Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement

1. Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical ConsultantTomoji 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 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 • Eccentricity : Marker to ARP • Antenna PCV : IGS_01.PCVAPC : ARP to L1/L2 Phase CenterPCV : Elevation Dependent Variation APC 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 EffectRCP 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. 1 10-2 10-4 10-6 10-8 10-10 10-12 Perturbations of Satellite Orbit GM GPS GEO J2,0 J2,2 Moon Acceleration (m/s2) Sun SRP Solid Tide Relativity J6,6 Air Drag J18,18 20000 0 30000 10000 Height (km)

14. GPS SRP Model • Precise GPS Specific SRP ModelROCK 4/42CODE RPRGSPM04.b • Eclipse ModelCylindric, Penumbra/Umbra

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) Backward (RMS:4.0cm) 0.3 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 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 : Previous Week PPP results • 3Pass Filter/Smoother • 24H+Overlap24H, Interval : 300sec

20. GpsTools (GT) ver.0.5.5

21. NRIL FAIR 60 N MAG0 ONSA ALGO IRKT DRAO NRC1 MATE AMC2 30 N LHAS MAS1 BAHR MKEA IISC KOUR 0 ASC1 COCO AREQ 30 S CEDU LPGS AUCK HOB2 KERG MAC1 60 S CAS1 DAV1 150 W 120 W 90 W 60 W 30 W 0 30 E 60 E 90 E 120 E 150 E 180 E IGS 40 Stations TROM YELL STJO POL2 VILL USNO TSKB PIE1 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 AccuracyOrbit : < 5cm, Clock : < 0.1nsec

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

25. 3D Radial 0.45 Along-Track Cross-Track 0.4 0.35 0.3 Position RMS Error (m) 0.25 0.2 0.15 0.1 0.05 0 GPS19 GPS20 GPS21 GPS22 GPS23 GPS24 GPS25 GPS26 GPS27 GPS28 GPS29 GPS30 GPS31 Average GPS06 GPS07 GPS14 GPS17 GPS18 GPS01 GPS03 GPS04 GPS05 GPS08 GPS09 GPS10 GPS11 GPS13 GPS15 GPS16 Orbit Accuracy by Satellites Orbit Error wrt IGS Final

26. RMS: 0.0385m 0.4 0.3 Position Error 3D (m) 0.2 0.1 0 10/3 10/4 10/5 Estimated Orbit (Example) PRN01 Orbit Error wrt IGS Final 0.2 Radial Along-Track 0.1 Cross-Track Position Error R/A/C (m) 0 -0.1 -0.2 RMS R: 0.0121m A: 0.0321m C: 0.0175m 10/6 10/7 10/8 10/9

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

28. 1.8 1.6 1.4 1.2 1 Clock Bias RMS Error (nsec) 0.8 0.6 0.4 0.2 0 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 Accuracy by Satellites Clock Error wrt IGS Final

29. Estimated Clock (Example) 5 x10 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 0 Clock Bias Error (ns) -0.5 -1 10/3 10/4 10/5 10/6 10/7 10/8 10/9

30. Estimated ZTD (Example) ALGO Tropospheric ZTD

31. 0.203 Xp (") 0.202 0.201 IGS Final 0.2 0.425 Yp (") 0.42 0.415 -0.4566 -0.4568 -0.457 UT1-UTC (sec) -0.4572 -0.4574 -0.4576 10/3 10/4 10/5 10/6 10/7 10/8 10/9 Estimated ERP

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

33. Conclusions • Orbit/Clock Determination of GPS Satellites using Carrier Phase Measurement • Accuracy wrt IGS FinalOrbit : 5.2cm (3D RMS)Clock : 0.14ns (Bias RMS) • Future Work : Real-Time Application Details : See http://gpspp.sakura.ne.jp