Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement

1
Precise Orbit Determination of GPS Satellites
using Carrier Phase Measurement

• 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 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.PCVAPC ARP to L1/L2 Phase
  CenterPCV 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 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
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
0
20000
10000
30000
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 (RMS66.9cm)
Backward (RMS4.0cm)
0.3
Smoothed (RMS3.6cm)
0.25
3D Position Error (m)
0.2
0.15
0.1
0.05
10/2 000
10/2 1200
10/3 000
10/3 1200
10/4 000
10/4 1200
10/5 000
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
• 24HOverlap24H, Interval 300sec

20
GpsTools (GT) ver.0.5.5
21
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 lt 5cm, Clock lt 0.1nsec

24
Estimated Orbit Accuracy
Average of 29 Satellites, wrt IGS Final
25
Orbit Accuracy by Satellites
Orbit Error wrt IGS Final
26
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
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
Estimated ERP
32
Station Geometry Dependency
Estimated Orbit/Clock RMS Error
8 Stations
12 Stations
24 Stations
5.7cm
12.3cm
7.7cm
0.25ns
0.20ns
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