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1、2118IEEETRANSACTIONSONACOUSTICS,SPEECH.ANDSIGNALPROCESSING.VOL.38.NO.17.DECEMBER1990ParameterEstimationofChirpSignalsPETARM.DJURICANDSTEVENM.KAY,FELLOW,IEEEAbstract-Theproblemoftheparameterestimationofchirpsignalsdedinwhitenoise,whichimpliesthat,first,aphaseun-isaddresse
2、d.Severalcloselyrelatedestimatorsareproposedwhosewrappingisaccomplished,and,second,linearregressionmaincharacteristicsaresimplicity,accuracy,andeaseofon-lineortechniquesappliedtoobtaintheestimatesoftheparame-off-lineimplementation.Formoderatelyhighsignal-to-noiseratiosth
3、eyters.Thisapproachissuitable,forexample,foraninstru-areunbiasedandattaintheCramer-Raobound.MonteCarlosimu-lationsverifytheexpectedperformanceoftheestimators.mentationradar,suchasahighprecisiontracker.Anestimatorofthefrequencyratewillalsobederived.Itwillbeeasytoextendthi
4、sapproachtosignalshavingI.INTRODUCTIONpolynomialsofanydegreeintheexponent.Allthederi-HIRPsignalsarecommoninvariousareasofscienceCvationswillbedoneundertheassumptionthatthesignal-andengineering(e.g.,physics,sonar,radar,com-to-noiseratioissufficientlyhigh.Inadditiontobeing
5、ac-munications).Forexample,theyareusedtoestimatetra-curate,theestimatorsareverysimpleforoff-lineoron-jectoriesofmovingobjectswithrespecttofixedreceiv-lineimplementation.ers.Inaddition,insituationswhereinterferencerejectionThepaperisorganizedasfollows.Firsttheproblemisisi
6、mportant,chirpsignalsprovideasuccessfuldigitalstated.Thenamethodforthejointestimationofphase,modulationscheme.Theestimationoftheirparametersfrequency,andfrequencyrateisproposedbasedonthehasbeenofinterestforalongtime.Mostofthemethodsapplicationofleastsquarestotheunwrapped
7、phaseofthethathavebeensuggestedintheliteratureyieldmaximumsignal.Theunwrappingschemeisverysimpleandlikelihoodestimates.Anecessaryconditionforthederi-stronglyexploitsthephasenatureofthisclassofsignals.vationoftheseestimatorsisastrongsignal-to-noiseratio.Inthefourthsection
8、theestimationofthefrequencyrateIn[2]themethodofinverseprobabilitywasused,whileisanalyzed.Aprocedureispr
