Kalman Filter Based Integer Ambiguity RltiResolution St tSt...
Transcript of Kalman Filter Based Integer Ambiguity RltiResolution St tSt...
ION GNSS 2010
Kalman‐Filter‐Based Integer Ambiguity R l ti St t f L B li RTK ithResolution Strategy for Long‐Baseline RTK with Ionosphere and Troposphere Estimation
Tokyo University of Marine Science and Technology
T ji TAKASU d Aki YASUDATomoji TAKASU and Akio YASUDA
ContentsContents
• Background• Strategy for Long‐Baseline RTKStrategy for Long Baseline RTK• Implementation• Performance Evaluation• Conclusion and Future WorkConclusion and Future Work
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BackgroundBackground
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RTK GPS/GNSSRTK‐GPS/GNSS
• Real‐Time Kinematic GPS/GNSS– cm‐level accuracy in real‐time– Kinematic positions of moving receiver (rover)
• Carrier‐Phase Based Relative PositioningCarrier Phase Based Relative Positioning– Transmit reference data to rover via wireless linkMust resolve integer ambiguity on the fly (OTF)– Must resolve integer ambiguity on‐the‐fly (OTF)
• Performance Depends on Baseline Length
ReferenceS i
RoverR i
Baseline
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Station Receiver
Effect of Baseline LengthEffect of Baseline LengthBL=0.3 km BL=13.3 km
W W
E‐W
‐S
E‐W
‐S
NU‐D
NU‐D
BL=32.2 km BL=60.9 km
W W
E‐W
N‐S
E‐W
N‐S
NU‐D
NU‐D
55: Fixed Solution : Float Solution)(24 hr Kinematic
Baseline Length and RTK StrategyBaseline Length and RTK StrategyBL Error Elimination
Strategy(km) StrategyEphem Ionos Tropos Others
S 0 10S 0 – 10 Broadcast ‐ ‐ ‐ ConventionalRTK
10 Dual‐Freq ‐ ‐M 10 –
100 Broadcast
Dual‐Freq ‐ ‐
Interpolation ‐ Network RTK
R l i LL 100 –
1,000
Real‐timePrecise(IGU)
Dual‐Freq EstimateZTD + MF
Earth Tides
Long‐BaselineRTK
VL >1,000Non‐RTPrecise(IGR IGS)
Dual‐Freq EstimateZTD + MF
EarthTides,Ph WU
Post‐Processingor PPP
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(IGR, IGS) Ph‐WU or PPP
Application of Long Baseline RTKApplication of Long‐Baseline RTK
100 km100 km
GPS TsunamiMonitoring System
( l k ff h )1,000 km
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(Currently ~15 km off‐shore)http://www.tsunamigps.com
Strategy forStrategy for Long‐Baseline RTKg
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Conventional AR StrategiesConventional AR Strategies
• Short‐Baseline RTK– Rapid initialization/re‐initialization (OTF‐AR)p / ( )– Efficient integer vector search algorithmIonosphere negligible in DD equations– Ionosphere negligible in DD equations
• Medium/Long‐Baseline Post‐Processing– Estimate WL/NL amb. by forming iono‐free LC– Sequential rounding of WL/NL ambiguitiesSequential rounding of WL/NL ambiguities– Slow convergenceL i d LC i ki i d
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– Larger noise due to LC in kinematic mode
Linear CombinationsLinear Combinations LC
Coefficients Terms in DD Equation DDNoise NotesLC Noise(cm)
NotesΦ1 Φ2 P1 P2 R+T I1 N1 N2
L1 λ1 1 1 λ1 0.6
L2 λ2 1 γ λ2 0.6
P1 1 1 ‐1 60
P2 1 1 ‐γ 60
L3 C λ C λ 1 0 C λ C λ 1 8 IonoL3 C1λ1 C2λ2 1 0 C1λ1 C2λ2 1.8 Iono‐FreeLCMW λWL ‐λWL
‐λNL/λ1
‐λNL/λ2
0 0 λWL ‐λWL 421 2
(L1+P1)/2 λ1/2 1/2 1 0 λ1/2 30 Alt.Iono‐Free(L2+P2)/2 λ2/2 1/2 1 0 λ2/2 30
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Free(L2+P2)/2 λ2/2 1/2 1 0 λ2/2 30
λ1=19cm, λ2=24cm, λWL=86cm, λNL=11cm, γ=f12/f22, C1= γ/(γ‐1), C2=‐1/(γ‐1)
AR Strategy for Long Baseline RTKAR Strategy for Long‐Baseline RTK
• No Linear Combination (LC)– Use all original phase and code observablesg p– Not generate WL or NL LCEstimate ionosphere terms explicitly– Estimate ionosphere terms explicitly
– Suppress carrier‐phase noises
• Directly Resolve L1 and L2 Ambiguities (N1, N2)– Search integer vector under ILS conditionSearch integer vector under ILS condition– Efficient process by LAMBDA/MLAMBDA with shrinking space by linear transformationshrinking space by linear transformation
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Other StrategiesOther Strategies
• Extended Kalman‐Filter for Real‐Time Est.• EphemerisEphemeris
– IGU Predicted Orbit (Accuracy ~ 5 cm)
• Troposphere– Estimate ZWD and gradient at ref and rover sites gwith mapping function (NMF)
• Other CorrectionsOther Corrections– Receiver/satellite antenna PCV: IGS05.ATX– Earth tides: solid earth tide model by IERS
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Results by Simple ImplementationResults by Simple Implementation: Fixed Solution : Float Solution
E‐W
N‐S
U‐D
Factor
AR Ratio
13BL=300.0 km STD=2.2,2.3,3.2cm, Fix Ratio=46.4%
Partial Fixing of AmbiguitiesPartial Fixing of Ambiguities
• Search Type AR Strategy under ILS Condition– All of ambiguities should be fixed at the same timeg– Rising satellites often disturb ambiguity fixing
N t All A bi iti t b Fi d• Not All Ambiguities must be Fixed – Trade‐off between accuracy vs. fixing ratio
• Some Criteria to Determine Fixed or FloatVariance of estimated ambiguity– Variance of estimated ambiguity
– Duration of continuous valid data
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– Satellite elevation angle
Feedback Fixed Ambiguity to FilterFeedback Fixed Ambiguity to FilterOpen Loop AR
RTK AmbiguityRover Float
SolutionFixed
SolutionFilter Resolution
Ref.
Rover Fixed SolutionFix and Hold Mode
RTKFilter
A bi it
RoverFloat
Solution
Fixed Solution
AmbiguityResolution
Ref.
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Integer Constraint for Fixed Ambiguities
Performance ImprovementPerformance Improvement: Fixed Solution : Float Solution
E‐W
N‐S
U‐D
Factor
AR Ratio
16BL=300.0 km STD=1.1,1.9,3.5cm, Fix Ratio=99.3%
Implementation
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RTKLIB v 2 4 1bRTKLIB v.2.4.1b• Open source program p p gpackage for GNSS positioning– Whole source codes are freelyyavailable
– License: GPLv3– 5000+ downloads (2.3.0)
• Portable library +Portable library +several APs– ANSI C + socket/pthreadANSI C + socket/pthread …– Portable command‐line APs– GUI APs for Windows
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GUI APs for Windowshttp://www.rtklib.com
RTKLIB APs on WindowsRTKLIB APs on Windows
RTKNAVI: Real‐time AP RTKPOST: Post‐Processing
19RTKCONV: RINEX converterRTKPLOT: Plotting solutions
Tests forTests for Performance EvaluationPerformance Evaluation
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Offline TestOffline TestJanuary 1‐7 2009 (Winter)January 1 7, 2009 (Winter)July 1‐7, 2009 (Summer)30 s x 1 week RINEXBL= 30 s x 1 week RINEX
Rover:477 GEONET Stations
29.9 km ‐1,099.9 km
477 GEONET StationsReference:
GEONET 2110 Tsukuba12110 GEONET 2110 Tsukuba1Ephemeris:
IGU (predicted)
Tsukuba1
IGU (predicted)Analysis S/W:
RTKPOST v2 4 1b1,000 km
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RTKPOST v2.4.1b
Offline Test ResultsOffline Test ResultsJanuary 1‐7, 2009 July 1‐7, 2009
W
BL=471.2 kmE‐W
‐SN
U‐D
BL=961.3 km
UW
STD=1.1,1.3,3.8 cm FIX=99.0%STD=0.7,0.9,2.3 cm FIX=99.8%
E‐W
‐SN‐
U‐D
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U
STD=1.1,1.5,3.6 cm FIX=96.2%STD=1.6,1.3,3.0 cm FIX=98.8%
Summary of Offline Test ResultsSummary of Offline Test ResultsJanuary 1‐7, 2009 July 1‐7, 2009
Ave=0.7,0.9,2.6cm Ave=1.4,1.6,5.2cm
0 0
Ave=97 8% Ave=93 4%
23Baseline Length (km) Baseline Length (km)
Ave=97.8% Ave=93.4%
Real Time TestReal‐Time TestSeptember 17‐20, 2009
MIZU1 Hz x 72 H
Rover: NovAtelSUWN BL=
435.7 kmBL=
OEMV‐3 + GPS‐702‐GGReference: BL
1,024.8 km Rover IGS MIZU and SUWN
MIZU
ReceiverNTRIP+RTCM v.3
SUWNBKGIGS‐IPServer
RTKNAVIv.2.4.1b
24CDDIS
…FTP (every 6H)
Real Time Test Results (1)Real‐Time Test Results (1)W
BL=435.7 km, STD=3.0,2.7,7.4cm, FIX=93.5%E‐W
‐SN‐
‐DU‐
W
BL=1024.8 km, STD=3.3,2.9,7.8cm, FIX=56.9%
E‐W
‐SN‐
‐D
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U‐
Real Time Test Results (2)Real‐Time Test Results (2)BL=435.7 km
f Sat
# of
ency
Late
Factor
BL=1024.8 km
Ratio
f Sat
# of
ency
Late
Factor
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F
Conclusion and Future Work
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Conclusion and Future WorkConclusion and Future Work
• A strategy for long‐baseline RTK proposed• Offline test in 30 ‐ 1,100 km baselinesOffline test in 30 1,100 km baselines• Real‐time test in 436 and 1,025 km baselines• Proposed strategy works well up to 1,000 km baseline
• Performance degraded in summer time• Need integration of meteorological info to improve troposphere correction
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