Extended-Chrip-Scaling

IEEETRANSACTIONSONGEOSCIENCEANDREMOTESENSING,VOL.34,NO.5,SEPTEMBER19961123ExtendedChirpScalingAlgorithmforAir-andSpaceborneSARDataProcessinginStripmapandScanSARImagingModes-Albert0Moreira,Member,ZEEE,JosefMittermayer,andRolfScheiberAbstruct-Thispaperpresentsageneralizedformulationoftheextendedchirpscaling(ECS)approachforhighprecisionprocessingofair-andspaceborneSARdata.Basedontheoriginalchirpscalingfunction,theECSalgorithmincorporatesanewazimuthscalingfunctionandasubapertureapproach,whichallowaneffectivephase-preservingprocessingofScanSARdatawithoutinterpolationforazimuthgeometriccorrection.Theazimuthscalingcanalsobeusedforautomaticazimuthcoregistrationofinterferometricimagepairswhichareacquiredwithdifferentsamplingdistances.Additionally,anovelrangescalingformulationisproposedforautomaticrangecoregistra-tionofinterferometricimagepairsorforimprovedrobustnessfortheprocessingofhighlysquinteddata.Severalsimulationandprocessingresultsofair-andspaceborneSARdataarepresentedtodemonstratethevalidityoftheproposedalgorithms.I.INTRODUCTIONARIMAGEFORMATIONisbasedonacoherentpro-Scessingapproachtobuildalongazimuthsyntheticaper-ture.Thiscoherentprocessingcanalsobeinterpretedasthecompressionofafrequencymodulatedpulse,wherebythefrequencymodulationiscausedbythenaturalmovementofthesensor(Dopplereffect).Inaddition,thetransmittedpulsesarealsotimedispersedandfrequencymodulated.Thisallowsmoreenergytobetransmitted(duetothetimedispersion)andalsoabetterrangeresolutiontobeachieved(duetothehighersignalbandwidth).Therangecompressedpulseisobtainedbymeansofacorrelationofthereceivedechowiththecomplex-conjugatedtime-invertedreplicaofthetransmittedpulse.Duetothecumtureandtherangevarianceoftheaz-imuthmodulation,SARimageformationisinherentlyatwo-dimensional(2-D)process[7].Commonly,the2-Dprocessingissplitintotwo1-Dstepsinordertosimplifytheimageformationprocess.Thisrequireshoweveraninterpolationtocompensatetherangemigrationbeforeazimuthprocessing.Anothereffectthatoccursforagreatamountofrangemigra-tion(e.g.,forhighsquintanglesandlorhighrangeresolutionorlowfrequencySARsystems)isthecouplingoftherangeandazimuthsignals,whichisalsorangedependent.Thiscouplingifnotcompensatedleadstoadefocusingoftherangeimpulseresponsefunction(IRF).Thedistortioncanbeapproximatelycompensatedbymeansofasocalledsecondaryrangecompression(SRC)whichconsistsbasicallyofslightlyManuscriptreceivedNovember15,1995;revisedApril19,1996.TheauthorsarewiththeGermanAerospaceResearchEstablishment(DLR),InstituteforRadioFrequencyTechnology,D-82230Oberpfaffenhofen,Germany.PublisherItemIdentifierS0196-2892(96)06823-4.modifyingtherangemodulationrateduringrangecompressionU41.Thefirststepinthecaseoftherange-Dopplerprocess-ingapproach[l],[5],[14],[25]istherangecompressioninthefrequencydomain.TheSRCappliediscorrectonlyforonereferencerangeandoneazimuthfrequencyvalue(normallytheDopplercentroid).Theinterpolationofthedataiscarriedoutintherange-Dopplerdomainusingatruncatedinterpolationkernel(e.g.,sin(z)/z).Afterapplyingtheazimuthcompressionphaseinthisdomain,thefinalimageisobtainedbyaninverseFastFourierTransform(IFFT).ThemaindisadvantagesofthisalgorithmarethelimitedSRCandtheneedofaninterpolation.Thewavenumberalgorithms[1],[3],[lo],[ll]canbeinterpretedas2-Dfrequencycorrelations,wherebya2-DFFTisusedtotransformthesignalfromthetimedomainintothewavenumberdomain.Inthesealgorithms,approximationsandtheneedforthesocalledStoltinterpolationincreasetheirimplementationcomplexityandcandegradetheirphasepreservingproperties.Thechirpscaling(CS)algorithmallowsthehighprecisionSARprocessingwithoutusinginterpolationintheSARpro-cessingchain[21],[22].ItconsistsbasicallyofmultiplyingtheSARdataintherange-Dopplerdomainwithaquadraticphasefunction(chirpscaling)inordertoequalizetherangecellmigrationtoareferencerange,followedbyarangecompressionandSRCinthewavenumberdomain.AlthoughtheSRCisstrictlycorrectonlyforonereferencerange,itisupdatedasafunctionoftheazimuthfrequency.TheprocessingproceedswithphasemultipliesandFFToperations,whichmakethealgorithmextremelyefficient.Reference[4]givesadetailedcomparisonofwavenumberdomainandchirpscalingprocessors.Theextendedchirpscaling(ECS)wasdevelopedoriginallyforprocessingairbornedatawithstrongmotionerrors(e.g.,E-SARsystem,[12])andwithvariableDopplercentroidinrangeand/orazimuth[13],[17].TheECSalgorithmallowsthefollowingstepstobeincludedintheprocessing:Dopplercentroidupdatewithrangebynieansofanazimuthspectrallengthextensionintherange-Dopplerdomain.Dopplercentroidupdatewithazimuthbymeansofaz-imuthsubapertureprocessing.Motionerrorcorrectionforairborneprocessingbymeansofanadditionaltransformationintothesignaldomain.0196-2892/96$05.0001996IEEE1124IEEETRANSACTIONSONGEOSCIENCEANDREMOTESENSING,VOL34,NO.5,SEPTEMBER19960Improvedprocessingofhighlysquinteddatabymeansofasubtractionoftheoffsetvaluefromthechirpscalingfunction.ThispaperpresentsageneralizedformulationoftheECSalgorithmwhichissuitableforair-andspaceborneSARandScanSARprocessing.Thegenerallessontobefoundintheoriginalchirpscalingmethodisthatamodifiedfrequen