geometric approach to position determination in space: advantages … · 2020. 1. 3. · 1 geodetic...

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Geodetic and Geoinformation Science

Geometric Approach to Position Determination in Space: Advantages

and LimitationsDorota Grejner-Brzezinska and Tae-Suk Bae

Department of Civil and Environmental Engineering

and Geodetic Science

The Ohio State University

and

Jay Kwon

Department of Earth Sciences

Sejong UniversityKorea

OSU

ION Annual Meeting 2002

Albuquerque, June 24-26 2002

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OutlineOutline

Kinematic POD with triple differencesKinematic POD with triple differences

Data screening (CS detection) Data screening (CS detection)

Orbit smoothing Orbit smoothing

Achievable accuracyAchievable accuracy

SummarySummary

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Kinematic PODKinematic POD

AdvantagesAdvantagesNo force model error affects the solutionNo force model error affects the solution

Fast (potential for nearFast (potential for near--real time)real time)

Quality solution for good PDOPQuality solution for good PDOP

DisadvantagesDisadvantagesNo dynamics to compensate for weak geometryNo dynamics to compensate for weak geometry

No solution or weak solution for weak geometryNo solution or weak solution for weak geometry

Requires correct coordinates for a starting epoch Requires correct coordinates for a starting epoch (forward solution only)(forward solution only)

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Triple Difference PODTriple Difference POD

Triple difference kinematic precision orbit Triple difference kinematic precision orbit determination (POD)determination (POD)

OSU software GODIVA (1995): triple difference OSU software GODIVA (1995): triple difference approach to GPS POD approach to GPS POD

OSU software OSU software PP--KODKOD ((PPrecision recision KKinematic inematic OOrbit rbit DDetermination)etermination)

Extension of GODIVA to handle LEO (Low Earth Extension of GODIVA to handle LEO (Low Earth Orbiter) POD in kinematic mode (2001)Orbiter) POD in kinematic mode (2001)

UTX (Byun, S. H., 1998) LEO kinematic PODUTX (Byun, S. H., 1998) LEO kinematic POD

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Triple Difference PODTriple Difference POD

Primary advantage: fast, no ambiguity fixing Primary advantage: fast, no ambiguity fixing

Disadvantage: epochDisadvantage: epoch--toto--epoch correlation (nonepoch correlation (non--

diagonal variancediagonal variance--covariance matrix)covariance matrix)Cholesky decomposition and decorrelation schemeCholesky decomposition and decorrelation scheme

Requires good approximated orbit to detect CS Requires good approximated orbit to detect CS

(large residuals)(large residuals)

Equivalent to double difference with float Equivalent to double difference with float

ambiguitiesambiguities

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PP--KOD Data Processing: CHAMP KOD Data Processing: CHAMP

24 hour data sets processed24 hour data sets processed65 IGS tracking stations65 IGS tracking stations

3030--s data sampling rates data sampling rate

Elevation cut off Elevation cut off angle angle 00ºº (CHAMP) and 10(CHAMP) and 10ºº ((stationsstations))

CS detection based on initial SNR prescreening, and CS detection based on initial SNR prescreening, and triple difference residual analysistriple difference residual analysis

NNormal matrix is accumulated until a singularity ormal matrix is accumulated until a singularity point is reached (too few observations or bad point is reached (too few observations or bad geometry)geometry)

Initial epoch released (forward/backward filter)Initial epoch released (forward/backward filter)

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P-KODE Processing FlowchartPP--KODE Processing FlowchartKODE Processing Flowchart

LEO orbit interpolation between epochs of observation

IGS reference stations and GPS orbit data or OSU

GODIVA

Station clock error estimation

LEO observation data

Construct triple phase differences

LEO POD Main Procedure

A priori values for LEO and station coordinates

Normal matrix

Reduce normal matrix

Solution and update of the a priori values

Data prescreeningSNR analysis

Binary local data base

Cycle slips detection

Forward/Backward Solution

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Example ResultsExample Results

Good orbit approximation available to clean Good orbit approximation available to clean (remove) CS as large triple difference residuals(remove) CS as large triple difference residuals

One iteration allows for convergenceOne iteration allows for convergence

Forward filtering (batch least squares)Forward filtering (batch least squares)

Backward filteringBackward filtering

Average percentage of CS in the dataAverage percentage of CS in the dataCHAMP: 5CHAMP: 5--66

Tracking stations: <0.5Tracking stations: <0.5

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873873# of Epochs with C/S# of Epochs with C/S

28802880Total # of EpochsTotal # of Epochs

20072007# of Epochs with no C/S# of Epochs with no C/S

Distribution of Cycle Slips: 24 h Data Set, June 15, 2001DistributionDistribution of Cycle Slips: of Cycle Slips:

24 h Data Set, 24 h Data Set, June 15, 2001June 15, 2001

269 (0.2%)269 (0.2%)9226 (5.5%)9226 (5.5%)

Total = 9495 (5.7%)Total = 9495 (5.7%)

Number of Number of C/SC/S

3% of all CS3% of all CS97% of all CS97% of all CS

Stations (65)Stations (65)CHAMPCHAMP

166495166495Total No. of Total No. of ObservationsObservations

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Number of Satellites and

GDOP per Epoch

Number of Number of Satellites and Satellites and

GDOP per EpochGDOP per Epoch

Observations and Baselines per

Epoch

Observations and Observations and Baselines per Baselines per

EpochEpoch

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Examples of Weak GeometryExamples of Weak GeometryExamples of Weak Geometry

13130.2980.2980.2660.2660.0750.0750.1110.1110683:07510683:0751 (068)(068)

2396:27912396:2791 (395)(395)

EpochsEpochs

0.2650.265

RMSRMSxx[m][m]

0.1790.179

RMSRMSyy[m][m]

0.3510.351

RMSRMSzz[m][m]

220.4750.475

No. of No. of IterationsIterations

RMSRMS3D3D[m][m]

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Statistics of SingularitiesStatistics of SingularitiesStatistics of Singularities

112792 ~ 27922792 ~ 279299

220752 ~ 07530752 ~ 075333

111080 ~ 10801080 ~ 108044

550678 ~ 06820678 ~ 068222

111392 ~ 13921392 ~ 139266111314 ~ 13141314 ~ 131455

1717SUMSUM

222394 ~ 23952394 ~ 239588111904 ~ 19041904 ~ 190477

330253 ~ 02550253 ~ 025511

DurationDurationEpochsEpochsSingularitySingularity

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Backward filter solutionRMSx = 0.079 mRMSy = 0.202 mRMSz = 0.155 mRMS3D = 0.266 m

Example ResultsExample Results

Forward filter solutionRMSx = 0.513 mRMSy = 0.865 mRMSz = 1.059 mRMS3D = 1.460 m

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Example Results: October 3, 2001Example Results: October 3, 2001

Data missingData missing-- Data gap : 56 epochsData gap : 56 epochs

-- Large clock error: 221 epochsLarge clock error: 221 epochs

Singularity due to weak geometry or Singularity due to weak geometry or insufficient datainsufficient data-- 15 epochs15 epochs

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Example Results: October 3, 2001Example Results: October 3, 2001



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SNR for CS DetectionSNR for CS Detection

CS caused by low SNR due to bad ionospheric CS caused by low SNR due to bad ionospheric conditions, multipath, high receiver dynamics or conditions, multipath, high receiver dynamics or low elevation anglelow elevation angle

Raw signal strengthRaw signal strength

3 types of SNR3 types of SNR-- S1, S2 : L1, L2 phase observationsS1, S2 : L1, L2 phase observations

-- SA : SNR for C/A channel (CHAMP ext.)SA : SNR for C/A channel (CHAMP ext.)

Related to the elevation angleRelated to the elevation angle

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SNR vs. ElevationSNR vs. Elevation

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Cycle Slip DetectionCycle Slip Detectionusing SNR: CHAMPusing SNR: CHAMP

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Cycle Slip Detection Using SNR: CHAMPCycle Slip Detection Using SNR: CHAMP

S A S 2 T D S N R 0 – 5 d e g

5 – 1 0 d e g

1 0 – 1 5 d e g

1 5 – 2 0 d e g

O O 8 0 2 9 0 0 O X 1 0 1 8 1 1 1 2 0 2 2 X O 1 7 2 1 0 0 O O 8 3 3 0 0 0 O X 7 1 7 1 1 1 2 1 2 2 X O 1 9 2 5 0 0 O O 8 4 3 1 0 0 O X 6 1 6 1 1 1 2 2 2 2 X O 2 0 2 7 0 0 O O 8 6 3 1 0 0 O X 4 1 6 1 1 1 2 3 2 2 X O 2 0 2 8 0 0 O O 8 7 3 2 0 0 O X 3 1 5 1 1 1 2 4 2 2 X O 2 3 2 8 0 0 O O 8 7 3 3 0 0 O X 3 1 4 1 1 1 2 5 2 2 X O 2 8 2 9 0 0

X X –– no C/S no C/S

0 0 –– C/SC/S

Total of 29 satellites tested over 500 epochsTotal of 29 satellites tested over 500 epochs

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Number of C/S in TD residuals: 1657Number of C/S in TD residuals: 1657

Total number of TD: 34374Total number of TD: 34374

500 epochs tested, all PRNs included500 epochs tested, all PRNs included

SA S2 # of C/S # of matched C/S 120 22 1708 (5.0%) 1336 (80.6%) 121 22 1817 (5.3%) 1354 (81.7%) 122 22 1910 (5.7%) 1372 (82.8%) 123 22 1938 (5.6%) 1395 (84.2%) 124 22 1984 (5.8%) 1415 (85.4%) 125 22 2099 (6.1%) 1417 (85.5%)

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OO OO –– C/S detected by both methods (TD residual and SNR)C/S detected by both methods (TD residual and SNR)

0X 0X –– C/S indicated by TD residual onlyC/S indicated by TD residual only

X0 X0 –– C/S indicated by SNR onlyC/S indicated by SNR only

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Corresponding Orbit Solution: initial Corresponding Orbit Solution: initial approximation good to ~ 5 mapproximation good to ~ 5 m



SA(123), S2(22)SA(123), S2(22)

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Orbit SmoothingOrbit Smoothing

Guerra and Tapia (1974)- built-in FORTRAN function

- works for the data with less than 25% error

Moving averaging windowMoving averaging window-- average of 20 data pointsaverage of 20 data points

Polynomial FittingPolynomial Fitting-- 99thth orderorder

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Polynomial fitting (n=9)RMSx = 0.099 mRMSy = 0.213 mRMSz = 0.154 mRMS3D = 0.280 m

Direct Form II TransposedRMSx = 0.092 mRMSy = 0.220 mRMSz = 0.154 mRMS3D = 0.283 m

Orbit SmoothingOrbit Smoothing

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SummarySummary

Kinematic triple difference POD works well for good Kinematic triple difference POD works well for good geometrygeometryShort processing time (less than Short processing time (less than 2 h, forward and 2 h, forward and backward, on 1.8 GHz Pentium processorbackward, on 1.8 GHz Pentium processor ))Problems with weak geometry Problems with weak geometry CS cleaning is not easy (high dynamics, LEO in the CS cleaning is not easy (high dynamics, LEO in the middle of the ionospheric layer)middle of the ionospheric layer)

SNR plus orbit smoothing give promising resultsSNR plus orbit smoothing give promising resultsMore work needs to be done on SNR threshold selectionMore work needs to be done on SNR threshold selection

Gaps in the solution Gaps in the solution –– reduced dynamics needed for reduced dynamics needed for orbit continuity and balance between geometry and orbit continuity and balance between geometry and force model force model

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ACKNOWLEDGEMENTSACKNOWLEDGEMENTS

This project is supported by a NASA This project is supported by a NASA Goddard Space Flight Center NIP Award Goddard Space Flight Center NIP Award OSU project number OSU project number 740809.740809.

geometric approach to position determination in space: advantages … · 2020. 1. 3. · 1 geodetic...

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