1=14500 and t2=14515.

34

cat DD_IND2_IND3_06_ALL.dat|gawk '{if ($6==14500||$6==14515) print $0}‘ >tmp.dat

• Selecting the two epochs:

cat tmp.dat | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;

printf "%14.4f %8.4f %8.4f %8.4f \n",$7, -cos(e2)*sin(a2)+cos(e1)*sin(a1),


• Building the equations system:


A.2.1. Baseline vector estimation with DDP1 (using all epochs)



Solving the equations system using octave (or MATLAB) and assessing the estimation error:

35

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx(1:3)'-10.9525 -14.7363 -1.7780

bsl_enu =[-10.1017 -15.3551 -0.0008]

x(1:3)-bsl_enu'-0.8507637486983020.618803236835673-1.777167174810606

Questions:1.- What is the level of accuracy?2.- Why does the solution degrade when taking only two epochs?





A.3.1 Estimate the baseline vector between IND2 and IND3 receivers using the L1 carrier measurements of file (DD_IND2_IND3_06_ALL.dat).


The following procedure can be applied:1. Compute the FLOATED solution, solving the equations system with

octave. Assess the accuracy of the floated solution.2. Apply the LAMBDA method to FIX the ambiguities. Compare the

results with the solution obtained by rounding directly the floated solution and by rounding the solution after decorrelation.

3. Repair the DDL1 carrier measurements with the DDN1 FIXED ambiguities and plot results to analyze the data.

4. Compute the FIXED solution.

A.3.1. Baseline vector estimation with DDL1 (using only two epochs)

A.3. IND2-IND3 Baseline vector estimation with L1 carrier(using the time-tagged reference station measurements)



A.3.1 Estimate the baseline vector between IND2 and IND3 receivers using the L1 carrier measurements of file (DD_IND2_IND3_06_ALL.dat).

37


3 66,3 6,31 1 16,7 6,77 61 1 1

6,30 6,3030 61 1 1

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

00

T

T

T

DDL DDNDDL DDN

DDL DDN

ρ ρ

ρ ρ r

ρ ρ



y =G x





3 66,3 6,31 11 1 1 16,7 6,77 61 1 1 11 1

6,30 6,3030 61 1 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

00

T

T

T


DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

3 66,3 6,32 21 2 1 16,7 6,77 61 2 1 12 2

6,30 6,3030 61 2 1 1

2 2

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

00

T

T

T


DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]







2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P








for the two epochs required t1=14500 and t2=14515, using the input file DD_IND2_IND3_06_ALL.dat generated before.


MakeL1BslMat.scr DD_IND2_IND3_06_ALL.dat 14500 14515Execute:








octave


y1=M1(:,1);G1=M1(:,2:11);



x(1:3)'-8.9463 -15.9102 -0.78636

bsl_enu =[-10.1017 -15.3551 -0.0008]

x(1:3)'-bsl_enuans= 1.1554 -0.555 -0.78556





2. Applying the LAMBDA method to FIX the ambiguities. The following procedure can be applied (justify the computations done)Compare the different results found:

octave

c=299792458;f0=10.23e+6;f1=154*f0;lambda1=c/f1a=x(4:10)/lambda1;Q=P(4:10,4:10);

afix=iZ*round(az);-8 20 -9 -8 -10 0 -8

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 3.31968973623500afixed(:,1)'-8 20 -9 -8 -10 0 -8

Rounding the decorrelated floated solutionround(a)'-10 21 -4 -11 -4 5 -3

Rounding directly the floated solution

Decorrelation and integer LS search solution






octaveamb=lambda1*afixed(:,1);save ambL1.dat amb

Using the previous file ambL1.dat and "DD_IND2_IND3_06_ALL.dat",generate a file with the following content:

----------------------------- DD_IND2_IND3_06_ALL.fixL1 ---------------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

[IND2 IND3 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2 DDN1]<---- IND3 ---->

------------------------------------------------------------------------------------------

Note: This file is identical to file "DD_IND2_IND3_06_ALL.dat", but with the ambiguities added in the last field #18.





grep -v \# ambL1.dat > na1cat DD_IND2_IND3_06_ALL.dat|gawk '{print $4}'|sort -nu|gawk '{print $1,NR}’ >sat.lstpaste sat.lst na1 > sat.ambL1

a) Generate a file with the satellite PRN number and the ambiguities:

cat DD_IND2_IND3_06_ALL.dat|gawk 'BEGIN{for (i=1;i<1000;i++) {getline <"sat.ambL1";A[$1]=$3}}

{printf "%s %02i %02i %s %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f \n",

$1,$2,$3,$4,$5,$6,$7,$8,$9,$10,$11,$12,$13,$14,$15,$16,$17,A[$4]}' > DD_IND2_IND3_06_ALL.fixL1

b) Generate the "DD_IND2_IND3_06_ALL.fixL1" file:





graph.py -f DD_IND2_IND3_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL1-lambda1*DDN1)-DDrho" --xl "time (s)" --yl "m"

c) Make and discuss the following plots



------------------------------------------------------------------------------------------

graph.py -f DD_IND2_IND3_06_ALL.fixL1 -x6 -y'($8-$11)' -so --yn -5 --yx 5 -l "(DDL1)-DDrho" --xl "time (s)" --yl "metres"

graph.py -f DD_IND2_IND3_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -20 --yx 20 -l "(DDL1-lambda1*DDN1)" --xl "time (s)" --yl "metres"





graph.py -f DD_IND2_IND3_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL1- DDN1)-DDrho" --xl "time (s)" --yl "m"



------------------------------------------------------------------------------------------






graph.py -f DD_IND2_IND3_06_ALL.fixL1 -x6 -y'($8-$11)' -so --yn -5 --yx 5 -l "DDL1-DDrho" --xl "time (s)" --yl "m"



------------------------------------------------------------------------------------------






graph.py -f DD_IND2_IND3_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -20 --yx 20 -l "(DDL1- DDN1)" --xl "time (s)" --yl "m"



------------------------------------------------------------------------------------------






1. Computing the FIXED solution (after FIXING ambiguities).


a) Build the equations system

[DDL1-lambda1*DDN1]=[Los_k - Los_06]*[baseline]

Note: it is the same system as with the code DDP1, but using “DDL1-lambda1*DDN1” instead of “DDP1”

cat DD_IND2_IND3_06_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;

printf "%14.4f %8.4f %8.4f %8.4f \n",$8-$18, -cos(e2)*sin(a2)+cos(e1)*sin(a1),

-cos(e2)*cos(a2)+cos(e1)*cos(a1), sin(e2)+sin(e1)}' > M.dat






50

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx(1:3)'-10.1144 -15.3615 0.0031

bsl_enu =[-10.1017 -15.3551 -0.0008]

Estimation error:

x(1:3)-bsl_enu'-0.01274540575222005-0.006427057649421640.00386638285676705





A.3.2. Using the DDL1 carrier with the ambiguities FIXED, compute the LS single epoch solution for the whole interval 145000< t <165000 with the program LS.f

Note: The program LS.f computes the Least Square solution for eachmeasurement epoch of the input file (see the FORTRAN code LS.f)

The following procedure can be applied:a) generate a file with the following content;

[Time], [DDL1-lambda1*DDN1], [ Los_k - Los_06]

where:Time= seconds of day DDL1-lambda1*DDN1= Prefit residulas (i.e., "y" values in program LS.f)Los_k-Los_06 = The three components of the geometry matrix


A.3.2. Baseline vector estimation with DDL1 (single epoch LS, whole interval)





cat DD_IND2_IND3_06_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$8-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),


[Time], [DDL1-lambda1*DDN1], [Los_k - Los_06]







Plot the baseline estimation error

graph.py -f L1fix.pos -x1 -y'($2+10.1017)' -s.- -l "North error" -f L1fix.pos -x1 -y'($3+15.3551)' -s.- -l "East error" -f L1fix.pos -x1 -y'($4+0.0008)' -s.- -l "UP error"

--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "Baseline error”

Note:bsl_enu =[-10.1017 -15.3551 -0.0008]





Baseline estimation error






A.3.3. Repeat previous computations, but using the Unsmoothed code P1. i.e., compute the LS single epoch solution for the whole interval 145000< t <165000 with the program LS.f

The same procedure as in previous case can be applied, but using the code DDP1 instead of the carrier “DDL1-lambda1*DDN1”

a) generate a file with the following content;

[Time], [DDP1], [ Los_k - Los_06]

where:Time= seconds of day DDP1= Prefit residulas (i.e., "y" values in program lms1)Los_k-Los_06 = The three components of the geometry matrix


A.3. IND2-IND3 Baseline vector estimation (using the time-tagged reference station measurements)

A.3.3. Baseline vector estimation with DDP1 (single epoch LS, whole interval)




cat DD_IND2_IND3_06_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$7,-cos(e2)*sin(a2)+cos(e1)*sin(a1),

-cos(e2)*cos(a2)+cos(e1)*cos(a1),-sin(e2)+sin(e1)}' > P1model.dat

[Time], [DDP1], [Los_k – Los_06]


cat P1model.dat |LS > P1.pos






with the unsmoothed

code Questions: 1.- Discuss the results by

comparing them with the previous ones with DDL1 carrier.

2.- Discuss the pattern seen in the plot.





Repeat the previous computations A.3., but using two epochs more distant in time : t1=14500 and t2=14600 (instead of t2=14515).

58

A.4. IND2- IND3 Baseline vector estimation Geometric diversity effect




A.3.1. Baseline estimation with L1 Geometry diversity effect.



Solving the equations system using octave (or MATLAB) and assessing the estimation error:

59

octave


y1=M1(:,1);G1=M1(:,2:11);

y2=M2(:,1);G2=M2(:,2:11);

W=inv(diag(ones(1,7))+ones(7))*2*1e-4;P=inv(G1'*W*G1+G2'*W*G2);x=P*(G1'*W*y1+G2'*W*y2);10.9525 -14.7363 -1.7780

bsl_enu =[-10.1017 -15.3551 -0.0008]

x(1:3)-bsl_enu'0.33169326648299170.1688471989256399-0.0813273504816880





octave


afix=iZ*round(az);-8 20 -9 -8 -10 0 -8










Optional:Repeat the computation taking t1=14500 and t2=15000

Questions: 1.- Has the accuracy improved?2.- Are the ambiguities well fixed?3.- Has the reliability improved? Why?





In the previous exercise we have considered an implementation of differential positioning where the user estimates the baseline vector from the time-tagged measurements of the reference station.

In the next exercises, we will consider the common implementation of Differential positioning, where the reference receiver coordinates are accurately known and used to compute range corrections for each tracked satellite in view. Then, the user applies these corrections to improve the positioning.

In the next example, a short baseline is processed (18 metres) and the range corrections are given as the measurements corrected by the geometric range. The differential atmospheric propagation errors can be assumed as zero for this very short baseline.

A.5. IND2-IND3 differential positioning with P1 code(using the computed differential corrections)

A.5.1. Differential positioning with DDP1 (using with all epochs)



Unlike in the previous implementation, the synchronism errors between the time-tagged measurements will be not critical in this approach, as the differential corrections vary slowly.

We will start positioning with the code C1 measurements, which is the simplest approach. Afterwards we will focus on positioning with L1 carrier by floating and fixing ambiguities.

As the target is to perform differential positioning with carrier and carrier ambiguity fixing, we will work with double differences of measurements from the beginning (to have integer ambiguities), although they are not needed for code positioning.




A.5.1 Using code DDP1 measurements, estimate the coordinates of receiver IND3 taking IND2 as a reference receiver.


64

[DDP1-DDRho]=[Los_k - Los_06]*[dr]

3 66,3 6,3

16,7 6,7 7 6

1

6,30 6,3030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDP DDDDP DD

DDP DD

ρ ρ

ρ ρ dr

ρ ρ

1 DDP1(involving satellites and )k jDDP j kˆ Line-Of-Sight unit vector to satelite k kρ


3 0, 3-IND INDdr r rNotation







65




Notation

1 1,j j j

ref refPRC PComputed corrections broadcast by the reference station.

3 66,3 6,3

16,7 6,7 7 6

1

6,30 6,3030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDP DDDDP DD

DDP DD

ρ ρ

ρ ρ dr

ρ ρ

1 1, 1,

1, 1, 1, 1,

k j k j k j k j k j k jusr usr ref ref

j j k k j j k kusr usr usr usr ref ref ref ref

DDP DD D P D P

P P P P

1 DDP1(involving satellites and )k jDDP j k




PRN06 (ref) PRN j


Note: Use the entire file (i.e. time interval [14500:16500]).

66

[DDP1-DDRho]=[Los_k-Los_06]*[dr]

6ρ ˆ jρ

3 66,3 6,3

16,7 6,7 7 6

1

6,30 6,3030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDP DDDDP DD

DDP DD

ρ ρ

ρ ρ dr

ρ ρ



3 0, 3-IND INDdr r rˆ cos( )sin( ), cos( )cos( ), sin( )j

j j j j jEl Az El Az Elρ



cat DD_IND2_IND3_06_ALL.dat | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;





[DDP1-DDRho] [Los_k - Los_REF] ------ ---------------------3.3762 0.3398 -0.1028 0.0714-7.1131 0.1725 0.5972 0.0691 4.3881 -0.6374 0.0227 0.2725


3 66,3 6,3

16,7 6,7 7 6

1

6,30 6,3030 61

ˆ ˆ

ˆ ˆ

ˆ ˆ

T

T

T

DDP DDDDP DD

DDP DD

ρ ρ

ρ ρ dr

ρ ρ




gAGE/UPC @ J. Sanz & J.M. Juan 68[DDPL1]=[Los_k - Los_06]*[baseline]

3 61 1

6,3 6,31 1 1 7 6

16,7 6,71 1 1

6,30 6,301 1 1

6,3 6,31 16,7 6,7

1 1

6,30 6,301 1

ˆ ˆ( ) ( )( ) ( ) ˆ ˆ( ) (( ) ( )

( ) ( )

( ) ( )( ) ( )

( ) ( )

T

n

n

n

t tDDP t DD t

tDDP t DD t

DDP t DD t

DDP t DD tDDP t DD t

DDP t DD t

ρ ρ

ρ ρ 1

30 61 1

3 6

7 6

30 6

)

ˆ ˆ( ) ( )

ˆ ˆ( ) ( )

ˆ ˆ( ) ( )

ˆ ˆ( ) ( )

T

T

T

n n

T

n n

T

n n

t

t t

t t

t t

t t

ρ ρdr

ρ ρ

ρ ρ

ρ ρ

The receiver was not moving (static) during the data collection. Therefore, we can merge all the epochs in a single system to compute the static

LS solution:

y =G x

T -1 Tx = (G G) G yT -1P = (G G)

Least Squares Solution





69

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx'-0.1892 -0.0305 -0.6504

Absolute coordinates of IND3.

Taking into account that the ”a priori” coordinates of IND3 are: IND3=[4787689.5146 183392.8859 4196160.1653 ]

Therefore the estimated absolute coordinates of IND3 are:IND3+ x(1:3)'ans= 4787689.3254 183392.8554 4196159.5149


Note: as we have used the true coordinates of IND3 as the ”a priori” to linerize the model, the vector x provides the estimation error directly.




A.5.2. Repeat the previous computation, but using just the two epochs: t1=14500 and t2=14515.

70

cat DD_IND2_IND3_06_ALL.dat|gawk '{if ($6==14500||$6==14515) print $0}‘ >tmp.dat

• Selecting the two epochs:

• Building the equations system:

A.5.2. Estimate baseline vector with DDP1 (using only two epochs)

cat tmp.dat | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;


-cos(e2)*cos(a2)+cos(e1)*cos(a1),-sin(e2)+sin(e1)}' > M.dat





71

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx(1:3)'-0.8509 0.6190 -1.7783


Taking into account that the ”a priory” coordinates of IND3 are: IND3=[4787689.5146 183392.8859 4196160.1653 ]

Thence the estimated absolute coordinates of IND3 are:IND3+ x(1:3)'ans= 4787688.6637 183393.5049 4196158.3870


Questions:What is the level of accuracy?Why does the solution degrade when taking only two epochs?




A.6.1 Using DDL1 carrier measurements, estimate the coordinates of receiver IND3 taking IND2 as a reference receiver.

Consider only the two epochs used in the previous exercise: t1=14500 and t2=14515.






A.6.1. Estimate IND3 coordinates with DDL1 (using only two epochs)

A.6. IND2-IND3 differential positioning with L1 carrier(using the computed differential corrections)



A.6.1 Estimate the coordinates of receiver IND3 taking IND2 as reference receiver, using the L1 carrier measurements of file (DD_IND2_IND3_06_ALL.dat)

73


3 66,3 6,3 6,31 1 16,7 6,7 6,77 61 1 1

6,30 6,30 6,3030 61 1 1

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ

00

Notation


y =G x





3 66,3 6,3 6,31 11 1 1 1 16,7 6,7 67 61 1 1 1 11 1

6,30 6,3030 61 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T

t tDDL t DD t DDNDDL t DD t DDNt t

DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

00 ,7

6,301 1DDN

3 66,3 6,3 6,32 21 2 2 1 16,7 6,7 67 61 2 2 1 12 2

6,30 6,3030 61 2 2

2 2

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

00 ,7

6,301 1DDN

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]







2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P

T -1 Tx = (G WG) G WyT -1P = (G WG) A.6.1. Estimate IND3 coordinates with

DDL1 (using only two epochs)








MakeL1DifMat.scr DD_IND2_IND3_06_ALL.dat 14500 14515Execute:








octave


y1=M1(:,1);G1=M1(:,2:11);



x(1:3)'0.9484 -0.3299 -0.8996

Taking into account that the ”a priori” coordinates of IND3 are: IND3=[4787689.5146 183392.8859 4196160.1653]

Thence the estimated absolute coordinates of IND3 are:IND3+ x(1:3)'4787690.4630 183392.5560 4196159.2657






octave


afix=iZ*round(az);-8 20 -9 -8 -10 0 -8









Questions: 1. - Can the ambiguities be well fixed?2. - Has the reliability improved? Why?3. - The values found for the ambiguities are

the same than in the previous case?







Using the previous file ambL1.dat and "DD_IND2_IND3_06_ALL.dat",generate a file with the following content:



------------------------------------------------------------------------------------------













The ambiguities do not change. Therefore, the file DD_IND2_IND3_06_ALL.fixL1generated in the previous exercise can be used here.







[DDL1-DDRho-lambda1*DDN1]=[Los_k - Los_06]*[dr]

Note: this is the same system as with the code DDP1, but using “DDL1-DDRho-lambda1*DDN1” instead of “DDP1”


printf "%14.4f %8.4f %8.4f %8.4f \n",$8-$11-$18, -cos(e2)*sin(a2)+cos(e1)*sin(a1),







83

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx-0.01278982304138015-0.006417005913869300.00369003097108713


Taking into account that the ”a priori” coordinates of IND3 are: IND3=[4787689.5146 183392.8859 4196160.1653 ]

Therefore the estimated absolute coordinates of IND3 are:IND3+ x(1:3)'4787689.5018 183392.8795 4196160.1690


Question: Is the accuracy similar to that in the previous case, when estimating the baseline vector?




A.6.2. Using the DDL1 carrier with the ambiguities FIXED, compute the LS single epoch solution for the whole interval 145000< t <165000 with the program LS.f

Note: The program "LS.f" computes the Least Square solution for eachmeasurement epoch of the input file (see the FORTRAN code "LS.f")

The following procedure can be applieda) generate a file with the following content;

[Time], [DDL1-DDRho-lambda1*DDN1], [ Los_k - Los_06]

where:Time= seconds of day DDL1-DDRho-lambda1*DDN1= Prefit residulas (i.e., "y" values in program LS.f)Los_k-Los_06 = The three components of the geometry matrix


A.6.2. Estimate IND3 coordinates with DDL1 (single epoch LS, whole interval)





cat DD_IND2_IND3_06_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$8-$11-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),


[Time], [DDL1-DDRho-lambda1*DDN1], [Los_k - Los_06]








graph.py -f L1fix.pos -x1 –y2 -s.- -l "North error" -f L1fix.pos -x1 –y3 -s.- -l "East error" -f L1fix.pos -x1 –y4 -s.- -l "UP error"

--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t “IND2-IND3: 18.38m: L1 ambiguities fixed”





Differential Positioning error




Question: compare this plot with that obtained previously when estimating the baseline from the time-tagged measurements. Are the errors similar?









OVERVIEW

88



Session B

Differential positioning of IND1- IND2 receivers

(baseline 7 metres andnot synchronised receivers)



The same exercises as in previous session will be repeated here for IND1 andIND2 receivers.

These receivers are located in the same environment as IND2 and IND3 andthe baseline is even shorter (7 metres, instead of 18 metres).

B. Differential positioning of IND1- IND2 receivers

The main difference in the receiver clock offset:• The receivers IND2 and IND3 apply clock

steering and have a very short clock offset(just a tenth of nanoseconds), while thereceiver IND1 has a large clock offset drift,accumulating up to 1 ms.

• The effect of the synchronization errors onthe two different implementations ofdifferential positioning used in the previoussession is one of the targets of thislaboratory session.

900000000909090909999990909009090009099909090090900909099900909009090909090000999009090900900900900090090009000090900900090999009000000909000090090000090000099990009000900090009909

IND1

IND2

IND3

IND1-IND2: 7.197 mIND2-IND3: 18.380 m



B.1. Double differences between receivers and satellites computation

91

B. IND1- IND2 Differential positioning


DDobs.scr obs.dat IND1 IND2 06 03



------------------------------------------------------------------------------------

generates the file



The script "DDobs.scr" computes double differences between receivers and satellites from file obs.dat.




Compute the double differences between receivers IND1 (reference) and IND2 and satellites PRN06 (reference) and [PRN 03, 07,11, 16, 18, 19, 21, 22, 30]

92


DDobs.scr obs.dat IND1 IND2 06 03DDobs.scr obs.dat IND1 IND2 06 07DDobs.scr obs.dat IND1 IND2 06 11DDobs.scr obs.dat IND1 IND2 06 16DDobs.scr obs.dat IND1 IND2 06 18DDobs.scr obs.dat IND1 IND2 06 19DDobs.scr obs.dat IND1 IND2 06 21DDobs.scr obs.dat IND1 IND2 06 22DDobs.scr obs.dat IND1 IND2 06 30


cat DD_IND1_IND2_06_??.dat|sort -n -k +6 > DD_IND1_IND2_06_ALL.dat

B.1. Double Differences computation



----------------------------- DD_IND1_IND2_06_ALL.dat --------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

[IND1 IND2 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2]<---- IND2 ---->

---------------------------------------------------------------------------------

OUTPUT file

Where the elevation (EL) and azimuth (AZ) are taken from station IND2 (the user)

and where (EL1, AZ1) are for satellite PNR06 (reference) and (EL1, AZ1) are for satellite PRNXX


B.1. Double Differences computation


PRN06 (ref) PRN j



Preliminary: Using octave (or MATLAB), and the receiver coordinates estimated before, compute the baseline vector between IND1-IND2. Give the results in the ENU local system (at IND2).

94

IND1=[4787678.1496 183409.7131 4196172.3056]IND2=[4787678.9809 183402.5915 4196171.6833]

IND2-IND1ans= 0.8313 -7.1216 -0.6223 (XYZ)

R=[ -sin(l) cos(l) 0 ; -cos(l)*sin(f) -sin(l)*sin(f) cos(f); cos(l)*cos(f) sin(l)*cos(f) sin(f)]

bsl_enu=R*(IND2-IND1)' ans -7.1482 -0.8359 0.0070 (ENU)

IND2 (lat and long):

l= 2.193768411 *pi/180f= 41.403018646 *pi/180

B.2. IND1-IND2 Baseline vector estimation with P1 code(using the time-tagged reference station measurements)



B.3.1 Estimate the baseline vector between IND1 and IND2 receivers using the L1 carrier measurements of file (DD_IND1_IND2_06_ALL.dat).







B.3.1. Baseline vector estimation with DDL1 (using only two epochs)

B.3. IND1-IND2 Baseline vector estimation with L1 carrier(using the time-tagged reference station measurements)



B.3.1 Estimate the baseline vector between IND1 and IND2 receivers using the L1 carrier measurements of file (DD_IND1_IND2_06_ALL.dat).

96


3 66,3 6,31 1 16,7 6,77 61 1 1

6,30 6,3030 61 1 1

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

00

T

T

T

DDL DDNDDL DDN

DDL DDN

ρ ρ

ρ ρ r

ρ ρ

Notation


y =G x





3 66,3 6,31 11 1 1 16,7 6,77 61 1 1 11 1

6,30 6,3030 61 1 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

T

T

T


DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

00

3 66,3 6,32 21 2 1 16,7 6,77 61 2 1 12 2

6,30 6,3030 61 2 1 1

2 2

ˆ ˆ( ) ( ) 1 0 0( )0 1 0ˆ ˆ( ) ( ) ( )

0 0 0 1( ) ˆ ˆ( ) ( )

00

T

T

T


DDL t DDNt t

ρ ρ

ρ ρ r

ρ ρ

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]







2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P


















octave


y1=M1(:,1);G1=M1(:,2:11);



x(1:3)'-8.8883 -2.2187 2.4998bsl_enu =[-7.1482 -0.8359 0.0070]

x(1:3)'-bsl_enuans= -1.7401 -1.3828 2.4928





octave


afix=iZ*round(az);7 -22 16 -18 -3 1 -8

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 1.61389475957901afixed(:,1)'17 -5 -2 4 -26 0 13

Rounding the decorrelated floated solutionround(a)'10 -11 13 -10 -8 7 10








Questions: 1. - Can the ambiguities be fixed?2. - Give a possible explanation about why the

ambiguities cannot be fixed

B.3. IND1-IND2 differential positioning with L1 carrier(using the computed differential corrections)





B.3.2. Baseline vector estimation with DDL1 (using t=14500, 15530)

Repeat previous processing, but using t1=14500 and

t2=15530















octave


y1=M1(:,1);G1=M1(:,2:11);



x(1:3)'-6.78678 -0.7794 -0.2434 bsl_enu =[-7.1482 -0.8359 0.0070]

x(1:3)'-bsl_enuans= 0.3614 0.0565 -0.2504





octave


afix=iZ*round(az);8 -17 24 -12 9 10 8

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 1.10192131979339afixed(:,1)'9 -16 22 -10 7 9 9

Rounding the decorrelated floated solutionround(a)'8 -17 24 -12 9 10 9








Questions: 1. - Can the ambiguities be fixed? 2. - Give a possible explanation about why the

ambiguities cannot be fixed






Repeat previous processing, but using t1=14500 and

t2=15000
















octave


y1=M1(:,1);G1=M1(:,2:11);



x(1:3)'-6.7640 -0.7441 -0.2256

bsl_enu =[-7.1482 -0.8359 0.0070]

x(1:3)'-bsl_enuans= 0.3842 0.0918 -0.2326





octave


afix=iZ*round(az);7 -18 26 -14 12 11 8









gAGE/UPC @ J. Sanz & J.M. Juan 112B.3.3. Baseline vector estimation with

DDL1 .

OPTIONAL:Repeat taking t1=14500 and t2=17000

Questions: 1. - Have the results improved?2. - Has the reliability improved?3. - Why it is not possible to fix the ambiguities?




Hint:

Check possible synchronism errors between the receivers’ time tags.

For instance, use the following sentence to compute the receiver clocks of IND1, IND2 and IND3 receivers with gLAB (the last field is the receiver clock offset):

gLAB_linux -input:obs IND10540.13O -input:nav brdc0540.13n -pre:dec 1|grep FILTERgLAB_linux -input:obs IND20540.13O -input:nav brdc0540.13n -pre:dec 1|grep FILTER gLAB_linux -input:obs IND30540.13O -input:nav brdc0540.13n -pre:dec 1|grep FILTER

Questions: Discuss how the relative receiver clock offset can affect the baseline estimation.

B.3.3. Baseline vector estimation with DDL1 .




In the previous exercise we have shown how the synchronism errors between the time-tagged measurements affect the ambiguity fixing when trying to estimate the baseline vector.



PRN06 (ref) PRN j

r


PRN06 (ref) PRN j

6ρ ˆ jρ

3 0, 3-IND INDdr r r

1 1,j j j

ref refPRC LComputed corrections broadcast by the reference station.1,

jrefL Time-tagged measurements

broadcast by reference station

6ρ ˆ jρ


IND1(ref) IND2(user) IND1(ref) IND2(user)



Next we are going to repeat the differential positioning, but using the computed differential corrections. In this case, as the corrections vary slowly, the synchronization errors will not be an issue.



PRN06 (ref) PRN j

6ρ ˆ jρr


PRN06 (ref) PRN j

6ρ3 0, 3-IND INDdr r r

1 1,j j j

ref refPRC LComputed corrections broadcast by the reference station.1,

jrefL Time-tagged measurements

broadcast by reference station

ˆ jρ


IND1(ref) IND2(user)IND1(ref) IND2(user)



B.4.1 Using DDL1 carrier measurements, estimate the coordinates of receiver IND2 taking IND1 as a reference receiver.




results with the solution obtained by rounding the floated solution directly and by rounding the solution after decorrelation.







B.4.1 Estimate the coordinates of receiver IND2 taking IND1 as the reference receiver, using the L1 carrier measurements of file (DD_IND1_IND2_06_ALL.dat)

117


3 66,3 6,3 6,31 1 16,7 6,7 6,77 61 1 1

6,30 6,30 6,3030 61 1 1

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ

00

Notation


y =G x

B.4.1. Estimate IND2 coordinates with DDL1 (using only two epochs)




3 66,3 6,3 6,31 11 1 1 1 16,7 6,7 67 61 1 1 1 11 1

6,30 6,3030 61 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

00 ,7

6,301 1DDN

3 66,3 6,3 6,32 21 2 2 1 16,7 6,7 67 61 2 2 1 12 2

6,30 6,3030 61 2 2

2 2

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

00 ,7

6,301 1DDN

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]







2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P

T -1 Tx = (G WG) G WyT -1P = (G WG) B.4.1. Estimate IND2 coordinates with









MakeL1DifMat.scr DD_IND1_IND2_06_ALL.dat 14500 14530Execute:


B.41. Estimate IND2 coordinates with DDL1 (using only two epochs)






octave


y1=M1(:,1);G1=M1(:,2:11);



x(1:3)'0.3132 -0.2648 0.6237Taking into account that the ”a priori” coordinates of IND2 are: IND2=[4787678.9809 183402.5915 4196171.6833]

Therefore the estimated absolute coordinates of IND3 are:IND2+ x(1:3)'4787679.2940 183402.3267 4196172.3070





octave


afix=iZ*round(az);9 -17 22 -10 6 10 7







2. Applying the LAMBDA method to FIX the ambiguities. The following procedure can be applied (justify the computations done)Compare the different results found.



Questions:

1.- Can the ambiguities be fixed now? Why?2.- Discuss why the synchronism errors affect the

two differential positioning implementations.







Using the previous the file ambL1.dat and "DD_IND1_IND2_06_ALL.dat",generate a file with the following content:



------------------------------------------------------------------------------------------
















graph.py -f DD_IND1_IND2_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL1-lambda1*DDN1)-DDrho" --xl "time (s)" --yl "m"




------------------------------------------------------------------------------------------

graph.py -f DD_IND1_IND2_06_ALL.fixL1 -x6 -y'($8-$11)' -so --yn -5 --yx 5 -l "(DDL1-Ddrho)" --xl "time (s)" --yl "metres"

graph.py -f DD_IND1_IND2_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -10 --yx 10 -l "(DDL1-lambda1*DDN1)" --xl "time (s)" --yl "metres"





graph.py -f DD_IND1_IND2_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.06 --yx 0.06 -l "(DDL1- DDN1)-DDrho" --xl "time (s)" --yl "m"



------------------------------------------------------------------------------------------






graph.py -f DD_IND1_IND2_06_ALL.fixL1 -x6 -y'($8-$11)' -so --yn -5 --yx 5 -l ”(DDL1-DDrho)" --xl "time (s)" --yl "m"



------------------------------------------------------------------------------------------






graph.py -f DD_IND1_IND2_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -10 --yx 10 -l "(DDL1- DDN1)" --xl "time (s)" --yl "m"



------------------------------------------------------------------------------------------









[DDL1-DDRho-lambda1*DDN1]=[Los_k - Los_06]*[dr]


printf "%14.4f %8.4f %8.4f %8.4f \n",$8-$11-$18, -cos(e2)*sin(a2)+cos(e1)*sin(a1),

-cos(e2)*cos(a2)+cos(e1)*cos(a1), sin(e2)+sin(e1)}' > M.dat






131

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx0.01182339916366036 0.00164435938676216 -0.00799007795850631


Taking into account that the ”a priori” coordinates of IND2 are: IND2=[4787678.9809 183402.5915 4196171.6833]

Therefore the estimated absolute coordinates of IND2 are:IND2+ x(1:3)'ans= 4787678.9927 183402.5931 4196171.6753


Question: Is the accuracy similar to that in the previous case, when estimating the baseline vector? Why?




B.4.2. Using the DDL1 carrier with the ambiguities FIXED, compute the LS single epoch solution for the whole interval 14500< t <16500 with the program LS.f

Note: The program "LS.f" computes the Least Square solution for eachmeasurement epoch of the input file (see the FORTRAN code "LS.f")


[Time], [DDL1-DDRho-lambda1*DDN1], [ Los_k- Los_06]

where:Time= seconds of day DDL1 - DDRho-lambda1*DDN1= Prefit residulas (i.e., "y" values in program LS.f)Los_k - Los_06 = The three components of the geometry matrix


B.4.2. Estimate IND2 coordinates with DDL1 (single epoch LS, whole interval)







[Time], [DDL1-DDRho-lambda1*DDN1], [Los_k - Los_06]









--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "IND1-IND2: 7.20m: L1 ambiguities fixed"









Question: Discuss the accuracy achieved and the possible error sources that could affect this result (e.g. Antenna Phase Centres…)



B.4.3. Repeat previous computations, but using the Unsmoothed code P1. i.e., compute the LS single epoch solution for the whole interval 14500< t <16500 with the program LS.f

The same procedure as in previous case can be applied, but using the code DDP1 instead of the carrier “DDL1-lambda1*DDN1”


[Time], [DDP1-DDRho], [ Los_k - Los_06]

where:Time= seconds of day DDP1 - DDrho= Prefit residuals (i.e., "y" values in program lms1)Los_k - Los_06 = The three components of the geometry matrix


B.4.3. Estimate IND2 coordinates with DDP1 (single epoch LS, whole interval)







[Time], [DDP1-DDRho], [Los_k – Los_06]







Positioning error with the P1 code



Question: Discuss the results by comparing them with the previous ones with DDL1 carrier in the relative positioning implementation.



B.4.4. Repeat the previous computations, but for the baseline vector estimation and using the time-tagged measurements of the reference station, instead of the differential corrections.That is, compute the LS single epoch solution for the whole interval 14500< t <16500 with the program LS.f

The same procedure as in previous exercise A.6.2 can be applied, a) generate a file with the following content;

[Time], [DDL1], [ Los_k - Los_06]

where:Time= seconds of day DDL1= Prefit residulas (i.e., "y" values in program lms1)Los_k - Los_06 = The three components of the geometry matrix


B.4. IND1-IND2 differential positioning with L1 carrier

B.4.4. Baseline vector estimation with DDL1 (single epoch LS, whole interval)






[Time], [DDL1-lambda1*DDN1], [Los_k - Los_06]








graph.py -f L1bslfix.pos -x1 -y'($2+7.1482)' -s.- -l "North error" -f L1bslfix.pos -x1 -y'($3+0.8359)' -s.- -l "East error" -f L1bslfix.pos -x1 -y'($4+0.0070)' -s.- -l "UP error"

--yn -.4 --yx .4 --xl "time (s)" --yl "error (m)" -t "Baseline error: IND1-IND2: 7.20m: L1 ambiguities fixed: synchronism errors”

Note:bsl_enu =[-7.1482 -0.8359 0.0070]









Question: Discuss why does the accuracy degrades respect to the previous case. Why this large error appears?







Session C: Differential positioning of PLAN-GARR receivers (baseline: 15 km, Night time): tropospheric effects


OVERVIEW

143



Session C

Differential positioning of PLAN- GARR receivers(baseline: 15 km. Night time)

Analysis of differential tropospheric error effects



The previous exercises have been done over short baselines (lessthan 20 metres), where the errors introduced by the troposphereand ionosphere completely cancel when making differences ofmeasurements.

C. PLAN- GARR Differential positioning

In this session we will consider alarger baseline (15 km) in orderto assess the effect of theatmosphere on the ambiguityfixing and positioning.

In this session we will considerNight time data in order to havea lower ionospheric error.

@ J. Sanz & J.M. Juan 145

PLAN-GARR: 15.228 km

Barcelona

Toulouse



C.1. Double differences between receivers and satellites computation

146



DDobs.scr obs.dat PLAN GARR 06 03



------------------------------------------------------------------------------------

generates the file


C.1. Double Differences computation





Compute the double differences between receivers PLAN (reference) and GARR and satellites PRN06 (reference) and [PRN 03, 07,11, 16, 18, 19, 21, 22, 30]

147


DDobs.scr obs.dat PLAN-GARR 06 03DDobs.scr obs.dat PLAN-GARR 06 07DDobs.scr obs.dat PLAN-GARR 06 11DDobs.scr obs.dat PLAN-GARR 06 16DDobs.scr obs.dat PLAN-GARR 06 18DDobs.scr obs.dat PLAN-GARR 06 19DDobs.scr obs.dat PLAN-GARR 06 21DDobs.scr obs.dat PLAN-GARR 06 22DDobs.scr obs.dat PLAN-GARR 06 30


cat DD_PLAN_GARR_06_??.dat|sort -n -k +6 > DD_PLAN_GARR_06_ALL.dat

C.1. Double Differences computation



C.2.1 Using DDL1 carrier measurements, estimate the coordinates of receiver GARR taking PLAN as a reference receiver.







C.2.1. Estimate GARR coordinates with DDL1 (using only two epochs)

C.2. PLAN-GARR differential positioning with L1 carrier(using the computed differential corrections)



C.2.1 Estimate the coordinates of receiver GARR taking PLAN as the reference receiver, using the L1 carrier measurements of file (DD_PLAN_GARR_06_ALL.dat)

149


3 66,3 6,3 6,31 1 16,7 6,7 6,77 61 1 1

6,30 6,30 6,3030 61 1 1

ˆ ˆ 1 0 00 1 0ˆ ˆ

0 0 0 1ˆ ˆ

T

T

T


DDL DD DDN

ρ ρ

ρ ρ dr

ρ ρ

00

Notation


y =G x





3 66,3 6,3 6,31 11 1 1 1 16,7 6,7 67 61 1 1 1 11 1

6,30 6,3030 61 1 1

1 1

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

00 ,7

6,301 1DDN

3 66,3 6,3 6,32 21 2 2 1 16,7 6,7 67 61 2 2 1 12 2

6,30 6,3030 61 2 2

2 2

ˆ ˆ( ) ( ) 1 0 0( ) ( )0 1 0ˆ ˆ( ) ( ) ( ) ( )

0 0 0 1( ) ( ) ˆ ˆ( ) ( )

T

T

T


DDL t DD tt t

ρ ρ

ρ ρ dr

ρ ρ

00 ,7

6,301 1DDN

1 1y =G xy1:=y[t1] G1:=G[t1]

2 2y = G xy2:=y[t2] G2:=G[t2]

The receiver was not moving (static) during the data collection. Therefore for each epoch we have the equations system:






2

2 1 11 2 1

2

1 1 1 2

1111

yP




; -1yy = G x W = P

T -1 Tx = (G WG) G WyT -1P = (G WG) C.2.1. Estimate GARR coordinates with







for the two epochs required t1=14500 and t2=14590, using the input file DD_PLAN_GARR_06_ALL.dat generated before.


MakeL1DifMat.scr DD_PLAN_GARR_06_ALL.dat 14500 14590Execute:








octave


y1=M1(:,1);G1=M1(:,2:13);



x(1:3)'0.6879 -0.2712 -0.7924 Taking into account that the ”a priori” coordinates of GARR are: GARR=[4796983.5170 160309.1774

4187340.3887]

Therefore the estimated absolute coordinates of GARR are:GARR+ x(1:3)'4796984.2049 160308.9062 4187339.5963





octave


afix=iZ*round(az);-19337 130765326 -1759092 -1498083 130765325

130765316 130765339 122888034 130765336

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 1.19278115892607 afixed(:,1)'-19337 130765326 -1759092 -1498083 130765325

130765316 130765339 122888034 130765336

Rounding the decorrelated floated solutionround(a)' -19337 130765326 -1759092-1498083 130765325 130765316 130765339 122888034 130765336

Rounding the floated solution directly







Questions:

1. Can the ambiguities be fixed with a certain degree of confidence?

2. Repeat the computations taking: t= 14500 and 14900.3. Repeat the computations taking: t= 14500 and 15900.4. Discuss why the ambiguities cannot be fixed.





Hint:

Plot the differential Tropospheric and Ionospheric delays (from the gLAB model) and discuss their potential impact on the ambiguity fixing.

graph.py -f DD_PLAN_GARR_06_ALL.dat -x6 -y'13' -so --yn -0.06 --yx 0.06 –cl g -l "DDIono"

-f DD_PLAN_GARR_06_ALL.dat -x6 -y'12' -so --cl r --yn -0.06 --yx 0.06

-l "DDTropo" --xl "time (s)" --yl "metres"




gAGE/UPC @ J. Sanz & J.M. Juan 157C.2.1. Estimate GARR coordinates with





Repeat the previous exercise, but correcting the measurements with the nominal tropospheric correction model.

C.3. PLAN-GARR differential positioning with L1 carrier(using the computed differential corrections including troposphere)



C.3.1 Using DDL1 carrier measurements, estimate the coordinates of receiver GARR taking PLAN as a reference receiver and correcting troposphere.







C.3.1. Estimate GARR coordinates with DDL1 (using tropospheric corrections)




The script MakeL1DifTrpMat.scr builds the equations system



[DDL1-DDRho-Trp]=[ Los_k- Los_06]*[dr] + [ A ]*[ 1*DDN1]

MakeL1DifTrpMat.scr DD_PLAN_GARR_06_ALL.dat 14500 14590

Execute:








octave


y1=M1(:,1);G1=M1(:,2:13);



x(1:3)'0.2140 -0.1732 0.1535

Taking into account that the ”a priori” coordinates of GARR are: GARR=[4796983.5170 160309.1774

4187340.3887]Therefore the estimated absolute coordinates of GARR are:GARR+ x(1:3)'4796983.7310 160309.0042 4187340.5422





octave


afix=iZ*round(az) -19333 130765338 -1759080 -1498083 130765319

130765324 130765334 122888028 130765333

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 2.47022808203678afixed(:,1)' -19333 130765338 -1759080 -1498083 130765319

130765324 130765334 122888028 130765333

Rounding the decorrelated floated solutionround(a)' -19334 130765336 -1759081

-1498083 130765320 130765323 130765334 122888029 130765334








Questions:

Can the ambiguities be fixed now?Discuss, why?







Using the previous file ambL1.dat and "DD_PLAN_GARR_06_ALL.dat",generate a file with the following content:

----------------------------- DD_PLAN_GARR_06_ALL.fixL1 ---------------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

[PLAN GARR 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2 DDN1]<---- GARR ---->

------------------------------------------------------------------------------------------

Note: This file is identical to file "DD_PLAN_GARR_06_ALL.dat", but with the ambiguities added in the last field #18.





grep -v \# ambL1.dat > na1cat DD_PLAN_GARR_06_ALL.dat|gawk '{print $4}'|sort -nu|gawk '{print $1,NR}’ >sat.lstpaste sat.lst na1 > sat.ambL1


cat DD_PLAN_GARR_06_ALL.dat|gawk 'BEGIN{for (i=1;i<1000;i++) {getline <"sat.ambL1";A[$1]=$3}}


$1,$2,$3,$4,$5,$6,$7,$8,$9,$10,$11,$12,$13,$14,$15,$16,$17,A[$4]}' > DD_PLAN_GARR_06_ALL.fixL1

b) Generate the "DD_PLAN_GARR_06_ALL.fixL1" file:





graph.py -f DD_PLAN_GARR_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.6 --yx 0.6 -l "(DDL1-lambda1*DDN1)-DDRho" --xl "time (s)" --yl "m"



[PLAN GARR 06 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrp DDIon El1 Az1 El2 Az2 DDN1]<---- GARR ---->

------------------------------------------------------------------------------------------

graph.py -f DD_PLAN_GARR_06_ALL.fixL1 -x6 -y'($8-$18-$11-$12)' -so --yn -0.6 --yx 0.6 -l "(DDL1-lambda1*DDN1)-DDRho-DDTrp" --xl "time (s)" --yl "m"



graph.py -f DD_PLAN_GARR_06_ALL.fixL1 -x6 -y'($8-$18-$12)' -so --yn -0.06 --yx 0.06 -l "(DDL1-lambda1*DDN1)-DDTrp" --xl "time (s)" --yl "m"

graph.py -f DD_PLAN_GARR_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -15000 --yx 15000 -l "(DDL1-lambda1*DDN1)" --xl "time (s)" --yl "m"



graph.py -f DD_PLAN_GARR_06_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.6 --yx 0.6 -l "(DDL1- DDN1)-DDRho" --xl "time (s)" --yl "m"





------------------------------------------------------------------------------------------




graph.py -f DD_PLAN_GARR_06_ALL.fixL1 -x6 -y'($8-$18-$11-$12)' -so --yn -0.6 --yx 0.6 -l "(DDL1- DDN1)-DDRho-DDTrp"--xl "time (s)" --yl "m"





------------------------------------------------------------------------------------------









------------------------------------------------------------------------------------------




graph.py -f DD_PLAN_GARR_06_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -15000 --yx 15000 -l "(DDL1- DDN1)"--xl "time (s)" --yl "m"





------------------------------------------------------------------------------------------







[DDL1-DDRho-DDTrp-lambda1*DDN1]=[Los_k - Los_06]*[dr]


printf "%14.4f %8.4f %8.4f %8.4f \n",$8-$11-$12-$18, -cos(e2)*sin(a2)+cos(e1)*sin(a1),







172

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx-0.00290189178833524 0.00354027112026342 0.04277612243282228

Absolute coordinates of GARR.

Taking into account that the ”a priori” coordinates of IND2 are: GARR=[4796983.5170 160309.1774 4187340.3887]

Therefore the estimated absolute coordinates of GARR are:GARR+ x(1:3)'ans= 4796983.5141 160309.1809 4187340.4315





C.3.2. Using the DDL1 carrier with the ambiguities FIXED, compute the LS single epoch solution for the whole interval 14500< t <16500 with the program LS.f

Note: The program LS.f computes the Least Square solution for eachmeasurement epoch of the input file (see the FORTRAN code "LS.f")


[Time], [DDL1-DDRho-Trp-lambda1*DDN1], [Los_k - Los_06]

where:Time= seconds of day DDL1 – DDRho –DDTrp – lambda1*DDN1= Prefit residulas (i.e., "y" values in program LS.f)Los_k – Los_06 = The three components of the geometry matrix (i.e., matrix "a" in program

LS.f)






cat DD_IND1_IND2_06_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$8-$11-$12-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),


[Time], [DDL1-DDRho-DDTrp-lambda1*DDN1], [Los_k - Los_06]









--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "PLAN-GARR: 15.2 km: L1 ambiguities fixed: No wet tropo estim."









Question: Discuss the possible sources of the bias found in the vertical component.




C.3.2. Estimate GARR coordinates with DDL1 (APC error effect)

Remember that the reference coordinates have been taken relative to the Antenna Phase Centre in the ionosphere-free combination LC

Question:Taking into account the following parameters of the PLAN and GARR antennas, calculate the relative error introduced by the difference between the L1 and LC APC of both receivers in the differential positioning.

According to the RINEX and ANTEX files, we have:

GARR: TRM41249.00 (millimetres)G01 0.28 0.49 55.91 NORTH / EAST / UPG02 0.15 0.46 58.00

PLAN: TRM55971.00 (millimetres)G01 1.29 -0.19 66.73 NORTH / EAST / UPG02 0.38 0.61 57.6





Then the relative error:DL1(GARR-PLAN)=+1.7cm

GARR:dL1=5.591 cmdL2=5.800 cmdLC=1/(g-1)*(g*dL1-dL2)=5.3cmThen:dL1=dLC+0.3 cm

L1 (PLAN)

L1 (GARR)

LC (GARR) LC (PLAN)

PLAN:dL1=6.673 cmdL2=5.769 cmdLC=1/(g-1)*(g*dL1-dL2)=8.1cmThen:dL1=dLC-1.4 cm

+0.3 cm

-1.4 cm

Solution:



Repeat the positioning error plot, but correcting for the relative Antenna Phase Centres (APCs):

graph.py -f L1fix.pos -x1 –y2 -s.- -l "North error" -f L1fix.pos -x1 –y3 -s.- -l "East error" -f L1fix.pos -x1 –y '($4-0.017)' -s.- -l "UP error"

--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "PLAN-GARR: 15.2 km: L1 amb. fixed: -1.7 cm dAPC_L1: No wet tropo estim."








Question: Discuss on the remaining error sources which could explain the error bias found in the vertical component.




C.3.3. Repeat the previous computations, but using the Unsmoothed code P1. i.e., compute the LS single epoch solution for the whole interval 145000< t <165000 with the program LS.f

The same procedure as in previous case can be applied, but using the code DDP1 instead of the carrier “DDL1 – lambda1*DDN1”


[Time], [DDP1-DDRho-DDTrp], [ Los_k - Los_06]

where:Time= seconds of day DDP1 – DDRho-DDTrp= Prefit residulas (i.e., "y" values in program lms1)Los_k – Los_06 = The three components of the geometry matrix



C.3.3. Estimate GARR coordinates (using tropospheric corrections)






[Time], [DDP1-DDRho-DDTrp], [Los_k – Los_06]



C.3. PLAN-GARR differential positioning (using the computed differential corrections including troposphere)




Positioning error with the

unsmoothed code

Question: Discuss the results by comparing them with the previous ones with DDL1 carrier.

C.3. PLAN-GARR differential positioning (using the computed differential corrections including troposphere)









Session D: Differential positioning of PLAN-GARR receivers (baseline: 15 km, Day time): tropospheric and Ionospheric effects

OVERVIEW

184



Session D

Differential positioning of PLAN- GARR receivers

(baseline: 15 km. Day time)Analysis of differential tropospheric

and Ionospheric error effects



The previous session has been carried out using measurements collected during the night time, when the effect of the ionosphere is lower.The effect of the ionosphere over a baseline of 15km (and in solar maximum conditions) will be assessed in this session using day-time measurements.The exercise will end with the computation of the unambiguous DDSTEC from dual-frequency carrier measurements (after fixing the ambiguities in both carriers).The solutions computed using the DDL1 carrier (with the ambiguity fixed) corrected by the unambiguous DDSTEC and corrected by the nominal Klobuchar model will be compared.Finally, the solution using the unambiguous DDLC carrier (iono-free combination) will be also computed to compare results.

D. Differential positioning of PLAN-GARR receivers



• Select the satellites within the time interval [39000:41300]. Exclude satellites PRN01 and PRN31 in order to have the same satellites over the whole interval

187

D.1 Measurements selection


cat ObsFile.dat|gawk '{if ($4>=39000 && $4<=41300 && $2!=01 && $2!=31) print $0}' > obs.dat




D.1 Model components computation



Compute the double differences between receivers PLAN (reference) and GARR and satellites PRN13 (reference) and [PRN 02, 04, 07, 10, 17, 20, 23, 32]

188

DDobs.scr obs.dat PLAN-GARR 13 02DDobs.scr obs.dat PLAN-GARR 13 04DDobs.scr obs.dat PLAN-GARR 13 07DDobs.scr obs.dat PLAN-GARR 13 10DDobs.scr obs.dat PLAN-GARR 13 17DDobs.scr obs.dat PLAN-GARR 13 20DDobs.scr obs.dat PLAN-GARR 13 23DDobs.scr obs.dat PLAN-GARR 13 32

Merge the files into a single file and sort by time:

cat DD_PLAN_GARR_13_??.dat|sort -n -k +6 > DD_PLAN_GARR_13_ALL.dat

D.2. Double Differences computation

D.2. Computing Double Differences



D.3.1 Using DDL1 carrier measurements, estimate the coordinates of receiver GARR taking PLAN as a reference receiver and correcting troposphere.







D.3.1. Estimate GARR coordinates with DDL1 (using tropospheric corrections)

D.3. PLAN-GARR differential positioning with L1 carrier(using the computed differential corrections including troposphere)








Execute:








octave


y1=M1(:,1);G1=M1(:,2:12);



x(1:3)'-0.3262 0.0268 0.09012







octave


afix=iZ*round(az) -1372641 1731966 2313787 592316 -878242 -401400 -475026 1855925

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 3.54169992923790afixed(:,1)'

-1372641 1731966 2313787 592316 -878242 -401400 -475026 1855925

Rounding the decorrelated floated solutionround(a)'

-1372640 1731967 2313786 592317 -878241 -401401 -475027 1855923










Using the previous the file ambL1.dat and "DD_PLAN_GARR_13_ALL.dat",generate a file with the following content:



------------------------------------------------------------------------------------------

Note: This file is identical to file "DD_PLAN_GARR_13_ALL.dat", but with the ambiguities added in the last field #18.







cat DD_PLAN_GARR_13_ALL.dat|gawk 'BEGIN{for (i=1;i<1000;i++) {getline <"sat.ambL1";A[$1]=$3}}


$1,$2,$3,$4,$5,$6,$7,$8,$9,$10,$11,$12,$13,$14,$15,$16,$17,A[$4]}' > DD_PLAN_GARR_13_ALL.fixL1

b) Generate the "DD_PLAN_GARR_13_ALL.fixL1" file:





graph.py -f DD_PLAN_GARR_13_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.6 --yx 0.6 -l "(DDL1-lambda1*DDN1)-DDRho" --xl "time (s)" --yl "m"



[PLAN GARR 13 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrp DDIon El1 Az1 El2 Az2 DDN1]<---- GARR ---->

------------------------------------------------------------------------------------------

graph.py -f DD_PLAN_GARR_13_ALL.fixL1 -x6 -y'($8-$18-$11-$12)' -so --yn -0.6 --yx 0.6 -l "(DDL1-lambda1*DDN1)-DDRho-DDTrp " --xl "time (s)" --yl "m"



graph.py -f DD_PLAN_GARR_13_ALL.fixL1 -x6 -y'($8-$18-$12)' -so --yn -0.06 --yx 0.16 -l "(DDL1-lambda1*DDN1)-DDTrp " --xl "time (s)" --yl "m"

graph.py -f DD_PLAN_GARR_13_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -15000 --yx 15000 -l "(DDL1-lambda1*DDN1)" --xl "time (s)" --yl "m"



graph.py -f DD_PLAN_GARR_13_ALL.fixL1 -x6 -y'($8-$18-$11)' -so --yn -0.6 --yx 0.6 -l "(DDL1- DDN1)-DDRho" --xl "time (s)" --yl "m"





------------------------------------------------------------------------------------------









------------------------------------------------------------------------------------------









------------------------------------------------------------------------------------------




graph.py -f DD_PLAN_GARR_13_ALL.fixL1 -x6 -y'($8-$18)' -so --yn -15000 --yx 15000 -l "(DDL1- DDN1)"--xl "time (s)" --yl "m"





------------------------------------------------------------------------------------------




4. Computing the FIXED solution for the whole interval (after FIXING ambiguities).




cat DD_PLAN_GARR_13_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;








201

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx

0.00224133050672853 0.00948643658103340 0.04065938792819074








D.3.2. Using the DDL1 carrier with the ambiguities FIXED, compute the LS single epoch solution for the whole interval 39000< t <41300 with the program LS.f





LS.f)






cat DD_PLAN_GARR_13_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$8-$11-$12-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),




















Question: Discuss on the remaining error sources which could explain the error found in the North, East and Vertical components.



Repeat the previous exercise, but positioning with the L2 carrier




D.4.1 Using DDL2 carrier measurements, estimate the coordinates of receiver GARR taking PLAN as a reference receiver and correcting troposphere.
















Execute:








octave


y1=M1(:,1);G1=M1(:,2:12);



x(1:3)'-0.2949 0.0163 0.0567







octave


afix=iZ*round(az) -1075655 1343160 938718 468181 -675593 -313616 -356299 1439836

[Qz,Zt,Lz,Dz,az,iZ] = decorrel (Q,a);[azfixed,sqnorm] = lsearch (az,Lz,Dz,2);afixed=iZ*azfixed;sqnorm(2)/sqnorm(1)ans = 15.3627929427384afixed(:,1)'

-1075655 1343160 938718 468181 -675593 -313616 -356299 1439836

Rounding the decorrelated floated solutionround(a)' -1075654 1343161 938718 468182-675592 -313617 -356299 1439835










Using the previous the file ambL2.dat and "DD_PLAN_GARR_13_ALL.fixL1",generate the a file with the following content:

----------------------------- DD_PLAN_GARR_13_ALL.fixL1L2 -----------------------------------1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

PLAN GARR 13 PRN DoY sec DDP1 DDL1 DDP2 DDL2 DDRho DDTrop DDIon El1 Az1 El2 Az2 DDN1 DDN2<---- GARR ---->

----------------------------------------------------------------------------------------------

Note: This file is identical to file "DD_PLAN_GARR_13_ALL.fixL1", but with the ambiguities added in the last field #19.







cat DD_PLAN_GARR_13_ALL.fixL1|gawk 'BEGIN{for (i=1;i<1000;i++) {getline <"sat.ambL2";A[$1]=$3}}

{printf "%s %02i %02i %s %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f %14.4f \n",

$1,$2,$3,$4,$5,$6,$7,$8,$9,$10,$11,$12,$13,$14,$15,$16,$17,$18,A[$4]}' >DD_PLAN_GARR_13_ALL.fixL1L2

b) Generate the "DD_PLAN_GARR_13_ALL.fixL1L2" file:





graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19-$11)' -so --yn -0.6 --yx 0.6 -l "(DDL2-lambda2*DDN2)-DDRho" --xl "time (s)" --yl "m"


graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19-$11-$12)' -so --yn -0.6 --yx 0.6 -l "(DDL2-lambda2*DDN2)-DDRho-DDTrp" --xl "time (s)" --yl "m"



graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19-$12)' -so --yn -0.06 --yx 0.16 -l "(DDL2-lambda2*DDN2)-DDTrp" --xl "time (s)" --yl "m"



----------------------------------------------------------------------------------------------

graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19)' -so --yn -15000 --yx 15000 -l "(DDL2-lambda2*DDN2)" --xl "time (s)" --yl "m"



graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19-$11)' -so --yn -0.6 --yx 0.6 -l "(DDL2- DDN2)-DDRho" --xl "time (s)" --yl "m"





----------------------------------------------------------------------------------------------




graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19-$11-$12)' -so --yn -0.6 --yx 0.6 -l "(DDL2- DDN2)-DDRho-DDTrp"--xl "time (s)" --yl "m"





----------------------------------------------------------------------------------------------




graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19-$11-$12)' -so --yn -0.06 --yx 0.16 -l "(DDL2- DDN2)-DDRho-DDTrp"--xl "time (s)" --yl "m"





----------------------------------------------------------------------------------------------




graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($10-$19)' -so --yn -15000 --yx 15000 -l "(DDL2- DDN2)"--xl "time (s)" --yl "m"





----------------------------------------------------------------------------------------------








cat DD_PLAN_GARR_13_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;








219

octave

load M.dat

y=M(:,1);G=M(:,2:4);

x=inv(G'*G)*G'*yx

0.00312473328403573 0.01680339170230549 0.06303852755939099




Question: Is the accuracy similar to that in the previous case, when estimating the baseline vector?





D.4.2. Using the DDL2 carrier with the ambiguities FIXED, compute the LS single epoch solution for the whole interval 39000< t <41300 with the program LS.f





LS.f)






cat DD_PLAN_GARR_13_ALL.fixL1 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;;printf "%s %14.4f%8.4f %8.4f %8.4f \n",$6,$10-$11-$12-$18,-cos(e2)*sin(a2)+cos(e1)*sin(a1),




















Question: Discuss the possible sources of the bias found in the vertical component.



Plot the unambiguous DDSTEC as a function of time and elevation, using Klobucharmodel (it corresponds to the field #13 of file DD_PLAN_GARR_13_ALL.fixL1L2).

graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 –y13 -so -l "DDIon (Klobuchar Iono Model)" --xl "time (s)"

--yl "(m L1 delay)" --yn -.1 --yx .1 -t "PLAN-GARR: 15.2 km: DDSTEC"



----------------------------------------------------------------------------------------------

graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 –x16 –y13-so -l "DDIon (Klobuchar Iono Model)" --xl "elevation (deg.)"


Execute:

D.5.1 PLAN-GARR differential positioning with L1 carrier(with ambiguity fixed and correcting from tropo. and Klobuchar iono.)

D.5.1. Estimate GARR coordinates with DDL1 (using tropo & Iono Klobuchar)



Modelled DDIono(Klobuchar)

as a function of time

Question: Discuss this plot





Modelled DDIono(Klobuchar) as a

function of elevationQuestion:

Why a larger dispersion is found at a low elevation?





Plot the prefit-residuals:Prefit= DDL1-DDRho-Lambda1*DDN1-DDTropo+DDIon:

graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'$8-$11-$18-$12+$13' -so -l "Prefit DDL1" --xl "time (s)" --yl "metres" --yn -.1 --yx .1 -t "PLAN-GARR: 15.2 km: DDL1-DDRho-DDTropo+DDIon-Lambda1*DDN1"



----------------------------------------------------------------------------------------------

1.- As a function of time





DDL1 Pre-fit residuals as a

function of time.

Question: Discuss the noise seen in the plot.






[Time], [DDL1-DDRho-DDTrp+DDIon-lambda1*DDN1], [Los_k-Los_13]

where:Time= seconds of dayDDL1 – DDRho –DDTrp + DDIon– lambda1*DDN1= Prefit residulas

(i.e., "y" values in program LS.f)Los_k – Los_13= The three components of the geometry matrix,i.e. matrix "a" in LS.f program.



D.5.1. Using the DDL1 carrier with the ambiguities FIXED, and correcting from both troposphere and Klobuchar ionosphere (DDSTEC), compute the LS single epoch solution for the whole interval 39000< t <41300 with the program LS.f.

Note: this correction (DD) is given in file DD_PLAN_GARR_13_ALL.fixL1L2 on thefield “DDIon” (i.e. #13) in meters of L1 delay.




cat DD_PLAN_GARR_13_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45}{e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;STEC1=$13;printf "%s %14.4f %8.4f

%8.4f %8.4f \n",$6,$8-$11-$18-$12+STEC1,-cos(e2)*sin(a2)+cos(e1)*sin(a1),-cos(e2)*cos(a2)+cos(e1)*cos(a1),

-sin(e2)+sin(e1)}' > L1model_Klob.dat

[Time], [DDL1-DDRho-DDTrp+DDIon-lambda1*DDN1], [Los_k - Los_13]


cat L1model_Klob.dat |LS > L1fixKlob.pos





Plot the positioning error

graph.py -f L1fixKlob.pos -x1 –y2 -s.- -l "North error" -f L1fixKlob.pos -x1 –y3 -s.- -l "East error" -f L1fixKlob.pos -x1 –y4 -s.- -l "UP error"

--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "PLAN-GARR: 15.2 km: L1 ambiguities fixed + Tropo + Klobuchar"






with L1, ambiguities fixed and troposphere

with ionosphere (from Klobuchar)

corrections

Question: Discuss the results.





D.6. Unambiguous DDSTEC determination


Using DDL1, DDL2 and the fixed ambiguities DDN1 and DDN2 obtained before, compute and plot the unambiguous DDSTEC as a function of time and elevation. Execute:

graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'($8-$18-$10+$19)*1.546' -so -l "DDL1-Amb1-(DDL2-Amb2)" --xl "time (s)"




----------------------------------------------------------------------------------------------

graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 –x16 -y'($8-$18-$10+$19)*1.546' -so -l "DDL1-Amb1-(DDL2-Amb2)" --xl "elevation (deg.)"




Unambiguous DDSTEC

as a function of time






Unambiguous DDSTEC

as a function elevation

Question: Why do we have an elevation-dependent pattern?





Plot the prefit-residuals:Prefit= DDL1-DDRho-Lambda1*DDN1-DDTropo+alpha1*STEC:

graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x6 -y'$8-$11-$18-$12+1.546*($8-$18-$10+$19)' -so -l "Prefit DDL1" --xl "time (s)" --yl “metres" --yn -.15 --yx .15 -t "PLAN-GARR: 15.2 km: DDL1-DDRho-Lambda1*DDN1-DDTropo+alpha1*STEC"



----------------------------------------------------------------------------------------------

1.- As a function of time



22

1 2 21 2

2

1 1.5461

7760

ff f

21 2

f2

f 2




function of time.






graph.py -f DD_PLAN_GARR_13_ALL.fixL1L2 -x16 -y'$8-$11-$18-$12+1.546*($8-$18-$10+$19)' -so -l "Prefit DDL1" --xl "elevation (deg.)" --yl “metres" --yn -.15 --yx .15 -t "PLAN-GARR: 15.2 km: DL1-DDRho-Lambda1*DDN1-DDTropo+alpha1*STEC"



----------------------------------------------------------------------------------------------

2.- As a function of elevation

Plot the prefit-residuals:Prefit= DDL1-DDRho-Lambda1*DDN1-DDTropo+alpha1*STEC:






function of elevation.

Question: Why do we have an elevation-dependent pattern?





D.6.1. Using the DDL1 carrier with the ambiguities FIXED, and correcting from both troposphere and ionosphere (DDSTEC), compute the LS single epoch solution for the whole interval 39000< t <41300 with the program LS.f


[Time], [DDL1-DDRho-DDTrp+ 1*DDSTEC-lambda1*DDN1], [Los_k - Los_13]

where:Time= seconds of dayDDL1 – DDRho –DDTrp + 1*DDSTEC– lambda1*DDN1= Prefit residulas

(i.e., "y" values in program LS.f)Los_k – Los_13 = The three components of the geometry matrix (i.e., matrix "a" in program

LS.f)

D.6.1 PLAN-GARR differential positioning with L1 carrier(with ambiguity fixed and correcting from tropo. and actual Iono.)

D.6.1. Estimate GARR coordinates with DDL1 (using tropo & actual Iono.)



The following sentence can be used:

cat DD_PLAN_GARR_13_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45}{e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;STEC1=1.546*($8-$18-$10+$19);printf

"%s %14.4f %8.4f %8.4f %8.4f \n",$6,$8-$11-$18-$12+STEC1,-cos(e2)*sin(a2)+cos(e1)*sin(a1),-cos(e2)*cos(a2)+cos(e1)*cos(a1),

-sin(e2)+sin(e1)}' > L1model_stec.dat

[Time], [DDL1-DDRho-DDTrp+ 1*DDSTEC-lambda1*DDN1], [Los_k - Los_13]


cat L1model_stec.dat |LS > L1fixStec.pos

D.6. PLAN-GARR differential positioning with L1 carrier(with ambiguity fixed and correcting from tropo. and DDSTEC)

D.6.1. Estimate GARR coordinates with DDL1 (using tropo & DDSTEC corrections)




graph.py -f L1fixStec.pos -x1 –y2 -s.- -l "North error" -f L1fixStec.pos -x1 –y3 -s.- -l "East error" -f L1fixStec.pos -x1 –y4 -s.- -l "UP error"

--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "PLAN-GARR: 15.2 km: L1 ambiguities fixed + Tropo + DDSTEC"






with L1, ambiguities fixed

with Tropo and DDSTEC removed.Question: Is any bias expected due to the L1-LC APCs, when removing the ionosphere using the unambiguous DDSTEC?





Repeat the previous exercise, but using the ionosphere free combination of carriers DDLC, with the ambiguities fixed.


[Time], [DD(LC-Amb)-DDRho-DDTrp], [Los_k - Los_13]

where:Time= seconds of day DD(LC-Amb) – DDRho –DDTrp = Prefit residulas

(i.e., "y" values in program LS.f)Los_k – Los_13 = The three components of the geometry matrix (i.e., matrix "a" in program

LS.f)

D.7. PLAN-GARR differential positioning with LC carrier(with ambiguities fixed and correcting troposphere)

D.7. Estimate GARR coordinates with DDLC FIXED (using tropo)



The following sentence can be used:cat DD_PLAN_GARR_13_ALL.fixL1L2 | gawk 'BEGIN{g2r=atan2(1,1)/45} {e1=$14*g2r;a1=$15*g2r;e2=$16*g2r;a2=$17*g2r;g=(77/60)**2;L1=$8-$18;L2=$10-$19;LC=(g*L1-L2)/(g-1);printf "%s %14.4f %8.4f %8.4f %8.4f \n", $6,LC-$11-$12,-cos(e2)*sin(a2)+cos(e1)*sin(a1),-cos(e2)*cos(a2)+cos(e1)*cos(a1),

-sin(e2)+sin(e1)}' > LCmodel.dat

[Time], [DD(LC-Amb)-DDRho-DDTrp], [Los_k - Los_13]


cat LCmodel.dat |LS > LCfix.pos






graph.py -f L1fixStec.pos -x1 –y2 -s.- -l "North error" -f L1fixStec.pos -x1 –y3 -s.- -l "East error" -f L1fixStec.pos -x1 –y4 -s.- -l "UP error"

--yn -.1 --yx .1 --xl "time (s)" --yl "error (m)" -t "PLAN-GARR: 15.2 km: LC ambiguities FIXED + Tropo"






with DDLC, ambiguities fixed.

Question: Compare this iono-free solution with that obtained with DDL1, removing the troposphere and ionosphere using the unambiguous DDSTEC. Are the results the same? Why?








• To the University of Delft for the MATLAB files of LAMBDA method.• To the INDRA company and Institut Cartogràfic de Catalunya for the

data files of receivers IND1,IND2, IND2 and PLAN, GARR, respectively.• To Adrià Rovira-Garcia for his contribution to the editing of this material

and gLAB updating and integrating this learning material into the GLUE.

The ESA/UPC GNSS-Lab Tool suite (gLAB) has been developed under theESA Education Office contract N. P1081434.

Acknowledgements

List of Acronyms

List of Acronyms

AGW Atmospheric Gravity Waves

ANTEX ANTenna EXchange format

APC Antenna Phase Centre

ARP Antenna Reference Point

ASCII American Standard Code for Information Interchange

A/S Anti-Spoofing

C/A Coarse/Acquisition

CDDIS Crustal Dynamics Data Information System

CODE Centre for Orbit Determination in Europe

CRF Celestial Reference Frame

CRS Conventional Celestial Reference System

CS Cycle Slip

DAT Data Analysis Tool

DCB Differential Code Bias

DLL Dynamic Link Library

DLR Deutsches Zentrum fur Luft- und Raumfahrt

DOP Dilution Of Precision

DoY Day of Year

DPC Data Processing Core

ECEF Earth-Centred, Earth-Fixed

ECI Earth-Centred Inertial

EMR Energy Mines and Resources

ENU East North Up

ESA European Space Agency

gAGE Research group of Astronomy and Geomatics

319

TM-23/2

GAL GALileo Satellite Identifier

GDOP Geometric Dilution Of Precision

GEO GEOstationary Satellite Identifier

GIPSY GPS Inferred Positioning SYstem

gLAB GNSS-LAB tool suite

GLO Glonass Satellite Identifier

Glonass GLObal NAvigation Satellite System

GNSS Global Navigation Satellite System

GNU GNU’s Not Unix

GPS Global Positioning System

GRACE Gravity Recovery and Climate Experiment

GRAPHIC Group and Phase Ionospheric Calibration

GFree Geometry Free

GUI Graphical User Interface

HDOP Horizontal Dilution Of Precision

HTML HyperText Markup Language

IAC Information Analytical Centre

ICD Interface Control Document

IFree Ionosphere Free

IGL IGS Glonass orbit products

IGRF International Geomagnetic Reference Field

IGS International GNSS Service

IGST IGS Time

IODE Issue Of Data Ephemerides

IODN Issue Of Data Navigation

IONEX IONosphere map EXchange format

IRI International Reference Ionosphere

ITRF International Terrestrial Reference Frame

JPL Jet Propulsion Laboratory

LEO Low Earth Orbit

LS Least Squares

320

List of Acronyms

LSTIDs Large-Scale TIDs

MC Satellite Mass Centre

MCC Mission Control Centre

MJD Modified Julian Day

MM Monument Marker

MSDOS Microsoft Disk Operating System

MSTID Medium-Scale Travelling Ionospheric Disturbance

MSTIDs Medium-Scale Travelling Ionospheric Disturbances

MW Melbourne–Wubbena

NANU Notice Advisory to NAVSTAR Users

NASA National Aeronautics and Space Administration

NEU North East Up

NGA National Geospatial-Intelligence Agency

NSE Navigation System Error

OS Operating System

PCO Phase Centre Offset

PCV Phase Centre Variation

PDOP Precision Dilution Of Precision

PNG Portable Network Graphics

PPP Precise Point Positioning

PRN Pseudo-Random Noise

PVT Position, Velocity, Time

PZ-90 Parametry Zemli 1990 (Parameters of Earth 1990)

RINEX Receiver INdependent EXchange format

RK4 Fourth-order Runge–Kutta

RMS Root Mean Square

RO Radio Occultation

S/A Selective Availability

SBAS Satellite-Based Augmentation System

SED Storm Enhancement Density

SINEX Solution (Software/technique) INdependent EXchange format

321

TM-23/2

SIS Signal In Space

SISRE Signal In Space Range Error

SOHO SOlar Helioscopic Observatory

SP3 Standard Product #3

SPP Standard Point Positioning

SPS Standard Positioning Service

SSI Signal Strength Indicator

STEC Slant Total Electron Content

STROP Slant TROPospheric delay

SU Soviet Union

SV Space Vehicle

SVN Space Vehicle Number

TDOP Time Dilution Of Precision

TEC Total Electron Content

TECU Total Electron Content Unit

TGD Total Group Delay

TID Travelling Ionospheric Disturbance

TRF Terrestrial Reference Frame

TRS Conventional Terrestrial Reference System

TUM Technische Universitat Munchen

UPC Technical University of Catalonia

USNO United States Naval Observatory

UTC Coordinated Universal Time

VDOP Vertical Dilution Of Precision

WGS-84 World Geodetic System 84

ZTD Zenith Tropospheric Delay

322

Documents

Laboratory Exercises