1. The 15th Workshop on JAXA Astrodynamics and Flight Mechanics, 2005
Precise Orbit Determination of GPS Satellites using Carrier Phase Measurements
Technical Consultant Tomoji TAKASU
Kasai Design Office Ltd. Shoji KASAI

2. Motivation
Precise Orbit/Clock Determination is Key Technology for Accurate Positioning with GPS/GNSS
Demands for Real-Time / Near Real-Time Precise GPS Orbit/Clock
Technique can be Applied to Precise Orbit Determination for Satellite equipped with GPS Receiver

3. Measurement Model Undifferenced (Zero-Differenced)
Ionosphere-Free Linear Combination of Carrier Phase Measurements (L1,L2)

4. Geometric Distance
Light-Time Equation

5. Time Synchronization

6. ECI to ECEF Transformation
Precession/Nutation Model : IAU1976/1980, IERS1996, IAU2000A
Earth Rotation Parameters

7. Tropospheric Delay Model
ZTD : Zenith Total Delay
GE ,GN : Tropospheric Gradient
Mdry,Mwet : Mapping Function (NMF etc)

8. Satellite Antenna Offset/PCV
Satellite Antenna Offset (m) Block II/IIA : (0.279,0,1.023), IIR : (0,0,0)
Satellite Antenna PCV
PRN22 Nadir Angle - Postfit Residuals (m)

9. Receiver Antenna Offset/PCV
APC
Eccentricity : Marker to ARP
Antenna PCV : IGS_01.PCV APC : ARP to L1/L2 Phase Center PCV : Elevation Dependent Variation
ARP
Marker

10. Site Displacements Solid Earth Tides Ocean Loading Polar Tides
Atmospheric Loading, Snow, ...
IERS Conventions 1996/2003

11. Relativity/Phase Wind-up Effect
Relativistic Effect to Satellite Clock
Phase Wind-up Effect RCP phase affected by Relative Rotation between Satellite/Receiver Antenna

12. Satellite Orbit Model Geopotential : JGM-3 + Tidal Effects
3rd Body : Moon/Sun, JPL DE405
Solar Radiation Pressure : GPS SRP Model
Relativity Effect

13. Perturbations of Satellite Orbit1
10-2
10-4
10-6
10-8
10-10
10-12 GM
GPS
GEO
J2,0
J2,2
Moon
Acceleration (m/s2)
Sun
SRP
Relativity
Solid Tide
Air Drag
J6,6
J18,18
10000
20000
30000
Height (km)

14. GPS SRP Model
Precise GPS Specific SRP Model : ROCK 4/42 CODE RPR GSPM04.b
Eclipse Model : Cylindric, Penumbra/Umbra
Ambiguous in Eclipse and Post-Eclipse Maneuver Period

15. Other State Transition Models
Satellite Clock : 1st order Gauss-Marcov
Receiver Clock : White-Noise
Tropos. Parameters : Random-Walk
Earth Rotation Parameters : Random-Walk
Carrier Phase Bias : Fixed in a Arc, Reinitialized on Cycle-Slip

16. Estimation Filter
Extended Kalman Filter

17. Backward Filter/Smoother
0.4
PRN01 Orbit Estimation Error (wrt IGS Final)
0.35
Forward (RMS:66.9cm)
0.3
Backward (RMS:4.0cm)
Smoothed (RMS:3.6cm)
0.25
3D Position Error (m)
0.2
0.15
0.1
0.05
10/2 0:00
10/2 12:00
10/3 0:00
10/3 12:00
10/4 0:00
10/4 12:00
10/5 0:00

18. Quality Control Prefit Residuals Test Postfit Residuals Test
Outlier Exclusion and Re-Filtering
Statistical Test of Outlier Rate, Prefit/Postfit Residuals RMS and Valid Data Outage
Bad Satellite/Station Exclusion and Rollback/Re-Estimation

19. Evaluation of Accuracy
GT ver.0.5.5
GPS Week 1291 (2004/10/3-10/9)
GPS 29 Satellites / IGS 40 Stations
Initial Orbit/Clock : Broadcast Ephemeris
Station Pos : Fixed to Previous Week PPP
3Pass Filter/Smoother
24H+Overlap24H, Interval : 300sec

20. GpsTools (GT) ver.0.5.5

21. IGS 40 Stations ALGO AMC2 AREQ ASC1 AUCK BAHR CAS1 CEDU COCO DAV1 DRAO
150 W
120 90 60 30 E
180 S N
ALGO
AMC2
AREQ
ASC1
AUCK
BAHR
CAS1
CEDU
COCO
DAV1
DRAO
FAIR
HOB2
IISC
IRKT
KERG
KOUR
LHAS
LPGS
MAC1
MAG0
MAS1
MATE
MKEA
NRC1
NRIL
ONSA
TROM
YELL
STJO
VILL
POL2
USNO
PIE1
TSKB
PIMO
THTI
REUN
PERT
RIOG

22. Estimated Parameters

23. IGS Final Orbit/Clock ~300 World-Wide GPS Stations
Weighted Average of 8 Analysis Centers CODE, ESA, GFZ, JPL, NRCan, MIT, NOAA, SOPAC
Various Analysis S/W Packages
Formal Accuracy Orbit : < 5cm, Clock : < 0.1nsec

24. Estimated Orbit Accuracy
Average of 29 Satellites, wrt IGS Final

25. Orbit Accuracy by Satellites
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
GPS01
GPS03
GPS04
GPS05
GPS06
GPS07
GPS08
GPS09
GPS10
GPS11
GPS13
GPS14
GPS15
GPS16
GPS17
GPS18
GPS19
GPS20
GPS21
GPS22
GPS23
GPS24
GPS25
GPS26
GPS27
GPS28
GPS29
GPS30
GPS31
Average
Position RMS Error (m) 3D
Radial
Along-Track
Cross-Track
Orbit Error wrt IGS Final

26. Estimated Orbit (Example)
0.1
0.2
0.3
0.4
RMS: m
Position Error 3D (m)
10/3
10/4
10/5
PRN01 Orbit Error wrt IGS Final
0.2
Radial
Along-Track
0.1
Cross-Track
Position Error R/A/C (m)
-0.1
-0.2
RMS R: m A: m C: m
10/6
10/7
10/8
10/9

27. Estimated Clock Accuracy
Average of 29 Satellites, wrt IGS Final

28. Clock Accuracy by Satellites
0.2
0.4
0.6
0.8 1
1.2
1.4
1.6
1.8
GPS01
GPS03
GPS04
GPS05
GPS06
GPS07
GPS08
GPS09
GPS10
GPS11
GPS13
GPS14
GPS15
GPS16
GPS17
GPS18
GPS19
GPS20
GPS21
GPS22
GPS23
GPS24
GPS25
GPS26
GPS27
GPS28
GPS29
GPS30
GPS31
Average
Clock Bias RMS Error (nsec)
Clock Error wrt IGS Final

29. Estimated Clock (Example)5
PRN01 Clock/Clock Error wrt IGS Final
3.67
3.668
Clock Bias (ns)
3.666
3.664
3.662 1
MEAN: 0.073ns RMS: 0.127ns
0.5
Clock Bias Error (ns)
-0.5 -1
10/3
10/4
10/5
10/6
10/7
10/8
10/9

30. Comparison with Others
Average of 29 Satellites, wrt IGS Final

31. Estimated ZTD (Example)
ALGO Tropospheric ZTD

32. Estimated ERP Xp (") Yp (") UT1-UTC (sec) 0.2 0.201 0.202 0.203 0.415
0.42
0.425
Yp (")
10/3
10/4
10/5
10/6
10/7
10/8
10/9
-0.457
UT1-UTC (sec)
IGS Final

33. Station Geometry Dependency
Estimated Orbit/Clock RMS Error
8 Stations
12 Stations
24 Stations
12.3cm
7.7cm
5.7cm
0.25ns
0.20ns
0.16ns
Average of 29 Satellites, wrt IGS Final

34. Details : See http://gpspp.sakura.ne.jp
Conclusions
Precise Orbit/Clock Determination of GPS Satellites by Carrier Phase Measurements
Accuracy wrt IGS Final Orbit : 5.2cm (3D RMS) Clock : 0.14ns (Bias RMS)
Future Work : Real-Time, LEO Sats. Orbit, ...
Details : See