Iterative calibration of relative platform position a new_method for_baseline_estimation
Transcript of Iterative calibration of relative platform position a new_method for_baseline_estimation
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Iterative Calibration of Relative PlatformPosition:
A New Method for Baseline Estimation
Tiangang Yin1, Emmanuel Christophe1, Soo Chin Liew1 ,Sim Heng Ong2
1CENTRE FOR REMOTE IMAGING, SENSING AND PROCESSING
2DEPT. OF ELECTRICAL AND COMPUTER ENGINEERING,NATIONAL UNIVERSITY OF SINGAPORE
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Outline
1 Motivation
2 IntroductionConceptBaseline CalibrationExpand
3 AlgorithmCoordinate SystemIteration
4 Validation
5 Conclusion
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Motivation
We have already knowBaseline precision is significant to the interferometricaccuracyPrecise estimation is required
IdeaInterferometric result can provide information on baselineConcept can be extended under multiple passes condition,from baseline to individual sensor positionIteration and Constraint
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Concept Baseline Calibration Expand
Outline
1 Motivation
2 IntroductionConceptBaseline CalibrationExpand
3 AlgorithmCoordinate SystemIteration
4 Validation
5 Conclusion
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Concept Baseline Calibration Expand
Concept
Baseline ConceptRefer to the relative distance between two sensorsHighlight “relative”
depends on the chosen master image as coordinate originbuild a coordinate system base on master image position,normally described using “parallel” and “perpendicular”
Initially estimated using orbital information, interpolatedfrom platform position vector
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Concept Baseline Calibration Expand
Baseline ErrorThe root of baseline estimation error is the inaccurateplatform position from orbit dataIt can happen on any of the interferometric pairAll the interferograms will be wrong with the sameinaccurate path
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Concept Baseline Calibration Expand
Geometrical ConstraintThe geometric representation of multiple platform positionscan be constructed as polygon(2D) or polyhedron(3D)Using the orbit estimated baseline, this geometricrepresentation can be constructed
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Concept Baseline Calibration Expand
Baseline CalibrationIn the past method, error of perpendicular baseline can bereduced by using GCP or reference DEMHowever, the correction is only on the relative distance. Noguarantee for the corrected baseline.
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Concept Baseline Calibration Expand
Expand
From baseline to relative positionWhen more information on platform position can be interpretedfrom data, global constraint of platform position is needed.Without constraint, the geometry of platform positions willbreak.
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Concept Baseline Calibration Expand
Expand
Because the problem will become very complicated in 3Dwhen more passes are used
An iterative optimization method will be provided undergeometry constraintGlobal baseline calibrationDetection and quantitative calibration of any pass withinaccurate orbit information
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Outline
1 Motivation
2 IntroductionConceptBaseline CalibrationExpand
3 AlgorithmCoordinate SystemIteration
4 Validation
5 Conclusion
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Coordinate System
Requirementeasy to transfer system from one master image to anothererror is small enough
TCN (Track, Cross-track and Normal) coordinates is chosen
n =−~P| P |
c =n × ~V
| n × ~V |t = c × n (1)
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Transfer Equation: ~Bji ' −~BijIs it valid?
Assumption can be made that all of the platform have thesame direction of ~VImage pixels within one range row will share the samebaseline TCN coordinates
∆θ = arctan
√| ~Bij · c |2 + | ~Bij · t |2
Ai + R(2)
Ai : the platform altitude of image i (691.65 km for ALOS)R: the radius of the earth (6378.1 km)
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
System Error
The baseline component along t is very smallTherefore, for baseline of 1 km along c, the axis error is0.0081◦
the baseline error is ~Bij · c × tan ∆θ ' 14 cm for this systemConclude: TCN coordinates system will be considered atcorresponding point between all passes
~Bji ' −~Bij (3)
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration: Starting PointK + 1 passes over same areaDifferential interferogram and baseline is generated for allcombinationsProcessed with both baseline vector and baselinechanging rateInitialization:
~Bji = −~Bij~Bji = −~Bij (4)
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration Steps
Take one pass as master image, calculate the baselineerror to be corrected
Average the result: ∆~P(n)i = 1
K ×∑
j 6=i ∆~Bij
Update all the baseline vectors: ~Bij = ~Bij + ∆~P(n)i
A weight coefficient 1n can be added before ∆~P(n)
i to slow down the convergence
Update the reversed baseline ~Bji
Change another master image and go back to first step,until all of the images have been taken once as masterimageCalculate the total displacement of all platform:∆~P(n) =
∑K +1i=1 | ∆~P(n)
i |Iteration n finished, Take n = n + 1 and restart
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration Steps
Take one pass as master image, calculate the baselineerror to be correctedAverage the result: ∆~P(n)
i = 1K ×
∑j 6=i ∆~Bij
Update all the baseline vectors: ~Bij = ~Bij + ∆~P(n)i
A weight coefficient 1n can be added before ∆~P(n)
i to slow down the convergence
Update the reversed baseline ~Bji
Change another master image and go back to first step,until all of the images have been taken once as masterimageCalculate the total displacement of all platform:∆~P(n) =
∑K +1i=1 | ∆~P(n)
i |Iteration n finished, Take n = n + 1 and restart
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration Steps
Take one pass as master image, calculate the baselineerror to be correctedAverage the result: ∆~P(n)
i = 1K ×
∑j 6=i ∆~Bij
Update all the baseline vectors: ~Bij = ~Bij + ∆~P(n)i
A weight coefficient 1n can be added before ∆~P(n)
i to slow down the convergence
Update the reversed baseline ~Bji
Change another master image and go back to first step,until all of the images have been taken once as masterimageCalculate the total displacement of all platform:∆~P(n) =
∑K +1i=1 | ∆~P(n)
i |Iteration n finished, Take n = n + 1 and restart
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration Steps
Take one pass as master image, calculate the baselineerror to be correctedAverage the result: ∆~P(n)
i = 1K ×
∑j 6=i ∆~Bij
Update all the baseline vectors: ~Bij = ~Bij + ∆~P(n)i
A weight coefficient 1n can be added before ∆~P(n)
i to slow down the convergence
Update the reversed baseline ~Bji
Change another master image and go back to first step,until all of the images have been taken once as masterimageCalculate the total displacement of all platform:∆~P(n) =
∑K +1i=1 | ∆~P(n)
i |Iteration n finished, Take n = n + 1 and restart
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration Steps
Take one pass as master image, calculate the baselineerror to be correctedAverage the result: ∆~P(n)
i = 1K ×
∑j 6=i ∆~Bij
Update all the baseline vectors: ~Bij = ~Bij + ∆~P(n)i
A weight coefficient 1n can be added before ∆~P(n)
i to slow down the convergence
Update the reversed baseline ~Bji
Change another master image and go back to first step,until all of the images have been taken once as masterimage
Calculate the total displacement of all platform:∆~P(n) =
∑K +1i=1 | ∆~P(n)
i |Iteration n finished, Take n = n + 1 and restart
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration Steps
Take one pass as master image, calculate the baselineerror to be correctedAverage the result: ∆~P(n)
i = 1K ×
∑j 6=i ∆~Bij
Update all the baseline vectors: ~Bij = ~Bij + ∆~P(n)i
A weight coefficient 1n can be added before ∆~P(n)
i to slow down the convergence
Update the reversed baseline ~Bji
Change another master image and go back to first step,until all of the images have been taken once as masterimageCalculate the total displacement of all platform:∆~P(n) =
∑K +1i=1 | ∆~P(n)
i |
Iteration n finished, Take n = n + 1 and restart
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion Coordinate System Iteration
Iteration Steps
Take one pass as master image, calculate the baselineerror to be correctedAverage the result: ∆~P(n)
i = 1K ×
∑j 6=i ∆~Bij
Update all the baseline vectors: ~Bij = ~Bij + ∆~P(n)i
A weight coefficient 1n can be added before ∆~P(n)
i to slow down the convergence
Update the reversed baseline ~Bji
Change another master image and go back to first step,until all of the images have been taken once as masterimageCalculate the total displacement of all platform:∆~P(n) =
∑K +1i=1 | ∆~P(n)
i |Iteration n finished, Take n = n + 1 and restart
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Outline
1 Motivation
2 IntroductionConceptBaseline CalibrationExpand
3 AlgorithmCoordinate SystemIteration
4 Validation
5 Conclusion
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Data Over Singapore8 passes of PALSAR over the Singapore betweenDecember 2006 and September 2009 are usedSRTM is used as reference DEMGAMMA software is used for the interferogramsPython used for programming
Starting Point:
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Results:Relative Position Iteration
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Relative Cross−Track Coordinate(m)
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20090928
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Before iterationAfter iteration
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(a) Global Relative Position Iteration
−95 −94.5 −94 −93.5 −93
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Relative Cross−Track Coordinate(m)
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)
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(b) for 20070923
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(c) for 20090928
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Results:Displacement plotting without weightcoefficient
The totaldisplacement∆~P(n)
converges
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Interation Number n
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Total Displacement ∆P(n)
2008122620061221200709232009092820090210200706232008111020090628
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Results:Displacement plotting with weight coefficient
Theconvergenceis slower butresult in asmaller valueSpeed canneither be tooslow nor toofast
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Interation Number n
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Total Displacement ∆P(n)
2008122620061221200709232009092820090210200706232008111020090628
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Results:Differential interferogram after calibration
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Relative Cross−Track Coordinate(m)
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Before iterationAfter iteration
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Outline
1 Motivation
2 IntroductionConceptBaseline CalibrationExpand
3 AlgorithmCoordinate SystemIteration
4 Validation
5 Conclusion
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Conclusion
ConceptSatellite platform position can be relatively calibrated frommultiple interferograms
ResultThe SAR passes which gives inaccurate platform positionare successfully detected and calibrated
DisadvantagePlatform position can only be calibrated alongperpendicular baseline
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Conclusion
ConceptSatellite platform position can be relatively calibrated frommultiple interferograms
ResultThe SAR passes which gives inaccurate platform positionare successfully detected and calibrated
DisadvantagePlatform position can only be calibrated alongperpendicular baseline
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Conclusion
ConceptSatellite platform position can be relatively calibrated frommultiple interferograms
ResultThe SAR passes which gives inaccurate platform positionare successfully detected and calibrated
DisadvantagePlatform position can only be calibrated alongperpendicular baseline
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Conclusion
ConceptSatellite platform position can be relatively calibrated frommultiple interferograms
ResultThe SAR passes which gives inaccurate platform positionare successfully detected and calibrated
DisadvantagePlatform position can only be calibrated alongperpendicular baseline
IGARSS 2010, Honolulu
Motivation Introduction Algorithm Validation Conclusion
Conclusion
Possible ApplicationOrbit refinement for SARBaseline problem for deformation monitoring, likeearthquake