2009年度GCOE地球惑星計測スクール

GPS Global Positioning System

東京海洋大学 高須 知二

GPS Global Positioning System

Part 1

Rev.A 2009/8/22

Outline: Part 1

• GPS/GNSS Basics and Principles

– GPS/GNSS Summary

– GPS Signal and Receiver Architecture

– Basic Measurement Models– Basic Measurement Models

– Navigation Processing

– Error Sources

– DGPS and SBAS

• Exercise: using GT 0.6.4

2

Outline: Part 2

• Precise Positioning with GPS/GNSS

– Time and Coordinate Systems

– Precise Measurement Models

– Relative Positioning– Relative Positioning

– Precise Point Positioning (PPP)

– Applications

• Exercise: PPP with GT 0.6.4

3

Self Introduction

?

4

GpsTools 0.6.4 RTKLIB 2.2.1

GpsTools

5

RTKLIB

2cm10m

6

NGS-VRS+

NovAtel OEMV

20cm10m

GPS/GNSS Summary

7

GPS/GNSS Summary

GPS

• NAVSTAR GPS (Global Positioning System)

– Satellite navigation system developed by US DoD

– Operated by US Air Force GPS Wing

• History• History

– 1978/2 First satellite launch

– 1983 Freely available for civilian use

– 1993 Fully operational (FOC)

– 2000/5 S/A Termination

– 2009/8 30 operational satellites

8

GNSS

• Global Navigation Satellite System

– GPS (US)

– GLONASS (Russia)

– Galileo (EU)– Galileo (EU)

– Compass (China)

• Regional Navigation Satellite System

– QZSS (Japan)

– IRNSS (India)

• Satellite Based Augmentation System (SBAS)

9

GPS/GNSS Applications

Air NavigationNonprecision approach and landing

Domestic en route

Oceanic en route

Terminal

Remote areas

Helicopter operations

Static positioning and timingOffshore resource exploration

Hydrographic surveying

Aids to navigation

Time transfer

Land surveying

Geographical information systems

Military Applications: ...

Civil Applications:

10

Helicopter operations

Aircraft attitude

Collision avoidance

Air Traffic Control

Land NavigationVehicle monitoring

Schedule improvement

Minimal routing

Law enforcement

Marine navigationOceanic

Coastal

Harbor/approach

Inland waterways

Geographical information systems

SpaceLaunch

In-flight/orbit

Reentry/landing

Attitude measurement

Search and RescuePosition reporting and monitoring

Rendezvous

Coordinated search

Collision avoidance

...(B.W.Parkinson, Introduction and Heritage of NAVSTAR, the

Global Positioning System, 1994)

GPS System

Space Segment

Ranging Signal

GPS

Satellites

Command,

Navigation Data

Control SegmentUser Segment

11

Ranging Signal

L1,L2,L5

Military

User

Civil User

MSC (Master

Control Station)

Monitor

Stations

Ground

Antennas

Telemetry,

Ranging Signal

Navigation Data

GPS Space Segment

• Satellite Constellation

– 6 Plane x 4 = 24 Satellites (Nominal)

– Altitude: 20,100km

– Inclination: 55°°– Period: 1/2 Sidereal Day (11h 58' 2")

(http://www.ion.org/museum) (http://en.wikipedia.org/wiki)

12

GPS Block II Satellite Orbit Planes

GPS Satellites

Block I

Block II

1980 1990 2000

Block IIA

Block IIR

Block IIR-M

Block IIF (2010-), Block IIIA (2014-)13

GPS Block IIR-M-8 Launch- 2009/8/17 10:35 UTC (6:35 a.m. EDT)

- US Cape Canaveral

- Launcher: Delta 2

- SVN50/PRN?

- Plane E/Slot 3

- Replace: IIA-26 (SVN40)

14

(Spaceflight Now: http://www.spaceflightnow.com)(United Launch Alliance,

Delta II GPS IIR-21 Mission Booklet)

GPS Ground Segment

(L.C.P.Harrington, GPS Status and Modernization, 2009)15

GLONASS (ГЛОНАСС)

• Development: USSR and Russia

• Satellite Constellation:

– 3 Plane x 8 = 24 Sats + 3 Spare (FOC)

– Altitude: 19,100 km, Inclination: 64.5°– Altitude: 19,100 km, Inclination: 64.5°– GLONASS, GLONASS-M (2003- ), GLONASS-K (2010- )

• Signals:

– L1C/A, L1P (FDMA: 1602+n x 0.5625 MHz)

– L2C/A, L2P (FDMA: 1246+n x 0.4375 MHz)

– L3 FDMA/CDMA (GLONASS-K- )

16

Galileo

• Development: EU and ESA

• Satellite Constellation:

– 3 Plane x 9 = 27 Sats + 3 Spare (FOC)

– Altitude: 23,200km, Inclination: 56°– Altitude: 23,200km, Inclination: 56°– Test Sats: GIOVE-A (2006), GIOVE-B (2008)

– IOV: 2011 (4 Sats), FOC: 2013/E

• Signals:

– E5a-I/Q (OS,CS), E5b-I/Q (OS,SOL,CS)

– E6-A (PRS), E6-B/C (CS), E1A (PRS), E1-B/C (OS,SOL,CS)

17

QZSS

• Development: Japan, JAXA

• Satellite Constellation:

– 1 sat (IOC), 3 sats (FOC)

– Altitude: ~36,000km, Inclination: 43°

QZSS Ground Track

– Altitude: ~36,000km, Inclination: 43°– Eccentricity: 0.075

– First Sat Launch: 2010

• Signals:

– L1C/A, L1C, L2C, L5-I/Q: GPS Compatible

– L1-SAIF, LEX: Augmentation

18

(IS-QZSS 1.1 Draft)

GNSS Constellation

System 2009 2012 2015 2018

GPS 30 32 32 32

GLONASS 17 (+3) 24 (+3) 24 (+3) 24 (+3)

Galileo 0 15 (+3) 27 (+3) 27 (+3)

Compass 2 12 30 35

QZSS 0 1 3 3

Number of Planned GNSS Satellites

19

QZSS 0 1 3 3

IRNSS 0 7 7 7

SBAS 7 8 8 8

Total 56 99 131 136

Planned GNSS Signal Frequencies

(Y.Yang, COMPASS: View on Compatibility and Interoperability, 2009)

L1/E1L2L5/E5a E5b E6/LEX L1L2L3

GPS Signal and

20

GPS Signal and

Receiver Architecture

GPS Signal 1

Carrier

Code

)2sin( φπ +ft

+1

-1

Signal

Data

K++ )2sin()()(2 φπfttDtCP

)(tC

)(tD

-1

+1

-1

21

GPS Signal 2Carrier Frequency Code Modulation Data Rate Satellite

L1 1575.42MHz

C/A BPSK (1) 50 bps

P(Y) BPSK (10) 50 bps

M-code BOC (10,5) ? IIRM-

L1C-d MBOC (6,1,1/11) 100 bps IIIA-

L1C-p MBOC (6,1,1/11) none IIIA-

L2 1227.60MHz

P(Y) BPSK (10) 50 bps

L2C BPSK (1) 25 bps IIRM-

M-code BOC (10,5) ? IIRM-

L5 1176.45MHzL5I BPSK (10) 100 bps IIF-

L5Q BPSK (10) none IIF-

Military Signal, Planned

22

PRN Codes

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10/10

C/A Code Generator

G1 Generator

C/A)(tCReset

X1 Epoch PRN Selector

23

1 2 3 4 5 6 7 8 9 10/10

G2 Generator

Auto-correlation function Cross-correlation function

dttCtCT

RT

ii∫ −=0

)()(1

)( ττ

-1 1

)(chipτ

0

1

)(chipτ

)()()(1

)(0

jidttCtCT

RT

ji ≠−= ∫ ττ

1

10.23MHz

Subframe 4

Navigation Data

GPS Week #, SV Accuracy and Health, SV Clock,...

Ephemeris

Ephemeris

Almanac and Health SV 25-32, Iono/UTC,... Page 1-25

30bits x 10words = 300 bits (50bps x 6 s)

1

2

3

4

Subframe

Subframe 4

Subframe 4Almanac and Health SV 25-32, Iono/UTC,...

Almanac and Health SV 1-24,...

TLM P HOW P P P P

P P P P P

Page 1-25

Page 1-25

6bits24bits

TOW Count (x 6s) ID

SubframePreamble

4

5

24

GPS ReceiversReceiver Products: $20 - $30,000

Handmade GPS receiver: $400

SiRF, u-blox, Garmin, Hemisphere, Trimble, Leica, Topcon, NovAtel, Javad, Magellan, ...

25

Receiver Architecture

Receiver/

Baseband Processors

Antenna

L1 RF

Front-End

Receiver/

Navigation

Processor

Reference Oscillator

Rcv Clock

L2 RF

Front-End

26

RF Front-End

BPF BPF BPF AGC ADC

Antenna

1st Down

Conversion

2nd Down

Conversion

BPF BPF BPF AGC ADC

Reference Oscillator

Frequency

Synthesizer

RF

Processing

27

Baseband

Processors

Baseband Processor

Σ

Σ

Σ

Σ

Front-

end I0

Q0

IE

IP

IL

QE

Q

Correlators AccumulatorsI and Q Sampling

Σ

Σ

E,P,L Reference

Code Generator

Carrier

NCO

Ic Qc

Code

NCO

Receiver

Processor

Rcv Clock

Q0 QP

QL

CE CP CL

Reference Oscillator

28

Receiver Processor

• Receiver Processor:

– Acquisition : Search Doppler Shift and Code Phase

– Code Tracking : DLL (Delay Lock Loop)

– Carrier Tracking: FLL/PLL (Freq/Phase Lock Loop)– Carrier Tracking: FLL/PLL (Freq/Phase Lock Loop)

– Navigation Data Decode

• Output to Navigation Processor:

– Pseudorange

– (Carrier-Phase, Doppler-Freq)

– Navigation Data (Ephemeris, SV Clock Parameter, ...)

29

Basic Measurement

30

Basic Measurement

Models

Pseudorange

Ps

rsr

sr

sr

Ps

rs

r

Pss

r

sr

sr

dTdtcTI

dTdtcttc

dTtdttc

ttcP

ερ

ε

ε

+−+++=

+−+−=

++−+=

−≡

)()(

)()(

))()((

)(

(2) Ionosphere

(3) Troposphere

(1) Geometric

Range

(4) Satellite

Clock Bias

Prrrr dTdtcTI ερ +−+++= )()(

At Satellite

At Receiver

st

rt

Time by Satellite Clock (s)

Time by Receiver Clock (s)c

Psr

31

(1) (2) (3) (4) (5) (5) Receiver

Clock Bias

Ephemeris 1

z

sreΩ&

Satellite

oeisicrsrcusuc TCCCCCCIDOTiAenM ,,,,,,,,,,,,,,, 000 ΩωΩ∆ &

Orbital plane

i

Ω

u

x

r

Aω

uE

yAe

r

32

Ephemeris 2

k

oek

EeME

ntMM

nAn

ttt

sin

/

0

3

+=

+=

+=

−=

∆µ

: Kepler Equation

Satellite Position (ECEF):

kt

Txz

s

oeeke

icis

rcrs

ucus

k

ururit

tt

CC

CC

CC

tIDOTi

EeA

i

r

u

eEEeATA

EeME

)0,sin,cos)(()()(

)(

2cos

2sin)cos1(

)cos,sin1(2

sin

0

0

2

−−=

−−+=

+

+

−=

+−−=

+=

RRr Ω

ωωΩΩΩ

φφ

φ

ωφ

&

: Kepler Equation

33

1oet 2oet 3oett TOW (s)

−=

−

=

−

=

100

0cossin

0sincos

)(

cos0sin

010

sin0cos

)(

cossin0

sincos0

001

)(

θθθθ

θ

θθ

θθθ

θθθθθ

z

y

x

R

R

R

SV Clock Parameters

GDrelocfocff ttttattaatdT ∆∆ ++−+−+= 2210 )()()(

ocGDfff tTaaa ,210 ,,,

Satellite Clock Bias:

2

sin2

c

EeAtrel

µ∆

−=

Relativity correction:

Differential code bias correction:

)/(

)(0

)2(

)1(2

22

1 ff

LC

LT

LT

t GD

GD

GD =

−

−

= γγ∆

34

Differential Code Bias 1

L1C/A

L1P(Y)

L2P(Y)

L2C

Electrical/Antenna DelayDCBP1-P2

35

L1C/A

L1P(Y)

L2P(Y)

L2C

L-Band

Modulator

L1

Transmitter

L2

TransmitterReference

Clock

(Cs/Rb)

Antenna

Code Generators

GPS Satellite

Differential Code Bias 2

1PdT2PdT

GDT

GDT⋅γ

21 PPDCB −

1CdT

11 CPDCB − 647.1/2

22

1 == ffγ

dT

3 0.8

Satellite

Clock Bias

36

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Satellite PRN1 3 5 7 9 11 13 1517 19 21 23 25 27 29 31

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Satellite PRN

DCBP1-P2(m) DCBP1-C1(m)

Geometric Range

)( ss tr

Signal Transmitted

)()()()( sssrrr

sr tttt rUrU −=ρ

(1)

(2)

)(/ ssrr

s tdTcPtt −−=

Signal Transmission Time

Signal Received

)( rr tr

srρ

)())(()( sssrezrr

sr tttt rRr −−≈ ωρ

c

xyyxtt r

sr

sess

rrsr

)()()(

−+−≈ω

ρ rr

(2)

)()/()( sssrezrr

sr tct rRr ρωρ −≈

(3)

(4)

Sagnac Effect Correction

37

Geometric

Range

eω

LOS Vector

Tune

srenuecef

senur

rs

rs

sr eee ),,(, , ==

−

−= → eEe

rr

rre

− λλ 0cossin

Line-of-Sight (LOS) Vector: U

E

N

AzEl

S

W

LOS

Vector

−−

−

=→

φλφλφφλφλφ

λλ

sinsincoscoscos

cossinsincossin

0cossin

enuecefE

u

ne

eEl

eeAz

arcsin

),(2ATAN

=

=

Satellite Azimuth/Elevation Angle:

N

EW

S

38

ES

Ionospheric Model

Klobuchar Model:

+=

+=

−+=

cos/sin

cos

022.0)11.0/(0137.0

Az

Az

El

ii

i

φψλλ

ψφφψ

32103210 ,,,,,,, ββββαααα

De

lay

Klobuchar

Model

39

≤

+−×+××

>××

=

−=

−×+=

+×=

−+=

+=

∑

∑

=

−

−

=

)57.1(242

1105

)57.1(105

/)50400(2

)53.0(0.160.1

1032.4

)617.1cos(064.0

cos/sin

4

1

429

9

3

0

3

4

xxx

F

xF

I

tx

ElF

tt

Az

n

nmn

n

nmn

i

iim

ii

φα

φβπ

λ

λφφ

φψλλ

0 4 8 12 16 20 24

Local Time (hr)V

ert

ica

lIo

no

sD

ela

y

Model

Troposphere Model

Standard Atmosphere:

10038.45T

4684.017.15Texp6.108=

15.273105.60.15

)102557.21(25.1013

3

2568.55

relhe

HT

Hp

×

−−

×

+×−=

×−×=−

−Tropospheric Delay

40

Saastamoinen Model:

−

++= ze

Tp

zT sr

2tan05.01255

cos

002277.0

H : Geopotential Height (m)

T : Temperature (K)

e : Partial Pressure of WV (hPa)

relh : Relative Humidity (%)

p : Pressure (hPa)

hrel=50%, z=90°

z( : Zenith Angle)

Navigation Processing

41

Navigation Processing

LSE: Least Square Estimation

HxHxyHxHxyyy

HxyHxyvv

∂

→+−−=

−−==+++=TTTTTT

TTmLS

J

vvvJ

min

)()(...22

22

1

vHxy +=

Measurement Equation:y : Measurement vector

x : Parameter vector

H : Design matrix

v : Residual vector

0HHxHy

HHxHxHyHHy0x

=+−=

++−−=∂

∂

TTT

TTTTTTTTLSJ

22

)()(

yHHHxyHxHH TTTT 1)(ˆˆ −=→=

Normal Equation (NEQ):

42

Weighted LSE:

WyHWHHxTT 1)(ˆ −= min)( →= Wvv

TWLSJ

Non-linear LSE

vxhy += )(

Measurement Equation:

...)()()( 00 +−+= xxHxhxh : Taylor Polynomial

∂ )( xh)()(

)()( 00

vxxHxhy

vxxHxhy

+−=−

+−+≈

))(()(ˆ 01

0 xhyHHHxx −+= − TT

ii

iTT

ii

xx

xhyHHHxx

ˆlimˆ

))ˆ(()(ˆˆ 11

∞→

−+

=

−+=

Iterative Solution (Gauss-Newton):

∂

∂=

= 0

)(

xxx

xhH

))(()ˆ(

)()(

00

00

xhyHxxHH

vxxHxhy

−=−

+−=−TT

43

Partial Derivatives

Numerical Solution of LSE

Solution Matlab Notation Exec. Time

NEQ+Gauss x=(H'*H)¥(H'*y); 5.3 s

NEQ+LU-Decomp x=inv(H'*H)*(H'*y); 6.0 s

NEQ+Cholesky R=chol(H'*H); x=R¥(R'¥(H'*y)); 5.2 s

QR-Decomp [Q,R]=qr(H,0); x=R¥(Q'*y); 11.8 s

SVD [U,D,V]=svd(H,0); x=V*(D¥(U'*y)); 46.4 s

Pseudo-Inverse x=pinv(H)*y; 51.9 s

size(H)=[5000,1000], Pentium 4 3.2GHz, Matlab 6.5.1, Windows XP Pro

44

Kalman Filter

ˆˆ +=−

kkkk

kkkk

vxHy

wxΦx

+=

+= −−− 111

)),0((

)),0(( 11

kk

kk

Rv

Qw

≈

≈ −−

Discrete Kalman Filter:

System Model:

Measurement Model:

Time Update (Projection):

)()()(

))(ˆ()(ˆ)(ˆ

))(()( 1

−−=+

−−+−=+

+++= −

kkkk

kkkkkk

kT

kkkT

kkk

PHKIP

xHyKxx

RHPHHPK

1111

1

)()(

)(ˆ)(ˆ

−−−−

−

++=−

+=−

kT

kkkk

kkk

QΦPΦP

xΦx

Measurement Update:

,...,, 321 yyy

)(

),(ˆ

+

+

k

k

P

x

)(

),(ˆ

−

−

k

k

P

x

45

,...ˆ,ˆ,ˆ321 xxx

Navigation Processing

−

−

−

=

++−+

++−+

++−+

=

==

1

1

1

ˆ

ˆ

ˆ

)ˆ(

),...,,,(,),(

3

2

1

3333

2222

1111

321

Tsr

Tsr

Tsr

sr

sr

ssr

sr

sr

ssr

sr

sr

ssr

Tsr

sr

sr

sr

TTr

m

TIcdTtdc

TIcdTtdc

TIcdTtdc

PPPPcdt

e

e

e

Hxh

yrx

MMM

ρρρ

−

++−+ 1

ˆ Tsr

sr

sr

ssr m

mmmm TIcdTtdc e

MMM

ρ

1s

2s3s

ms

r

TTri

i

iTT

ii

T

tdc )ˆ,ˆ(ˆlimˆ

))ˆ(()(ˆˆ

)0,0,0,0(ˆ

11

0

rxx

xhyHHHxx

x

==

−+=

=

∞→

−+

Single-Point Solution + Receiver Clock Bias

46

Partial Derivatives

r

rs

rs

rs

r

sr

TssssTrrrr

x

zzyyxx

x

zyxzyx rr

∂

−+−+−∂=

∂∂

≡≡

ρ )()()(

),,(,),,(

222

Partial Derivatives of Range by Receiver Position:

Tsrs

r

Tr

s

sr

rs

sr

rs

sr

rs

r

sr

r

sr

r

sr

r

sr

sr

rs

rs

rs

rs

rs

r

rs

rs

rs

rs

zzyyxx

zyx

xx

zzyyxx

xx

x

xxzzyyxx

err

r−=

−−=

−−−−=

∂

∂

∂

∂

∂

∂=

∂

∂

−−=

−+−+−

−−=

∂

−∂−+−+−=

−

ρρρρ

ρρρρ

ρ

)(,,,,

)(

)()()(2

)(2

)()()()(

2

1

222

22/1222

LOS Vector

47

Solution Convergence

i x (m) y (m) z (m) cdt (m)

(0) X= 0.0000000 0.0000000 0.0000000 0.0000000

(1) X=-4739338.8790644 3968053.3426383 4470195.0681293 1290751.6350707

(2) X=-3990084.5939062 3334559.7805777 3763444.6383541 50195.3310677

(3) X=-3957255.7455862 3310242.1098583 3737755.6233736 510.7878812

Estimated Parameters in LSE Iteration Loop

48

(3) X=-3957255.7455862 3310242.1098583 3737755.6233736 510.7878812

(4) X=-3957205.2229884 3310203.7001970 3737718.0508664 432.5789153

(5) X=-3957205.1820501 3310203.6651692 3737718.0078941 432.4910365

(6) X=-3957205.1820116 3310203.6651363 3737718.0078537 432.4909539

(7) X=-3957205.1820116 3310203.6651363 3737718.0078536 432.4909538

(8) X=-3957205.1820116 3310203.6651363 3737718.0078536 432.4909538

(9) X=-3957205.1820116 3310203.6651363 3737718.0078536 432.4909538

(10)X=-3957205.1820116 3310203.6651363 3737718.0078536 432.4909538

2001/1/1 0:00:00, TKSB, processed by RTKLIB 2.2.1, n=8

Single-Point Solution1999/1/1 24hr, TSKB 2001/1/1 24hr, TSKB

RMS Error:

E: 21.51m

N: 33.81m

U: 59.65m

RMS Error:

E: 2.02m

N: 4.10m

U: 5.70m

100m100m

49

2004/1/1 24hr, TSKB 2009/1/1 24hr, TSKB

RMS Error:

E: 1.73m

N: 2.51m

U: 4.24m

RMS Error:

E: 1.10m

N: 1.44m

U: 3.92m

100m100m

10m10m

Error Sources

50

Error Sources

Error Sources

• Error sources of GPS positioning

– Ephemeris

– SV clock Parameter

– Ionospheric Delay– Ionospheric Delay

– Tropospheric Delay

– Multipath

– S/A: Selective Availability

– Code Tracking Noise

• Satellites-Receiver Geometry

51

Ephemeris/SV Clock Parameter2004/4/1-4/7 (PRN08) 2009/4/1-4/7 (PRN08)Ephemeris Error

52

SV Clock Parameter Error

Ionospheric Error

5

10

15Io

no

-De

lay (

m)

Zenith Ionospheric Delay (L1) at TSKB

2004/11/03-11/09

53

0

Ion

o

11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10-10

-5

0

5

10

Ion

o-D

ela

y E

rro

r (m

)

Klobuchar Model IGS TEC Final

Tropospheric Error

2009/1/1-2009/1/31 2009/7/1-2009/7/31

ZTD (Zenith Total Delay) at TSKB

54

Saastamoinen Model Estimated by PPP

MultipathGeodetic-Grade Antenna

NovAtel

GPS-702-GG

Direct

Signal

Signal

reflected by

a building

55

Consumer-Grade Antenna

GPS-702-GG

u-blox ANN-MSSignal

reflected by

the ground

GPS

Antenna

Satellites-Receiver Geometry

Dilution of Precision (DOP):

== −

tttutnte

utuuunue

ntnunnne

eteuenee

T

qqqq

qqqq

qqqq

qqqq

1)( HHQ

−

−

−

=

1

1

1

,

,

,

2

1

Tsenur

Tsenur

Tsenur

me

e

e

H

MM

uu

nnee

uunnee

ttuunnee

qVDOP

qqHDOP

qqqPDOP

qqqqGDOP

=

+=

++=

+++=

56

GDOP=1.2 PDOP=1.0

HDOP=0.5 VDOP=0.9

# of satellites = 27# of satellites = 7

GDOP=2.5 PDOP=2.1

HDOP=1.2 VDOP=1.8

# of satellites = 5

GDOP=33.4 PDOP=25.9

HDOP=8.1 VDOP=24.7

Positioning Error Budget

Error Source Single-PointDGPS

(BL=100km)SBAS

Ephemeris Error1.0 m

0.1 m0.1 m

SV Clock Param Error 0.0 m

Ionospheric Error 1.5 m 0.2 m 0.2 m

Tropospheric Error 0.3 m 0.1 m 0.3 m

57

Tropospheric Error 0.3 m 0.1 m 0.3 m

Multipath 1.0 m 1.2 m 1.0 m

S/A 0.0 m 0.0 m 0.0 m

Rcv Tracking Noise 0.3 m 0.3 m 0.3 m

UERE 2.1 m 1.3 m 1.1 m

HDOP/VDOP 1.5 2.5 1.5 2.5 1.5 2.5

Horizontal/Vertical

RMS Error3.2 m 5.3 m 2.0 m 3.3 m 1.7 m 2.8 m

DGPS and SBAS

58

DGPS and SBAS

DGPS

• Differential GPS

– Fixed Reference Stations at Known Position

– Generate Correction Messages

– Broadcast Correction Messages to User

59

– Broadcast Correction Messages to User

– Eliminate Most of Errors of Positioning

• Service of DGPS

– Space Based DGPS: OmniSTAR, SkyFix, StarFix

– Maritime DGPS: Marine Beacons

– National DGPS: VHF-band, Cellular Network, Internet

– GDGPS: StarFire

RTCM SC-104

Type Message

1 Differential GPS Corrections

3 GPS Reference Station Parameters

10 P-Code Differential Corrections

11 C/A-Code L1, L2 Delta Corrections

17 GPS Ephemerides

Type Message

1001 L1-Only GPS RTK Observables

1002 Extended L1-Only GPS RTK Observables

1003 L1&L2 GPS RTK Observables

1004 Extended L1&L2 GPS RTK Observables

1005 Stationary RTK Reference Station ARP

RTCM 2.3 Messages RTCM 3.1 Messages

60

17 GPS Ephemerides

18 RTK Uncorrected Carrier Phase

19 RTK Uncorrected Pseudorange

20 RTK Carrier Phase Corrections

21 RTK Pseudorange Corrections

22 Extended Reference Station Parameter

23 Antenna Type Definition Record

24 Antenna Reference Point (ARP)

59 Proprietary Messages

1005 Stationary RTK Reference Station ARP

1006 Stationary RTK Ref. Stn. ARP with Hgt.

1007 Antenna Descriptor

1008 Antenna Descriptor & Serial Number

1013 System Parameters

1014 Network Auxiliary Station Data

1015 GPS Ionospheric Correction Differences

1016 GPS Geometric Correction Differences

1019 GPS Ephemerides

RTCM: The Radio Technical Commission for Marine Service

SBAS

System Development OperationGEO Satellite

PRN Name Location

WAAS US, DOT, FAA 2003/7-135 Galaxy 15 133W

138 Anik F1R 107.3W

120 Inmarsat-3 AOR-E 15.5W

SBAS: Satellite Based Augmentation Systems

61

EGNOSESA, EC,

Eurocontrol

2005/7-

(IOC)

120 Inmarsat-3 AOR-E 15.5W

124 Artemis 21.5E

126 Inmarsat-3 IOR-W 25E

MSAS Japan, JCAB 2007/9-129 MTSAT-IR 140E

137 MTSAT-II 145E

GAGANIndia, AAI,

ISRO2011- 127 GSAT-4? ?

SBAS Coverage Map

62

(by GENEQ Inc.)

SBAS MessagesType Message

0 For WAAS Testing

1 PRN Mask assignment

2-5 Fast Corrections

6 Integrity Information

7 Fast Correction Degration Factor

9 GEO Navigation Messages

Minimum Operational Performance

Standards for Global Positioning

System/Wide Area Augmentation System

Airborne Equipment

(Nov 28,2001)

RTCA/DO-229C

63

9 GEO Navigation Messages

10 Degradation Parameters

12 WAAS Network Time/UTC Offset

17 GEO Satellite Almanac

18 Ionospheric Grid Mask

24 Mixed Fast/Long Term Satellite Correct.

25 Long Term Satellite Error Corrections

26 Ionospheric Delay Corrections

27 WAAS Service Messages

6-bit Message Type ID (0-63)

8-bit Preamble

212-bit Data Field

24-bit Parity

250 bits - 1 Second

RTCA: Radio Technical Commission for

Aeronautics

SBAS Performance

Single-Point MSAS

RMS Error:

E: 1.02m N: 1.36m U: 4.00m

RMS Error:

E: 0.43m N: 0.57m U: 1.21m

64

(2007/10/16 24hr, Antenna: NovAtel GPS-702-GG, Receiver: u-blox AEK-4T (raw),

Processing S/W: RTKLIB 2.1.0, All Corrections=ON, Ranging=ON)

Exercise 1

Using GT 0.6.4

65

Using GT 0.6.4