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

−200 −100 0 100 200 300−150

−100

−50

0

50

100

150

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250

Relative Cross−Track Coordinate(m)

Rel

ativ

e N

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20061221

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20090928

20090210

20070623

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20090628

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(a) Global Relative Position Iteration

−95 −94.5 −94 −93.5 −93

159

159.5

160

Relative Cross−Track Coordinate(m)

Rel

ativ

e N

orm

al C

orrd

inat

e(m

)

Before iterationAfter iteration

(b) for 20070923

72 74 76 78

11

12

13

14

15

16

Relative Cross−Track Coordinate(m)

Rel

ativ

e N

orm

al C

orrd

inat

e(m

)

Before iterationAfter iteration

(c) for 20090928

IGARSS 2010, Honolulu

Motivation Introduction Algorithm Validation Conclusion

Results:Displacement plotting without weightcoefficient

The totaldisplacement∆~P(n)

converges

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

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20

Interation Number n

Dis

plac

emen

t ∆P

(m)

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

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

Interation Number n

Dis

plac

emen

t ∆P

(m)

Total Displacement ∆P(n)

2008122620061221200709232009092820090210200706232008111020090628

IGARSS 2010, Honolulu

Motivation Introduction Algorithm Validation Conclusion

Results:Differential interferogram after calibration

71 72 73 74 75 76 77 78 79

11

12

13

14

15

16

Relative Cross−Track Coordinate(m)

Rel

ativ

e N

orm

al C

orrd

inat

e(m

)

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