2009年度GCOE地球惑星計測スクール

GPS Global Positioning System

Part 1

東京海洋大学 高須 知二
Rev.A 2009/8/22

Outline: Part 1
• GPS/GNSS Basics and Principles
– GPS/GNSS Summary
– GPS Signal and Receiver Architecture
– 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
– Precise Point Positioning (PPP)
– Applications
• Exercise: PPP with GT 0.6.4

Self Introduction

?
GpsTools 0.6.4 RTKLIB 2.2.1

4
GpsTools

RTKLIB

10m 2cm

10m 20cm
NGS-VRS+
NovAtel OEMV
6
 GPS/GNSS Summary

GPS
• NAVSTAR GPS (Global Positioning System)
– Satellite navigation system developed by US DoD
– Operated by US Air Force GPS Wing
• 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)
– Compass (China)
• Regional Navigation Satellite System
– QZSS (Japan)
– IRNSS (India)
• Satellite Based Augmentation System (SBAS)
9

GPS/GNSS Applications
Military Applications: ...
Civil Applications:
Air Navigation Static positioning and timing
Nonprecision approach and landing Offshore resource exploration
Domestic en route Hydrographic surveying
Oceanic en route Aids to navigation
Terminal Time transfer
Remote areas Land surveying
Helicopter operations Geographical information systems
Aircraft attitude Space
Collision avoidance Launch
Air Traffic Control In-flight/orbit
Land Navigation Reentry/landing
Vehicle monitoring Attitude measurement
Schedule improvement Search and Rescue
Minimal routing Position reporting and monitoring
Law enforcement Rendezvous
Marine navigation Coordinated search
Oceanic Collision avoidance
Coastal ...
Harbor/approach (B.W.Parkinson, Introduction and Heritage of NAVSTAR, the
Inland waterways Global Positioning System, 1994)
10
 GPS System
Space Segment
GPS
Satellites

Ranging Signal Command,

L1,L2,L5 Telemetry, Navigation Data
Ranging Signal
MSC (Master
Military Control Station)
User Monitor
Stations
Civil User
Ground
Antennas
User Segment Control Segment
11

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")
GPS Block II Satellite Orbit Planes

(http://www.ion.org/museum) (http://en.wikipedia.org/wiki)
12
 GPS Satellites
1980 1990 2000
Block I

Block II

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)

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

Delta II GPS IIR-21 Mission Booklet)
14
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°
– 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°
– 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 QZSS Ground Track

• Satellite Constellation:
– 1 sat (IOC), 3 sats (FOC)
– Altitude: ~36,000km, Inclination: 43°
– Eccentricity: 0.075
– First Sat Launch: 2010
• Signals:
(IS-QZSS 1.1 Draft)
– L1C/A, L1C, L2C, L5-I/Q: GPS Compatible
– L1-SAIF, LEX: Augmentation

18
GNSS Constellation
Number of Planned GNSS Satellites
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
IRNSS 0 7 7 7
SBAS 7 8 8 8
Total 56 99 131 136

L3 Planned GNSS Signal Frequencies

L5/E5a E5b L2 L2 E6/LEX L1/E1 L1

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

19

GPS Signal and

Receiver Architecture

20
GPS Signal 1

Carrier
sin( 2πft + φ )
+1
Code
-1
C (t )
+1
Data
-1
D(t )

Signal
2 P C (t ) D (t ) sin( 2πft + φ ) + K

21

GPS Signal 2
Carrier Frequency Code Modulation Data Rate Satellite
C/A BPSK (1) 50 bps
P(Y) BPSK (10) 50 bps
L1 1575.42MHz 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-
P(Y) BPSK (10) 50 bps
L2 1227.60MHz L2C BPSK (1) 25 bps IIRM-
M-code BOC (10,5) ? IIRM-
L5I BPSK (10) 100 bps IIF-
L5 1176.45MHz
L5Q BPSK (10) none IIF-
Military Signal, Planned
22
PRN Codes
C/A Code Generator
G1 Generator
1 2 3 4 5 6 7 8 9 10

X1 Epoch PRN Selector

Reset C (t )
C/A
/10 1 2 3 4 5 6 7 8 9 10
10.23MHz
G2 Generator

Auto-correlation function Cross-correlation function

1 1

τ (chip ) τ (chip )
-1 1 0
1 T 1 T
R (τ ) =
T ∫
0
C i (t )C i (t − τ )dt R (τ ) =
T ∫
0
C i (t )C j (t − τ )dt (i ≠ j )

23

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

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

2 Ephemeris

3 Ephemeris

4 Almanac and Subframe

Health SV 425-32, Iono/UTC,... Page 1-25

5 AlmanacSubframe 4 SV 1-24,...
and Health Page 1-25

Preamble Subframe 24bits 6bits

TLM P HOW P P P P
P P P P P

TOW Count (x 6s) ID

24
GPS Receivers
Receiver Products: $20 - $30,000

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

Handmade GPS receiver: $400

25

Receiver Architecture
Antenna

Baseband Processors

L1 RF
Front-End
Receiver/
Navigation
Processor
L2 RF
Front-End

Rcv Clock
Reference Oscillator
26
RF Front-End

Antenna
1st Down 2nd Down
Conversion Conversion

BPF BPF BPF AGC ADC

RF Baseband
Processing Frequency Processors
Synthesizer

Reference Oscillator

27

Baseband Processor
I and Q Sampling Correlators Accumulators
IE
Σ
IP
Front- Σ
end I0 IL
Σ
QE
Σ
Q0 QP
Σ
Ic Qc QL Receiver
Σ Processor
CE CP CL
Carrier Code E,P,L Reference
NCO NCO Code Generator

Rcv Clock
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)
– Navigation Data Decode
• Output to Navigation Processor:
– Pseudorange
– (Carrier-Phase, Doppler-Freq)
– Navigation Data (Ephemeris, SV Clock Parameter, ...)

29

Basic Measurement
Models

30
Pseudorange
(4) Satellite
Prs ≡ c(tr − t ) s Clock Bias

= c((tr + dt ) − (t s + dT s )) + ε P (1) Geometric

Range
= c(tr − t s ) + c(dtr − dT s ) + ε P (2) Ionosphere
(3) Troposphere
= ( ρ rs + I rs + Trs ) + c(dtr − dT s ) + ε P
(1) (2) (3) (4) (5) (5) Receiver
Clock Bias
At Satellite ts Time by Satellite Clock (s)

Prs
At Receiver c tr Time by Receiver Clock (s)

31

Ephemeris 1
M 0 , ∆n, e, A , Ω 0 , i0 , ω , Ω& , IDOT , Cuc , Cus , Crc , Crs , Cic , Cis , Toe

Orbital plane Satellite

z
Ω& e
rs

r r
E u u
ω y
A Ae Ω
i
x

32
Ephemeris 2
Satellite Position (ECEF):
tk = t − toe

n = µ / A3 + ∆n
tk
M = M 0 + ntk
E = M + e sin E : Kepler Equation
t oe1 t oe 2 t t oe 3 TOW (s)
2
φ = ATA 2( 1 − e sin E , cos E − e) + ω
1 0 0 
 
u   φ   Cus Cuc  R x (θ ) =  0 cos θ sin θ 
      sin 2φ  0
 − sin θ cos θ 
 r  =  A(1 − e cos E )  +  Crs Crc  
cos 2φ  cos θ 0 − sin θ 
 i   i + IDOT t   C Cic    
R y (θ ) =  0
  0 k   is 1 0 
 sin θ 0 cos θ 
 
Ω = Ω 0 + (Ω& − ωe )tk − ωetoe  cos θ sin θ 0 
 
R z (θ ) =  − sin θ cos θ 0 
r s (t ) = Rz (−Ω ) Rx (−i )(r cos u , r sin u , 0)T  0 0 1 


33

SV Clock Parameters
a f 0 , a f 1, a f 2 , TGD ,toc

Satellite Clock Bias:

dT (t ) = a f 0 + a f 1 (t − toc ) + a f 2 (t − toc ) 2 + ∆trel + ∆tGD

Relativity correction:
− 2 µ Ae sin E
∆trel =
c2
Differential code bias correction:
 −TGD ( L1)

∆tGD = − γ TGD ( L 2) (γ = f12 / f 2 2 )
 0 ( LC )

34
 Differential Code Bias 1
DCBP1-P2
Electrical/Antenna Delay
L1C/A
L1P(Y)
L2P(Y)
L2C

L1C/A L1
L1P(Y) Transmitter
L-Band
L2P(Y) Modulator
L2
Reference
L2C Transmitter Antenna
Clock
(Cs/Rb) Code Generators
GPS Satellite

35

Differential Code Bias 2

γ ⋅ TGD
TGD Satellite
dTC1 Clock Bias
dTP 2 dTP1 dT
DCBP1− P 2 DCBP1−C1 γ = f12 / f 22 = 1.647
3 0.8
2.5
DCBP1-P2(m) DCBP1-C1(m)
0.6
2 0.4
1.5
0.2
1
0
0.5
0 -0.2
-0.5 -0.4
-1 -0.6
-1.5 -0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Satellite PRN Satellite PRN
36
Geometric Range
Signal Transmitted Signal Transmission Time
t s = tr − Prs / c − dT (t s )
r s (t s )
(1)
ρ rs = U (tr )rr (tr ) − U (t s )r s (t s )

(2)
ρ rs ≈ rr (tr ) − Rz (ωe (tr − t s ))r s (t s )
Signal Received
Geometric (3)
rr (tr )
Range
ρ rs ≈ rr (tr ) − Rz (ωe ρ rs / c)r s (t s )
ρrs
(4)
s s s ωe ( x s yr − y s xr )
ρ r ≈ rr (tr ) − r (t ) +
c
ωe Sagnac Effect Correction
37

LOS Vector
Line-of-Sight (LOS) Vector: U LOS
Vector
r s − rr W N
ers = , ers,enu = Eecef →enu ers = (ee , en , eu )T El
r s − rr Az

 − sin λ cos λ 0 
  S E
Eecef →enu =  − sin φ cos λ − sin φ sin λ cos φ 
 cos φ cos λ cos φ sin λ sin φ  N


Satellite Azimuth/Elevation Angle:

W E
Az = ATAN2(ee , en )
El = arcsin eu
S
38
Ionospheric Model
α 0 ,α1,α 2 ,α 3 , β 0 , β1, β 2 , β 3
Klobuchar Model:
ψ = 0.0137 /( El + 0.11) − 0.022
φi = φ + ψ cos Az Klobuchar

Vertical Ionos Delay

λi = λ + ψ sin Az / cosφi Model
φm = φi + 0.064 cos(λi − 1.617)
t = 4.32 × 104 λi + t
F = 1.0 + 16.0 × (0.53 − El )3
3
x = 2π (t − 50400) / ∑β φ
n =0
n m
n

0 4 8 12 16 20 24
Local Time (hr)
 F × 5 × 10−9 ( x > 1.57)

I =  4
 x 2 x 4  


F ×  5 × 10−9 +
 ∑ α nφm
n 
×


1 − +
2 24  
( x ≤ 1.57)
 n =1 
39

Troposphere Model
Standard Atmosphere:
p = 1013.25 × (1 − 2.2557 × 10−5 H )5.2568 Tropospheric Delay
T = 15.0 − 6.5 × 10−3 H + 273.15
17.15T − 4684.0  hrel
e = 6.108 × exp ×
 T − 38.45  100
p : Pressure (hPa)
H : Geopotential Height (m)
T : Temperature (K)
e : Partial Pressure of WV (hPa)
hrel : Relative Humidity (%)
hrel=50%, z=90°
Saastamoinen Model:
0.002277   1255  
Trs = p +  + 0.05 e − tan 2 z  ( z : Zenith Angle)
cos z   T  
40
 Navigation Processing

41

LSE: Least Square Estimation

Measurement Equation:
y : Measurement vector H : Design matrix
y = Hx + v v : Residual vector
x : Parameter vector
J LS = v12 + v2 2 + ... + vm 2 = v T v = ( y − Hx )T ( y − Hx )
= yT y − yT Hx − x T H T y + x T H T Hx → min
∂J LS
= 0 T − yT H − ( H T y )T + ( H T Hx )T + x T H T H
∂x
= −2 y T H + 2 x T H T H = 0
Normal Equation (NEQ):
H T Hxˆ = H T y → xˆ = ( H T H ) −1 H T y
Weighted LSE:
xˆ = ( H T WH ) −1 H T Wy ( JWLS = v T Wv → min)
42
Non-linear LSE
Measurement Equation:
y = h( x ) + v
h( x ) = h( x0 ) + H ( x − x0 ) + ... : Taylor Polynomial

y ≈ h( x 0 ) + H ( x − x 0 ) + v
 
y − h( x 0 ) = H ( x − x 0 ) + v  H = ∂h( x ) 
 ∂x 
H T H ( xˆ − x0 ) = H T ( y − h( x0 ))  x = x0 
Partial Derivatives
T −1 T
xˆ = x0 + ( H H ) H ( y − h( x0 ))

Iterative Solution (Gauss-Newton):

xˆ i +1 = xˆ i + ( H T H ) −1 H T ( y − h( xˆ i ))
xˆ = lim xˆ i
i →∞
43

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
Discrete Kalman Filter:
System Model: x k = Φk −1 x k −1 + w k −1 ( w k −1 ≈  (0, Qk −1 ))
Measurement Model: yk = H k x k + v k (v k ≈  (0, Rk ))

Time Update (Projection):

xˆ k (−) = Φk −1 xˆ k (+)
Pk (−) = Φk −1Pk −1 (+)Φk −1T + Qk −1
xˆ k ( −), xˆ k ( + ),
Pk ( −) Measurement Update: Pk ( + )
K k = Pk ( + ) H k T ( H k Pk ( + ) H k T + Rk ) −1
xˆ k ( + ) = xˆ k ( − ) + K k ( yk − H k xˆ k ( −))
y1, y2 , y3 ,... xˆ1, xˆ 2 , xˆ 3 ,...
Pk ( + ) = ( I − K k H k ) Pk ( −)

45

Navigation Processing
x = (rr T , cdt )T , y = ( Prs1 , Prs2 , Prs3 ,..., Prsm )T

 ρ rs1 + cdˆt − cdT s1  s1 T 

 + I rs1 + Trs1   − er 1
 ρ rs2 + cdˆt − cdT s2  s2 T 
+ I rs2 + Trs2   − er 1
 s3  H = 
h( xˆ ) =  ρ rs3 + cdˆt − cdT s3 s3
+ I r + Tr  T 
 − ers3 1
 
 s
M
  M M
 ρ m + cdˆt − cdT sm sm
+ I r + Tr  sm   s T 
 r  − er
m 1

xˆ 0 = (0,0,0,0)T s3
s2
xˆ i +1 = xˆ i + ( H T H ) −1 H T ( y − h( xˆ i ))
s1 sm
xˆ = lim xˆ = ( rˆ T , cdˆt )T
i r
i→∞

Single-Point Solution + Receiver Clock Bias r

46
Partial Derivatives
Partial Derivatives of Range by Receiver Position:
rr ≡ ( xr , yr , zr )T , r s ≡ ( x s , y s , z s )T

s 2 s 2 s 2
∂ρ rs ∂ ( x − xr ) + ( y − yr ) + ( z − zr )
=
∂ xr ∂ xr

= {
1 s
2
( x − xr ) 2 + ( y s − yr ) 2 + ( z s − zr ) 2 } −1 / 2 ∂ ( x s − xr ) 2
∂xr
− 2( x s − xr ) − ( x s − xr )
= =
2 ( x s − xr ) 2 + ( y s − yr ) 2 + ( z s − zr ) 2 ρ rs

∂ρ rs  ∂ρ rs ∂ρ rs ∂ρ rs   x s − xr y s − yr z s − zr  s T
 = − (r − rr ) = −ers
T
= , , = − , ,
∂rr  ∂xr ∂yr ∂zr   ρs
 r ρ s
r ρ rs 

s
ρr
LOS Vector

47

Solution Convergence
Estimated Parameters in LSE Iteration Loop
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
(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

48
Single-Point Solution
1999/1/1 24hr, TSKB 2001/1/1 24hr, TSKB

RMS Error: RMS Error:

E: 21.51m E: 2.02m
N: 33.81m N: 4.10m
U: 59.65m U: 5.70m

100m 100m

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

RMS Error: RMS Error:

E: 1.73m E: 1.10m
N: 2.51m N: 1.44m
U: 4.24m U: 3.92m

10m 10m
49

Error Sources

50
Error Sources
• Error sources of GPS positioning
– Ephemeris
– SV clock Parameter
– Ionospheric Delay
– Tropospheric Delay
– Multipath
– S/A: Selective Availability
– Code Tracking Noise
• Satellites-Receiver Geometry

51

Ephemeris/SV Clock Parameter

2004/4/1-4/7 (PRN08) Ephemeris Error 2009/4/1-4/7 (PRN08)

SV Clock Parameter Error

52
Ionospheric Error
Zenith Ionospheric Delay (L1) at TSKB
2004/11/03-11/09
15
Iono-Delay (m)

10

5
Iono

0
10
Iono-Delay Error (m)

5
0
-5
-10
11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10
Klobuchar Model IGS TEC Final

53

Tropospheric Error

ZTD (Zenith Total Delay) at TSKB

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

Saastamoinen Model Estimated by PPP

54
Multipath
Geodetic-Grade Antenna
Signal
reflected by
a building
Direct
Signal
NovAtel
GPS-702-GG

Consumer-Grade Antenna
GPS
Antenna

Signal
reflected by u-blox ANN-MS
the ground 55

Satellites-Receiver Geometry
Dilution of Precision (DOP):
GDOP = qee + qnn + quu + qtt  qee qen qeu qet   s1 T 
   − er ,enu 1
PDOP = qee + qnn + quu  s T 
T −1  qne qnn qnu qnt 
 − er ,2enu 1
Q = (H H ) =  H =
HDOP = qee + qnn q qun quu qut   M 
 ue   M
q qtt   − ers,menu
T
VDOP = quu  te qtn qtu
 1

# of satellites = 5 # of satellites = 7 # of satellites = 27

GDOP=33.4 PDOP=25.9 GDOP=2.5 PDOP=2.1 GDOP=1.2 PDOP=1.0

HDOP=8.1 VDOP=24.7 HDOP=1.2 VDOP=1.8 HDOP=0.5 VDOP=0.9
56
Positioning Error Budget
DGPS
Error Source Single-Point SBAS
(BL=100km)
Ephemeris Error 0.1 m
1.0 m 0.1 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
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
3.2 m 5.3 m 2.0 m 3.3 m 1.7 m 2.8 m
RMS Error
57

DGPS and SBAS

58
DGPS
• Differential GPS
– Fixed Reference Stations at Known Position
– Generate Correction Messages
– 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
59

RTCM SC-104
RTCM 2.3 Messages RTCM 3.1 Messages
Type Message Type Message
1 Differential GPS Corrections 1001 L1-Only GPS RTK Observables
3 GPS Reference Station Parameters 1002 Extended L1-Only GPS RTK Observables
10 P-Code Differential Corrections 1003 L1&L2 GPS RTK Observables
11 C/A-Code L1, L2 Delta Corrections 1004 Extended L1&L2 GPS RTK Observables
17 GPS Ephemerides 1005 Stationary RTK Reference Station ARP
18 RTK Uncorrected Carrier Phase 1006 Stationary RTK Ref. Stn. ARP with Hgt.
19 RTK Uncorrected Pseudorange 1007 Antenna Descriptor
20 RTK Carrier Phase Corrections 1008 Antenna Descriptor & Serial Number
21 RTK Pseudorange Corrections 1013 System Parameters
22 Extended Reference Station Parameter 1014 Network Auxiliary Station Data
23 Antenna Type Definition Record 1015 GPS Ionospheric Correction Differences
24 Antenna Reference Point (ARP) 1016 GPS Geometric Correction Differences
59 Proprietary Messages 1019 GPS Ephemerides
RTCM: The Radio Technical Commission for Marine Service
60
SBAS
SBAS: Satellite Based Augmentation Systems
GEO Satellite
System Development Operation
PRN Name Location
135 Galaxy 15 133W
WAAS US, DOT, FAA 2003/7-
138 Anik F1R 107.3W
120 Inmarsat-3 AOR-E 15.5W
ESA, EC, 2005/7-
EGNOS 124 Artemis 21.5E
Eurocontrol (IOC)
126 Inmarsat-3 IOR-W 25E
129 MTSAT-IR 140E
MSAS Japan, JCAB 2007/9-
137 MTSAT-II 145E

India, AAI,
GAGAN 2011- 127 GSAT-4? ?
ISRO

61

SBAS Coverage Map

(by GENEQ Inc.)

62
SBAS Messages
Type Message
RTCA/DO-229C 0 For WAAS Testing
Minimum Operational Performance 1 PRN Mask assignment
Standards for Global Positioning
2-5 Fast Corrections
System/Wide Area Augmentation System
Airborne Equipment 6 Integrity Information
(Nov 28,2001) 7 Fast Correction Degration Factor
9 GEO Navigation Messages
10 Degradation Parameters
250 bits - 1 Second
12 WAAS Network Time/UTC Offset
212-bit Data Field 17 GEO Satellite Almanac

6-bit Message Type ID (0-63) 18 Ionospheric Grid Mask

8-bit Preamble 24-bit Parity 24 Mixed Fast/Long Term Satellite Correct.
25 Long Term Satellite Error Corrections
26 Ionospheric Delay Corrections
RTCA: Radio Technical Commission for
Aeronautics 27 WAAS Service Messages
63

SBAS Performance
Single-Point MSAS
RMS Error: RMS Error:
E: 1.02m N: 1.36m U: 4.00m E: 0.43m N: 0.57m U: 1.21m

(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)
64
Exercise 1

Using GT 0.6.4

65