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基于UKF的参数和状态联合估计.docx

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基于UKF的参数和状态联合估计 Introduction Inmanyengineeringapplications,itisessentialtoestimateboththeparameterandthestateofasystem.Theparametercanrepresentthecharacteristicsofthesystem,andthestaterepresentsthecurrentconditionsofthesystem.Theparameterandstateareoftenlinkedtoeachotherthroughequations,andonecanestimatethemsimultaneouslyusingajointestimationapproach.Inthispaper,wewilldiscusstheUnscentedKalmanFilter(UKF)methodforjointparameterandstateestimation.WewillfirstintroducethebasicconceptofUKF,andthendiscusshowitcanbeappliedtojointestimation.WewillalsocomparetheUKFmethodwithothertraditionalapproachesanddemonstrateitsadvantagesthroughsimulationexamples. Background TheKalmanFilter(KF)isawell-establishedmethodforstateestimation.Givenasystem'sdynamicmodelandmeasurementmodel,theKFestimatesthesystem'sstatebasedonmeasurements.TheKFisoptimalwhenthesystemislinearandGaussian.However,inmanycases,thesystemisnonlinear,andtheKFcannotbeapplieddirectly.TheExtendedKalmanFilter(EKF)extendstheKFtononlinearsystemsbylinearizingthesystemdynamicsandmeasurementmodels.However,theEKFisbasedontheassumptionofGaussiannoise,whichmaynotalwaysbevalidinpractice.TheUnscentedKalmanFilter(UKF)wasintroducedtosolvetheseproblems.TheUKFusesasetofsigmapointstorepresentthenon-Gaussiandistributionandpropagatesthemthroughnonlinearfunctions.TheUKFdoesnotrequirelinearizationandcanhandleGaussianandnon-Gaussiannoise. TheUKFiswidelyusedinmanyfields,suchasrobotics,aerospace,andsignalprocessing.However,insomeapplications,bothmodelparametersandsystemstatesneedtobeestimatedsimultaneously.Thejointestimationproblemismorechallengingthantraditionalstateestimationbecausetheparametersaffectthesystemdynamicsandmeasurementmodels.TheJointUKF(JUKF)methodwasdevelopedtosolvethisproblem.TheJUKFconsiderstheparametersaspartofthestatevector,andestimatesboththestateandparametersiteratively. Methodology TheUKFalgorithmconsistsoftwosteps:predictionandupdate.Inthepredictionstep,theUKFestimatesthesystem'sstatebasedonthepreviousstateestimateandthed