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

2

BackgroundBackground

3

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

4

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

6

(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

7

(Currently ~15 km off‐shore)http://www.tsunamigps.com

Strategy forStrategy for Long‐Baseline RTKg

8

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

9

– 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

10

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

12

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.

i f15

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

17

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

22

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

25

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

26Ratio

 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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