GE1 GPS Lecture 3[1]

8/8/2019 GE1 GPS Lecture 3[1]

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To beam or not to beam

POSITIONING ACCURACIESPOSITIONING ACCURACIESWITH GPSWITH GPS

GE 1 Earth Trek

Lecturer: Ariel C. Blanco

1 2

Ranging TechniquesRanging Techniques

Two-way ranging: Active

Electronic distance measuring devices (EDMs)Radar, Sonar, Lidar

One-way ranging: PassiveGPS

Light beam

Range

Range = C x Time/2

reflector

3

OneOne--way Ranging with GPSway Ranging with GPS

Range

Radio Signal

Range = C x Time

1 microsecond error = ~ 300 meters1 nanosecond error = ~ 1 foot

z

Sphere ofposition

6

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How GPS Works in 6 StepsHow GPS Works in 6 Steps

Trilateration from satellites is

basis of system. Satellite

geometry expressed in DOP

values is important

1

To trilaterate, GPS

measures distance

using speed of light2

To measure the distance you

need good clocks and a fourth

SV

Once you know the distance,

you need to know SV's

position

5Then correct for

atmospheric delays

Selective availability

and differential


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TrilaterationTrilaterationOne measurement narrows downour position to the surface of a sphere

Were somewhere on

the surface of this

sphere

19,000km

TrilaterationSecond measurement narrows itdown to intersection of two spheres

20,000km

19,000km

Intersection of

two spheres is a

circle

TrilaterationThird measurement narrows tojust two points

20,000

km

19,000kmIntersection of

three spheres isonly two points

21,000km

Trilateration

In practice 3 measurements areenough

One point will be a ridiculous answer

Out in space

Or moving at high speed

4th measurement required

To cancel out receiver clock errors


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Satellite RangingRadio signals travel at the speedof light (300,000 km/sec) :

Done by measuring travel

time of radio signals

Time (sec) x 300,000= km travelled

Distance known as pseudorange

Pseudorange

Use the same code at the receiver and satellite

Synchronize the satellites and receivers so they aregenerating the same code at the same time

Then we look at the incoming code from the satelliteand see how long ago our receiver generated the same

code

from satellite

from ground receiver

measure time

difference between

same part of code

When did the Signal leave the Satellite?

Need Accurate Clocks

Accurate clocks necessary tomeasure travel time

Satellites have atomic clocks

Ground receivers need consistent clocks

Adding a fourth satellite eliminates receiver clockerrors

Accurate ClocksThe ideal situation: in 2D for sakeof drawing

This is where we really are

4 secs 6 secs


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Accurate ClocksAdding a third measurement

Third measurement would go

through our position if correct

4 secs 6 secs

5 secs

Accurate Clocks

With fast clocksBad position because clock is off by

one second

5 secswrong

time

7 secswrong

time

Accurate ClocksThird measurement with fast clocks

6 secs

Wont go through the other two

5 secs

wrong

time

7 secs

wrong

time

Differential corrections will remove

this error

Knowing Where the Satellites Are

Monitor Stations(Control Segment)

Keep SV positions

updated

SV positiontransmitted to user -

ephemeris

High orbit(Space Segment)

Very stable orbit

No atmospheric

drag

Survivability

Earth coverage

4

(User

Segment)


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Reference Ellipsoid

a

b

a = semi-major axisb = semi-minor axis

Flattening f(a b)

a=

b

H

heightlellipsoidaH

longitude

latitude

WGS-84 Ellipsoid

a = 6378137.000000 m

b = 6356752.314245 m

1/f = 298.2572235630

GPS Heights vs. Elevations

e = Orthometric Height

H = Ellipsoid Height

N = Geoid Height

e = H - N

NN

N

e ee

H H

H

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Determining Orthometric Heights

Ortho. HeightOrtho. Height == H.A.E.H.A.E.Geoid HeightGeoid Height

Earth Surface

Ellipsoid GeoidHeight

Height above MSL(Orthometric height)

H.A.E.

Geoid height= H.A.E.

Geoid

Atmospheric CorrectionsAtmospheric Corrections

Ionosphere is a band of

charged particles

Troposphere is ourweather

Differential correctionsremove this error

Ionosphere

Troposphere


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Selective Availability

U.S. Government can introduce errors

When they do its the largest source of error

Differential corrections remove this error

Post process RTCM (Real Time Corrections)

Selective Availability (SA) - Term given to the act ofpurposefully limiting the accuracy of GPS : Error Budget

Metres

S/A

Atmospheric

Receivers

Ephemeris

Satellite Clocks

0 20 40 60 80 100

The Integer Ambiguity = First Partial Wavelength

N = Integer Ambiguity

Solving for theInteger

Ambiguity yields

centimeter precision

Carrier Phase Results

Baseline or Vector

(cm precision)

Azi = 212o 42 49.8244

Dist = 557.05307 m

Elev = 4 .8751 m

X = -408.251 m

Y = -84.830 m

Z = -369.413 mOR


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GPS AccuracyGPS Accuracy

Discussion of factors influencing GPS

Position accuracy

How accurate is GPS ?How accurate is GPS ?

The answer:

IT DEPENDS !

Range of GPS Accuracy

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Accuracy of Code vs. Phase Solutions


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GPS Accuracy Issues

GPS position accuracy depends upon a number ofissues:

Available satellite geometry

Atmospheric error

Receiver errorsMultiPath error

Satellite position error

Clock error

Satellite Geometry

The more separated thesatellites are - the betterthe geometry, and thebetter the position

solution

The closer the satellitesare in space, the worsethe geometry, and thepoorer the solution

Good Satellite Geometry Poor Satellite Geometry


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Dilution of Precision (DOP)

Point representing position is

really a square

4 secs

6 secs

Uncertainty

Uncertainty

Indicator of position quality from satellite geometry Dilution of Precision (DOP)Even worse at some angles

Box gets bigger if satellites

close together

Atmospheric Effects

< 10 km > 10 km

Multipath


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How Accurate is It?

Depends on some variables

Time spent on measurements

Design of receiver/software

Relative positions of satellites

cm to mm accuracies from survey products


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Receiver attributes# of Channels

One channelrequired for each

frequency (L1, +/-

L2)

8 minimum (4 SVs);12 or more desirable

Antenna Remote, fixed

Power source

Internal, external

Data Storage

Way-points vs. datalogging

Positions vs. raw

data

Data upload &download

Data dictionary

upload for storing

positions by

attributes (pt., line,area)

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Receiver attributesIonosphere Correction or model

Dual channel vs. single channel receiver

Troposphere model?

DGPS capable

Beacon antenna for real-time DGPS

Download and post-process

WAAS capable

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WAAS

How good is WAAS?How good is WAAS?

+ -3 meters

+-15

meters

With Selective Availability set to

zero, and under ideal conditions,

a GPS receiver without WAAS

can achieve fifteen meter

accuracy most of the time.*

Under ideal conditions a

WAAS equipped GPS receiver

can achieve three meter

accuracy 95% of the time.*

* Precision depends on good satellite geometry, open sky view, and no user induced errors.


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GPS EquipmentHandHand--helds $100helds $100--$450$450 navigation instrumentsnavigation instruments

Garmin

Magellan

GPS forPDAs

Way Points collection

Manual entry into GIS,no attribute info. stored

Differential ready butno post-processing

For survey apps.:

+/- ~15 meters

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GPS EquipmentSub Meter (x, y) Accuracy, HandSub Meter (x, y) Accuracy, Hand--helds: $1000helds: $1000--$5000$5000

Trimble

Ashtech

Topcon

Sokkia

others

Datalogging with datadictionary to upload/store

attribute info.

GPS signal data collection for

later post-processingCustom RTK and beacon

antennae feasible

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GPS EquipmentGeodeticGeodetic--quality Instrumentsquality Instruments

TrimbleTrimble

LeicaLeica

AshtechAshtech

SokkiaSokkia

OthersOthers

Cm mm in x and y; 2 cm in z

Stationary AntennaLarge memory for continuous

data collection

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Why test GPS accuracy?Manufacturers specifications are for open sites and long data sets

Open Sites:What the GPS salesman said. 1 meter

13 meters

Forested Sites:What can really happen in forested sites with short data sets.


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Thanks!

49GPS+

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GE1 GPS Lecture 3[1]