precise orbit determination of gps satellites using carrier phase measurement technical consultant...
TRANSCRIPT
![Page 1: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/1.jpg)
Precise Orbit Determination of Precise Orbit Determination of GPS Satellites using Carrier GPS Satellites using Carrier
Phase MeasurementPhase Measurement
Technical ConsultantTechnical Consultant Tomoji TAKASUTomoji TAKASU
Kasai Design Office Ltd.Kasai Design Office Ltd. Shoji KASAIShoji KASAI
![Page 2: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/2.jpg)
http://gpspp.sakura.ne.jp
MotivationMotivation
• 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
![Page 3: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/3.jpg)
http://gpspp.sakura.ne.jp
LCphwrel
pcvrpcvsLC
LLLC
NTdTdtc
CC
)(
21 2211
Measurement ModelMeasurement Model
Undifferenced (Zero-Differenced)Ionosphere-Free Linear Combination of Carrier Phase Measurements (L1,L2)
)/(2)/(1 22
21
22
22
21
21 fffCfffC
![Page 4: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/4.jpg)
http://gpspp.sakura.ne.jp
Geometric DistanceGeometric Distance
)'''()(
)(
apcrsdisprT
apcss
dtt
cdtt
ΔΔrU
Δr
Light-Time Equation
sr
'' sdispr Δr
'apcrΔ
apcsΔ
![Page 5: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/5.jpg)
http://gpspp.sakura.ne.jp
Time SynchronizationTime Synchronization
ttttr
GMttt s
sEss )()(2
1)()( 23
vrr
2233333
)(
)()(3
)(2),(
)(
)(t
tr
tt
tr
GMttt
t
tts
Tss
sE
rrs
s
rr
11Φr
r
)(
)(
)()()( t
tt
tttt s
s
sssLC
r
r
rrr
T
antrsdisprT
antss
s
dtttt
tt
)'''()()(
)(
ΔΔrUΔr
r
)/( cdtt
![Page 6: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/6.jpg)
http://gpspp.sakura.ne.jp
ECI to ECEF TransformationECI to ECEF Transformation
)()()()()()( ttGASTyxt zpxpy PNRRRU
• Precession/Nutation Model :IAU1976/1980, IERS1996, IAU2000A
• Earth Rotation Parameters
)(sec19
))1(()10(
cos
TAIUTCtt
UTCUTtrUTGMSTGMST
GMSTGAST
GPSTUTC
UTCh
![Page 7: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/7.jpg)
http://gpspp.sakura.ne.jp
Tropospheric Delay ModelTropospheric Delay Model
))(1)((
)(
ZHDZTDgGgGElM
ZHDElMT
NNEEwet
dry
)coscotsincot( AzElgAzElg NE
• ZTD : Zenith Total Delay
• GE ,GN : Tropospheric Gradient
• Mdry,Mwet : Mapping Function (NMF etc)
)00028.02cos00266.01/(0022768.0 0 HPZHD
![Page 8: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/8.jpg)
http://gpspp.sakura.ne.jp
Satellite Antenna Offset/PCVSatellite Antenna Offset/PCV
PRN22 Nadir Angle - Postfit Residuals (m)
• Satellite Antenna Offset (m)Block II/IIA : (0.279,0,1.023), IIR : (0,0,0)
• Satellite Antenna PCV
)( pcvspcvssataoecisatapcs ΔEΔ
![Page 9: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/9.jpg)
http://gpspp.sakura.ne.jp
Receiver Antenna Offset/PCVReceiver Antenna Offset/PCV
• Eccentricity : Marker to ARP
• Antenna PCV : IGS_01.PCVAPC : ARP to L1/L2 Phase CenterPCV : Elevation Dependent Variation
)(2)(1
21'
21
21
ElΔCElΔCΔ
CC
pcvrpcvrpcvr
apcrapcrecceceflocalapcr
ΔΔΔEΔ
APC
ARP
Marker
![Page 10: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/10.jpg)
http://gpspp.sakura.ne.jp
Site DisplacementsSite Displacements
• Solid Earth Tides
• Ocean Loading
• Polar Tides
• Atmospheric Loading, Snow, ...
• IERS Conventions 1996/2003
)(' polaroceansolideceflocalsdisp ΔΔΔEΔ
![Page 11: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/11.jpg)
http://gpspp.sakura.ne.jp
Relativity/Phase Wind-up EffectRelativity/Phase Wind-up Effect
• Relativistic Effect to Satellite Clock
• Phase Wind-up EffectRCP phase affected by Relative Rotation between Satellite/Receiver Antenna
)'/'(cos)21( 121 DDDD CCΔphw
sr
sr rrrrkykxkkxDykxkkxD /)(')'('')(
cΔ ssrel /2 vr
![Page 12: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/12.jpg)
http://gpspp.sakura.ne.jp
Satellite Orbit ModelSatellite Orbit Model
• Geopotential : JGM-3 + Tidal Effects
• 3rd Body : Moon/Sun, JPL DE405
• Solar Radiation Pressure : GPS SRP Model
• Relativity Effect
relsrprdbodygeop
sEs
r
GMaaaa
rr 33
''
![Page 13: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/13.jpg)
http://gpspp.sakura.ne.jp
Perturbations of Satellite Orbit Perturbations of Satellite Orbit A
ccel
erat
ion
(m/s
2 )
1
10-2
10-4
10-6
10-8
10-10
10-12
0 10000 20000 30000Height (km)
GEOGPS
GM
J2,0
J2,2 Moon
Sun
SRPSolid TideRelativity
J6,6
J18,18
Air Drag
![Page 14: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/14.jpg)
http://gpspp.sakura.ne.jp
GPS SRP ModelGPS SRP Model
• Precise GPS Specific SRP ModelROCK 4/42CODE RPRGSPM04.b
• Eclipse ModelCylindric, Penumbra/Umbra
![Page 15: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/15.jpg)
http://gpspp.sakura.ne.jp
Other State Transition ModelsOther 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
![Page 16: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/16.jpg)
http://gpspp.sakura.ne.jp
Estimation FilterEstimation Filter
kT
kkkkkk
t
tkkk
tttt
dk
k
QΦPΦP
xxxx
),()(),()(
)),(ˆ()(ˆ)(ˆ
111
11
)()()(
)))(ˆ(()(ˆ)(ˆ
))(()( 1
kkkk
kkkkk
kT
kkkT
kkk
PHKIP
xhzKxx
RHPHHPK
Extended Kalman Filter
kz
![Page 17: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/17.jpg)
http://gpspp.sakura.ne.jp
Backward Filter/SmootherBackward Filter/Smoother
)(ˆ)()(ˆ)()()()(ˆ 11111 ttttttTt bbb xPxPPPx
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
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
3D P
ositi
on E
rror
(m
)
Forward (RMS:66.9cm)Backward (RMS:4.0cm)Smoothed (RMS:3.6cm)
PRN01 Orbit Estimation Error (wrt IGS Final)
![Page 18: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/18.jpg)
http://gpspp.sakura.ne.jp
Quality ControlQuality 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
![Page 19: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/19.jpg)
http://gpspp.sakura.ne.jp
Evaluation of AccuracyEvaluation 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
![Page 20: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/20.jpg)
http://gpspp.sakura.ne.jp
GpsTools (GT) ver.0.5.5GpsTools (GT) ver.0.5.5
![Page 21: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/21.jpg)
http://gpspp.sakura.ne.jp
IGS 40 StationsIGS 40 Stations
150 W 120 W 90 W 60 W 30 W 0 30 E 60 E 90 E 120 E 150 E 180 E
60 S
30 S
0
30 N
60 N
ALGO
AMC2
AREQASC1
AUCK
BAHR
CAS1
CEDU
COCO
DAV1
DRAO
FAIR
HOB2
IISC
IRKT
KERG
KOUR
LHAS
LPGS
MAC1
MAG0
MAS1MATE
MKEA
NRC1
NRIL
ONSA
PERT
PIE1
PIMO
POL2
REUN
RIOG
STJO
THTI
TROM
TSKBUSNO VILL
YELL
![Page 22: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/22.jpg)
http://gpspp.sakura.ne.jp
Estimated ParametersEstimated Parameters
ParametersNumberof States
Sats/Stas Total
Satellite Position/Velocity 6 29 174Satellite SRP Parameters 4 29 116Satellite Clock 2 29 58Station Tropos. ZTD 1 40 40Station Tropos. Gradient 5 40 200Station Receiver Clock 1 40 40Carrier Phase Bias 1 29 x 40 1160Earth Rotation Parameters 3 1 3Total Parameters per Epoch 1788
![Page 23: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/23.jpg)
http://gpspp.sakura.ne.jp
IGS Final Orbit/ClockIGS 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
![Page 24: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/24.jpg)
http://gpspp.sakura.ne.jp
Estimated Orbit AccuracyEstimated Orbit Accuracy
3D RadialAlong-Track
Cross-Track
PositionRMSError
5.18cm 1.97cm 3.43cm 3.12cm
Average of 29 Satellites, wrt IGS Final
![Page 25: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/25.jpg)
http://gpspp.sakura.ne.jp
Orbit Accuracy by SatellitesOrbit Accuracy by Satellites
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
GP
S01
G
PS
03
GP
S04
G
PS
05
GP
S06
G
PS
07
GP
S08
G
PS
09
GP
S10
G
PS
11
GP
S13
G
PS
14
GP
S15
G
PS
16
GP
S17
G
PS
18
GP
S19
G
PS
20
GP
S21
G
PS
22
GP
S23
G
PS
24
GP
S25
G
PS
26
GP
S27
G
PS
28
GP
S29
G
PS
30
GP
S31
A
vera
ge
Pos
ition
RM
S E
rror
(m
)
3DRadialAlong-TrackCross-Track
Orbit Error wrt IGS Final
![Page 26: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/26.jpg)
http://gpspp.sakura.ne.jp
Estimated Orbit (Example)Estimated Orbit (Example)
0
0.1
0.2
0.3
0.4RMS: 0.0385m
Pos
itio
n E
rror
3D
(m
)
10/3 10/4 10/5 10/6 10/7 10/8 10/9
-0.2
-0.1
0
0.1
0.2
RMS R: 0.0121m A: 0.0321m C: 0.0175mPos
itio
n E
rror
R/A
/C (
m)
RadialAlong-TrackCross-Track
PRN01 Orbit Error wrt IGS Final
![Page 27: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/27.jpg)
http://gpspp.sakura.ne.jp
Estimated Clock AccuracyEstimated Clock Accuracy
With BIAS Without BIAS
Clock BiasRMS Error 0.135ns 0.099ns
Average of 29 Satellites, wrt IGS Final
![Page 28: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/28.jpg)
http://gpspp.sakura.ne.jp
Clock Accuracy by SatellitesClock Accuracy by Satellites
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
GP
S01
G
PS
03
GP
S04
G
PS
05
GP
S06
G
PS
07
GP
S08
G
PS
09
GP
S10
G
PS
11
GP
S13
G
PS
14
GP
S15
G
PS
16
GP
S17
G
PS
18
GP
S19
G
PS
20
GP
S21
G
PS
22
GP
S23
G
PS
24
GP
S25
G
PS
26
GP
S27
G
PS
28
GP
S29
G
PS
30
GP
S31
A
vera
ge
Clo
ck B
ias
RM
S E
rror
(ns
ec)
Clock Error wrt IGS Final
![Page 29: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/29.jpg)
http://gpspp.sakura.ne.jp
Estimated Clock (Example)Estimated Clock (Example)
3.662
3.664
3.666
3.668
3.67x10
5
Clo
ck B
ias
(ns)
10/3 10/4 10/5 10/6 10/7 10/8 10/9-1
-0.5
0
0.5
1
Clo
ck B
ias
Err
or (
ns)
MEAN: 0.073ns RMS: 0.127ns
PRN01 Clock/Clock Error wrt IGS Final
![Page 30: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/30.jpg)
http://gpspp.sakura.ne.jp
Estimated ZTD (Example)Estimated ZTD (Example)ALGO Tropospheric ZTD
![Page 31: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/31.jpg)
http://gpspp.sakura.ne.jp
Estimated ERPEstimated ERP
0.2
0.201
0.202
0.203
Xp
(")
0.415
0.42
0.425
Yp
(")
10/3 10/4 10/5 10/6 10/7 10/8 10/9-0.4576-0.4574-0.4572-0.457
-0.4568-0.4566
UT
1-U
TC
(se
c)
IGS Final
![Page 32: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/32.jpg)
http://gpspp.sakura.ne.jp
Station Geometry DependencyStation Geometry Dependency
8 Stations 12 Stations 24 Stations
12.3cm 7.7cm 5.7cm
0.25ns 0.20ns 0.16ns
Estimated Orbit/Clock RMS Error
Average of 29 Satellites, wrt IGS Final
![Page 33: Precise Orbit Determination of GPS Satellites using Carrier Phase Measurement Technical Consultant Tomoji TAKASU Kasai Design Office Ltd. Shoji KASAI](https://reader035.vdocuments.site/reader035/viewer/2022062305/5697bffb1a28abf838cc0ef3/html5/thumbnails/33.jpg)
http://gpspp.sakura.ne.jp
ConclusionsConclusions
• 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