Noise covariance model for time-series InSAR analysis

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1、Noisecovariancemodelfortime-seriesInSARanalysisPiyushAgram,MarkSimonsMotivation•Noisecovarianceinindividualinterferogramshasbeenwellstudied.(Hanssen,2001)•Extendthenoisemodeltonetworksofinterferograms–time-seriesapplications.•Developuncertaintymeasuresfortime-seriesInSARproducts

2、.•BuildanInSARnoisecovariancemodelfromfirstprinciples.IndependentObservations?SimplenetworkSimplestAXofcoherentinterferogrampixelsinasinglenetworkYinterferogram.CBZ•IsinformationcontainedininterferogramBCdifferentfrominformationinABandAC?•IsinformationatX,YandZpixelsindependent?

3、•Conventionallyanycovariancesareignored.–Simplicity.–Easeofimplementingalgorithms.SinglepixelphasemodelNoisetermsAtmosphericSpatiallycorrelated.PhaseScreenCorrelatedinpairswithcommonscene.DecorrelationSpatiallyindependent.phasenoiseTemporallycorrelated.PhasenoisefromSpatiallyand

4、Temporallyuncorrelatedindependent.sourcesPixelxininterferogram(i,j)iandjareindicesofSARacquisitions.VectorPhasemodelMInterferograms,NSARscenes,PpixelsArepresentstheincidencematrix[+1,0,-1].Pixel-by-pixelstackofphaseobservations.PhaseCovariancemodelInabsenceofdeformation,ournoise

5、estimateisAssumingstatisticalindependenceofthenoiseterms.Totalcovariancematrixisacombinationofthreemodels.AtmosphereScattering/decorrelationSystemnoiseAtmosphericPhaseModelsS.Jonsson(PhDthesis)Hanssen(2001)DerivedfromthedataitselfEmardsonetal.(2003)usingradontransform.Lohman&

6、Simons(2005)APSCovariancemodel1)SpatialcovarianceforaSARscene.2)CovarianceofallpixelsinoneSARscene.3)CovarianceofallpixelsinallSARscenes.4)CovarianceofallpixelsinallIFGs.DecorrelationmodelB•ZebkerandVillasenor(1992),BamlerandJust(1993).•SARpixelmadeupofinfiniteGaussianscatterers

7、.Observable:InSARcoherence•InSARcoherenceisafunctionofphasenoise.•Wederiveamodeltorelatecoherencedirectlytonoisecovariancematrix.•Actualtemporalbehaviorofscatterersnotknown.•Weuseasignalmodelinstead.JustandBamler(1994)GaussiansignalmodelCoherence=>SignalModel=>StatsSARphasecorre

8、lationInSARphasevarianceObservedInSARcoherenceN