GPS衛星の高精度軌道・時計決定
Precise Orbit/Clock Determination of GPS Satellites
2005/10/08 Home

目次
搬送波位相観測値を使用したGPS衛星の高精度軌道決定
GPS衛星軌道及び時計準リアルタイム推定アルゴリズムの開発及びその評価
GPS衛星軌道・時計精度
GPS衛星軌道・時計による精密単独測位(PPP)精度
推定パラメータによるGPS衛星軌道精度の変化
GpsToolsによるGPS軌道推定記録

搬送波位相観測値を使用したGPS衛星の高精度軌道決定
Precise Orbit Determination of GPS Satellites using Carrier Phase Measurements

高須知二, 笠井晶二
Tomoji Takasu, Shoji Kasai

Abstract

For the precise positioning with GPS, it is necessary to provide accurate satellite orbit and clock. We have developed a software package to determine high precision GPS satellite orbit and clock. In the software, using undifferenced carrier phase measurements, satellite orbit and clock are estimated by Extended Kalman Filter (EKF). For the improvement of the orbit and clock accuracy, backward filter and iterated filter can be added to the conventional 1-pass forward filter. In the measurement model, geometric distance is computed by light-time iteration synchronized to GPS Time, corrected by the receiver clock bias. Ionospheric delay is eliminated by the liner combination of two frequency carrier phase measurements. Tropospheric delay is estimated as ZTD (Zenith Total Delay) and horizontal gradient parameters using tropospheric mapping function. Receiver clock, Earth Rotation Parameters and phase bias are estimated simultaneously. Additionally, the measurement model contains precise measurement corrections such as antenna phase center offsets, phase-windup effect, relativistic effects and station displacements by earth tides. Site displacements include solid earth tides, ocean loading and polar tides models, computed according to IERS conventions. The satellite orbit model incorporates geopotential of JGM-3, gravity correction by earth tides, third body of sun/moon, eclipse by earth/moon, relativistic effects and various GPS-specific SRP (Solar Radiation Pressure) models. Quality control and outliers' detection are done using prefit and postfit residuals. Abnormal satellites and stations are excluded by statistical check of the residuals.
For the test, using world-wide 40 IGS (International GPS Service) stations' observation data, 29 GPS satellites' orbit and clock were estimated. A priori satellite position and clock bias are obtained from GPS broadcast ephemerides. Initial tropospheric delay parameters are acquired by the standard atmosphere model. Station positions are fixed to the estimated values by PPP (Precise Point Positioning) with previous week's IGS final orbit/clock. Compared with IGS final orbit/clock, estimated satellite position 3D RMS error was 5.2 cm. Clock bias RMS error was 0.14 nsec.

GPSによる精密測位のためには高精度のGPS衛星軌道・時計推定値が必要となる。我々はGPS衛星軌道・時計を高精度に決定するためのプログラムパッケージを開発した。このソフトウェアではゼロ差の搬送波位相観測値を使用し拡張カルマンフィルタ(EKF)によりGPS衛星軌道・時計を決定する。決定精度を改善するため通常の1パスforwardフィルタに加えてbackwardフィルタ及びiterationを適用することもできる。観測モデルでは受信機時計誤差を補正しGPS時刻系に同期した光差方程式を解いて幾何距離を算出する。電離層遅延は二周波搬送波位相観測値の線形結合により除去する。対流圏遅延はマッピング関数を使って天頂全遅延(ZTD)及び水平勾配パラメータとして推定する。衛星位置・速度、時計に加え、受信機時計、地球回転パラメータ及び搬送波位相バイアスについてもパラメータとして推定する。観測モデルにはアンテナ位相中心オフセット、phase-windup効果、相対論効果及び地球潮汐による局位置変動の精密補正も含んでいる。衛星運動モデルにはJGM-3地球重力モデル、地球潮汐による重力補正、月・太陽重力、地球・月による食、相対論効果及びGPS衛星独自の精密太陽輻射圧(SRP)モデルを含む。品質管理のためprefit及びpostfit残差によるアウトライア検出を行う他、残差の統計値チェックにより異常衛星・観測局を識別し除外することもできる。試験のため全世界のIGS (International GPS Service) 観測局40局の観測データを使い、GPS 29衛星の軌道・時計を決定した。衛星軌道・時計の初期値は放送暦を、対流圏遅延の初期値は標準大気モデルを使用した。観測局位置は前週のIGS最終暦を使って精密単独測位 (PPP) 法により決定した座標に固定した。IGS最終暦と比較した衛星位置の3D RMS誤差は5.2cm、同じく時計バイアスのRMS誤差は0.14nsであった。

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高須知二, 笠井晶二, 搬送波位相観測値を使用したGPS衛星の高精度軌道決定, 平成17年度アストロダイナミクスシンポジウム (PDF 256KB)
Tomoji Takasu, Shoji Kasai, Precise Orbit Determination of GPS Satellites using Carrier Phase Measurements, The 15th Workshop on JAXA Astro Dynamics and Flight Mechanics, 2005

高須知二, 笠井晶二, 搬送波位相観測値を使用したGPS衛星の高精度軌道決定, 平成17年度アストロダイナミクスシンポジウム(発表資料) (Power Point 1.50MB)
Tomoji Takasu, Shoji Kasai, Precise Orbit Determination of GPS Satellites using Carrier Phase Measurements, The 15th Workshop on JAXA Astro Dynamics and Flight Mechanics, 2005

GPS衛星軌道・時計推定結果詳細
GPS Satellite Orbit/Clock Estimation Results


GPS衛星軌道及び時計準リアルタイム推定アルゴリズムの開発及びその評価
Development and evaluation of GPS satellite orbit and clock near-realtime estimation algorithm

高須知二, 笠井晶二
Tomoji Takasu, Shoji Kasai

Abstract

For the realtime precise positioning by GPS, it is necessary to provide high precision satellite orbit and clock. We have developed a near-realtime algorithm to estimate high precision GPS satellite orbit and clock. In the algorithm, using zero-difference ionosphere-free carrier phase as the basic observable, satellite orbit and clock are estimated by Extended Kalman Filter (EKF). Tropospheric delay, receiver clock, ERP and phase bias are obtained as well. Measurement model contains precise corrections such as antenna phase center offsets, relativistic effects and site displacement by earth tides. The satellite orbit model incorporates geogravity, moon/sun gravity and various SRP models. For the test, using IGS 40 stations' observation data as input, GPS satellite orbit and clock were estimated. Compared with IGS final orbit/clock, satellite position 3D RMS errors were 9.3cm (1pass) and 6.0cm (3pass). Clock bias RMS errors were 0.16ns (1pass) and 0.15nsec (3pass).

GPSによるリアルタイム精密測位のためには高精度の衛星軌道及び時計が提供されることが必要である。私たちはGPS衛星軌道及び時計を準リアルタイムで高精度に推定するアルゴリズムを開発した。このアルゴリズムにおいてはゼロ差の電離層フリー搬送波位相を基本観測量とし、拡張カルマンフィルタ (EKF)を用いて衛星軌道及び時計を推定する。対流圏遅延、受信機時計、地球回転パラメータ及び搬送波位相バイアスが同時に得られる。観測モデルにはアンテナ位相中心オフセット、相対論効果、地球潮汐による観測点位置変位等の高精度補正が含まれる。衛星運動モデルには地球重力、月及び太陽重力及び各種の太陽輻射圧モデルを含んでいる。試験のためIGS観測局40局の観測データを入力としてGPS衛星軌道及び時計を推定した。IGS最終暦と比較した衛星位置の3DRMS誤差は9.3cm (1pass) および6.0cm (3pass) であった。時計バイアスRMS誤差は0.16ns (1pass) 及び0.15ns (3pass) であった。

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高須知二,笠井晶二, GPS衛星軌道及び時計準リアルタイム推定アルゴリズムの開発及びその評価, 2005年地球惑星科学関連学会合同大会(予稿)(PDF: 236KB)
Tomoji Takasu, Shoji Kasai, Development and evaluation of GPS satellite orbit and clock near-realtime estimation algorithm, 2005 Joint Meeting for Earth and Planetary Science (preliminary paper)

高須知二,笠井晶二, GPS衛星軌道及び時計準リアルタイム推定アルゴリズムの開発及びその評価, 2005年地球惑星科学関連学会合同大会(発表資料)(PowerPoint: 953KB)
Tomoji Takasu, Shoji Kasai, Development and evaluation of GPS satellite orbit and clock near-realtime estimation algorithm, 2005 Joint Meeting for Earth and Planetary Science (draft handsout)

GPS衛星軌道・時計推定結果詳細 (1pass推定、衛星軌道)
GPS Satellite Orbit Estimation Results (1pass Estimation)

GPS衛星軌道・時計推定結果詳細 (1pass推定、衛星時計)
GPS Satellite Clock Estimation Results (1pass Estimation)

GPS衛星軌道・時計推定結果詳細 (3pass推定、衛星軌道)
GPS Satellite Orbit Estimation Results (3pass Estimation)

GPS衛星軌道・時計推定結果詳細 (3pass推定、衛星時計)
GPS Satellite Clock Estimation Results (3pass Estimation)

推定衛星軌道・時計を使用したPPP測位結果詳細 (1pass推定)
PPP Results by Estimated Satellite Orbit/Clock (1pass Estimation)

推定衛星軌道・時計を使用したPPP測位結果詳細 (3pass推定)
PPP Results by Estimated Satellite Orbit/Clock (3pass Estimation)


GPS衛星軌道・時計精度
GPS Satellite Orbit/Clock Accuracy

Realtime/Near-Realtime Orbit/Clock Accuracy
Realtime/Near-Realtime Orbit/Clock Analysis software RMS Error
Satellite Orbit Satellite Clock
GpsTools 1pass Estimation GpsTools ver.0.5.4 9.3cm 0.16ns
IGS Ultra Rapid Predicted 6H - 14.9cm 1.98ns
Observed 6H - 7.7cm 0.40ns


Precise/Final Orbit/Clock Accuracy
Precise/Final Orbit/Clock Analysis software RMS Error
Satellite Orbit Satellite Clock
GpsTools 3pass Estimation GpsTools ver.0.5.4 6.0cm 0.15ns
GpsTools ver.0.5.5 5.2cm 0.14ns
IGS Rapid - 2.4cm 0.08ns
IGS AC Solutions CODE Bernese ver.5.0 3.3cm 0.11ns
NRCan(EMR) GIPSY/OASIS-II ver.2.6 3.8cm 0.10ns
ESOC BAHN,GPSOBS,BATUSI 14.2cm 0.13ns
GFZ EPOS.P.V.2 3.1cm 0.09ns
JPL GIPSY/OASIS-II 5.5cm 0.15ns
MIT GAMIT ver.10.02,GLOBK ver.5.08 5.3cm 0.31ns
NOAA page5 9.9cm -
SOPAC GAMIT ver.9.72,GLOBK ver.4.17 7.5cm -

(GPS Week1291, Orbit : 3DRMS, Average of 29 GPS Satellites, wrt IGS Final Orbit/Clock)


GPS衛星軌道・時計による精密単独測位(PPP)精度
Precise Point Poisitioning (PPP) Accuracy with GPS Satellite Orbit/Clock

PPP Accuracy with Realtime/Near-Realtime Orbti/Clock
Realtime/Near-Realtime Orbit/Clock RMS Error Repeatability
East North Up East North Up
GpsTools 1pass Estimation 10.5mm 6.4mm 13.6mm 6.0mm 3.9mm 9.0mm
IGS Ultra Rapid Predicted 6H 204.8mm 146.6mm 321.9mm 180.5mm 133.0mm 277.9mm
Observed 6H 22.8mm 9.2mm 43.8mm 21.1mm 7.9mm 39.7mm


PPP Accuracy with Precise/Final Orbti/Clock
Precise/Final Orbit/Clock RMS Error Repeatability
East North Up East North Up
GpsTools 3pass Estimation 3.8mm 3.0mm 7.5mm 2.8mm 1.5mm 4.7mm
IGS Rapid 3.5mm 2.3mm 6.7mm 2.0mm 1.3mm 4.2mm
IGS Final 3.2mm 2.2mm 6.1mm 1.7mm 1.2mm 3.6mm
IGS AC Solutions CODE 4.6mm 2.5mm 7.3mm 2.1mm 1.5mm 4.3mm
NRCan(EMR) 3.3mm 2.5mm 7.0mm 2.1mm 1.2mm 4.3mm
ESOC 3.8mm 3.8mm 11.3mm 2.5mm 1.5mm 4.5mm
GFZ 3.9mm 2.2mm 7.0mm 2.0mm 1.2mm 4.2mm
JPL 5.9mm 3.1mm 9.3mm 2.6mm 1.7mm 4.8mm
MIT 4.1mm 2.7mm 6.4mm 2.6mm 1.5mm 4.5mm

(GPS Week1291, 24H solution by GT0.5.4 static PPP, Average of 20 IGS Stations, wrt IGS Final Position)


推定パラメータによるGPS衛星軌道精度の変化
Orbit Accurcay with Various Estimation Parameters

Orbit Accuracy Dependancy to the Estimation Parameters
Analysis ID Estimation Parameters Orbit Error Note
200410c GT0.5.4
3pass, 24H+overlap6H, Est Interval: 300s,
29 Satellites, 40 Stations, Station Positions: fix to prev. week PPP results, Meas. Noise:1cm, Min Elevation: 10deg, Meas. Correction: All except for multi-pass, Station Displacement: All, Geopotential: 8degree, SRP Model: CODE+4par, Earth Tides: Solid Earth, Relativitistic Effect: on, Process Noise (1/sqrt(sec))
Sat Velocity: 1E-9m/s, Sat Clock Bias: 1E-2m, SRP: 1E-5, Geocenter Offset : fix to 0, ERP Var. Correction: on, Sat Clock Model: Gauss-Marcov
6.92cm Reference
(Details)
200410c-1pass 1pass, 24H+overlap0H 10.16cm
200410c-1pass-30s 1pass, 24H+overlap0H, Est Interval: 30s 26.07cm Error
200410c-1pass2 1pass, 24H+overlap0H, Process Noise Sat Velocity: 1E-10m/s 9.34cm
200410c-1pass3 1pass, 24H+overlap0H, Process Noise SRP: 1E-4 11.50cm
200410c-12ov1 overlap12H, Earth Tides: Solid+Ocean 6.59cm
200410c-12ov2 overlap12H, Earth Tides: Solid+Ocean, Process Noise Sat Velocity: 1E-10m/s 6.08cm
200410c-12ov3 overlap12H, Earth Tides: Solid+Ocean, Process Noise Sat Velocity: 1E-10m/s, Geopotential: 10degree 6.28cm
200410c-12ov4 overlap12H, Earth Tides: Solid+Ocean, Process Noise Sat Velocity: 1E-10m/s, SRP:1E-6 6.01cm
200410c-12ov5 overlap12H, Earth Tides: Solid+Ocean, Process Noise Sat Velocity: 1E-10m/s, SRP:1E-6 6.02cm
200410c-18ov1 overlap18H, others: same as 200410c-12ov4 5.80cm
200410c-24ov1 GT0.5.5alpha2
overlap 24H, meas noise factor: 0.6, std dev factor of predet states: 4, others: same as 2004c-12ov4
5.42cm
200410c-24ov2 GT0.5.5alpha1
60 Stations, others: same as 200410c-24ov1
5.78cm
1291c-prn2 GT0.5.5
35 Stations, Sat Antenna Pcv Corr. on, Process Noise: ZTD 1E-4m
others: same as 200410c-24ov1
5.32cm
1291c-prn4 GT0.5.5
37 Stations, Sat Antenna Pcv Corr. on, Process Noise: ZTD 1E-4m, Sat Velocity PRN29 5E-8m/s
, others: same as 200410c-24ov1
5.23cm
1291c-40rcv GT0.5.5
40 Stations, Initial ERP: IGS Final, others: same as 1291c-prn4
5.18cm
200410c-8rcv 8 Stations 12.79cm
200410c-12rcv 12 Stations 9.78cm
200410c-24rcv 24 Stations 7.35cm
200410c-30s Est Interval: 30s 7.92cm
200410c-150s Est Interval: 150s 7.11cm
200410c-el5 Min Elevation: 5deg 6.97cm
200410c-el15 Min Elevation: 15deg 7.01cm
200410c-pos Station Position: fix to IGS Final 7.63cm
200410c-geo Station Position: fix to IGS Final, Geocenter offset: Estimated 8.08cm
200410c-sclk Sat Clock Model: white-noise 7.60cm
200410c-odisp Station Displacement Ocean Loading: off 6.85cm
200410c-phwin Meas. Corrections: phase-windup off 7.15cm
200410c-erpv ERP Var Correction: off 29.73cm Error
200410c-rock4 SRP Model:ROCK4/42 14.63cm
200410c-gspm SRP Model:GSPM.04b 9.05cm
200410c-code SRP Model:CODE+3par 7.36cm
200410c-code3 SRP Model:CODE+6par 7.09cm
200410c-otide Earth Tides: Solid+Ocean 6.90cm
200410c-reloff Relativitistic Effect: off 6.96cm
200410c-noise Meas. Noise: 1.5cm 6.93cm
200410c-nose2 Meas. Noise: 1.2cm 6.90cm
200410c-nose3 Meas. Noise: 0.8cm 6.94cm
200410c-prn Process Noise Sat Velocity: 5E-10m/s 6.73cm
200410c-prn2 Process Noise Sat Velocity: 2E-10m/s 6.66cm
200410c-prn3 Process Noise Sat Velocity: 1E-10m/s 6.65cm
200410c-prn4 Process Noise SRP: 1E-6 6.91cm
200410c-prn5 Process Noise Sat Velocity: 0m/s 6.64cm
200410c-prn6 Process Noise SRP: 1E-7 6.91cm
200410c-prn7 Process Noise SRP: 1E-8 6.91cm
200410c-prn8 Process Noise Sat Clock Bias: 5E-3m 6.95cm



GpsToolsによるGPS軌道推定記録
Orbit Accuracy Records by GpsTools

Date 3D RMS Error Version
2004/07/02 31.6cm GT 0.2
2004/07/13 19.8cm GT 0.3
2004/07/14 17.0cm GT 0.4.2beta2
2004/07/25 12.5cm GT 0.4.2
2004/10/21 12.0cm GT 0.4.4
2004/11/10 10.0cm GT 0.5.2
2005/04/07 6.9cm GT 0.5.4
2005/04/25 6.0cm GT 0.5.4
2005/05/31 5.8cm GT 0.5.4
2005/06/09 5.7cm GT 0.5.5alpha
2005/06/25 5.4cm GT 0.5.5alpha2
2005/07/12 5.2cm GT 0.5.5



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