运动误差对机载双基SAR定位精度的影响1

InfluenceoftheMotionErrorstoAirborneBiSARGeolocationAccuracyYaLiYongLiCollegeofElectronicandInformationEngineering,NanjingUniversityofAstronauticsandAeronauticsNo.29YudaoStreet,Nanjing,[e-mail]—Theimagebasedgeolocationaccuracyisimportantinevaluatingtheperformanceofthebistaticsyntheticapertureradar(BiSAR)system.Mostoftheerrorsareoriginatedfromtheinsufficientmeasurementaccuracyofthemotionparameters.Inthispaper,giventheBiSARgeometricmodel,theinfluenceongeolocationaccuracycausedbythetransmitter'smotionerrorsfromtheviewpointsofimagingismainlyanalyzed.TheNewtoniterationmethodisamethodusedtosolvethenonlinearequations.MathematicexpressionscanbederivedusingtheNewtoniterationmethod.Usingthederivedmathematicexpressionsinthetext,thesimulationresultsareprovidedtoshowthequantitativeimpactofmotionerrorsontheimageandtargetpositioning.Keywords-bistaticsyntheticapertureradar(BiSAR);geolocation;parametererrorI.INTRODUCTIONGeolocationaccuracyisoneofthekeytermsappliedtoevaluateperformanceofsyntheticapertureradar(SAR)systems,whosedefinitionisthedegreeofclosenessbetweenthespatialentity'scoordinate-datesandtherealpositionoftheentity.Thoseevaluatedperformancebythelocation-errorissignificanttoSARapplication:inthemilitaryreconnaissance,decision-makershavetostrictlypositioningtargetsontheground;intheoceansurveillance,vesselmonitoringandsearescueshavetoaccuratepositioningtheships.Bistaticsyntheticapertureradar(BiSAR)hasseparatedtransmitterandreceiver[1].ComparedwiththemonostaticSAR,BiSARhasmanyadvantagessuchaslongerdetectionrange,accesstomoreabundantinformation,highermobilityandhigherelu-sivness,betterECCMcapabilityandanti-interceptcapability,henceBiSARhasstrongerlivingability.TheseadvantagesmakeBiSARbepromisinginmilitaryapplication[6].ThefactorsthatcaninfluencepositioningaccuracyoftheairborneSARincludemotionerrorsofthetransmitterandreceiver,theheighterrors,etc.Inthispaper,theinfluencetothepositioningaccuracybecauseofthemotionerrorscausedbythetransmitterismainlyanalyzedfromgeometricalmodeloftheBiSAR[2][3].II.GEOMETRICALMODELOFBISARTheFigure.1isthegeometricmodelofthebistaticSAR.AssumethatthetransmitterandreceiverflyingatvelocitiesoftVandrVrespectively,andassumethattheplatformsarenotparallel.Relativetothereferencepointontheground,thesquintanglesrespectivelyaretandratthezeromoment.stRandsrRaretherangesbetweentheradarAPCandthereferencepoints.ReceivingstationTransmittingstationVtVrRstRsrXYZrtFigure1.GeometricmodelofBiSARAtt,thesloperangeis(t)R(t)RR(t)tr(1)where2)tV()(sinRtV2-2R(t)R2)tV()(sinRtV2-2R(t)Rrrsrrsrrttsttstt(2)III.FORMULADEDUCTIONTheimagingareawillnotbechangedthoughthereareerrors,stillintheeffectofthewave.However,thepositionofthereferencepointwillbechangedbecauseofthemotionerrors[2].A.InfluencecausedbythemotionerrorstotheimagingLinearRange-Doppler(LRD)algorithmwillbeappliedintheimagingprocessing[7],themotionerrorswillchangetherangesandtheDoppler-frequency,sothepositionofthereferencepointwillbechanged,hence,thepositionofthetargetsonthegroundalsobechanged.Thevariationoftherangeswillcausedistance-drift,andthevariationoftheDoppler-frequencywillcauseazimuth-drift.Distancevariationcausedbythemotionerrorscanbeexpressedasfollows:2r2or2or2t2ot2ot2r2or2or2t2ot2otH)'YY()'XX(H)'YY()'XX(H)YY()XX(H)YY()XX(r(3)Where）（0,,OOYXisthecoordinateofthereferencepointbeforeintroducingerrors,and），（0','OOYXisthecoordinatesafterintroducingerrors.Wecanobtainthedriftunitsattherange-direction:prNr/r,whereprisresolutioninslantrange.Doppler-frequencyvariationscausedbythemotionerrorscanbeexpressedasfollows:2222222221()()()()1()()()()1()(')()(')(')(')1(')('-txottyottztdotottrxorryorrzrororrtxexottyeyottzeztotottrxexoVXXVXXVHfXXyYHVXXVYYVHXXYYHVVXXVVYYVVHXXYYHVVXX（）222)(')(')'(')(')rryeyorrzezrororrVVYYVVHXXYYH（）(4)Where）（tztyVVV,,txand）（rzryVVV,,rxarethevelocitiesofthetransmitterandthereceiveratX,Y,Zdirections.）（ezeyVVV,,ex,）（‘’‘ezeyVVV,,exarethevelocity-errorofthetransmitterandthereceiver.NaPRFfdNa,wherePRFisthepulserepeatfrequency.NaPRF/isresolutioninazimuth.B.InfluencetothepositioningThemotionerrorscausetheimagedrift,hencetheremustbepositioningerrors.(/2)/(/2)pdcaaarefrrrffmNNPRFNRRnNNp(5)where,2)ZZ(2)YY(2)XX(2)ZZ(2)YY(2XXRorororotototref）（(6)Where,mandnarecoordinatesofthecorrespondingpointinsimulatedimaging.UsingtheNewtoniterationmethod[8],newcoordinateofthetarget）（',','pppZYXcanbededuced.Iftherearenoerrors,thecoordinateofthetargetis）（PPPZYX,,.Sothepositioningerroris:ppppppY'YYX'XX(7)2p2pYXE(8)IVSIMULATIONRESULTSAccordingtotherelativetheoryaboutimagingandtargetspositioning[4][7][9][10][11].Asisshowedinfigure1thereferencepointOislocatedattheoriginofcoordinatesystem,parametersaresettedastable1.TodeducetheinfluencecausedbyvelocityerrorsofthetransmitteratX-directionorY-direction.Theerror-bandis(-1.0m,1.0m)atregularinterval,suchas0.1m.TABLE1SIMULATIONPARAMETERSparametersTransmittervaluesReceiver