Comments on Cram r–Rao lower bound for tracking multiple targets.pdf

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1、CommentsonCrame´rRaolowerboundfortrackingmultipletargetsB.RisticandM.MorelandeAbstract:Inarecentpaper,Risticetal.,2004,proposedasimpleandexactderivationofthetheor-eticalCrame´rRaolowerbound(CRLB)fortrackingmultipletargetsusingintensitymapsasmeasurements.Althoughtheformulationandthetheo

2、reticalderivationspresentedintheirworkareindeedcorrect,theanalysisoftheproposedboundandtheconclusionsthatfollowarewrong.Here,acorrectanalysisispresentedwiththekeyobservationthat[asopposedtotheclaimmadeintheworkofRisticetal.(2004)],theproposedCRLBreflectstheinteractionbetweenthetargets,e

3、veniftheirmotionisindependent.Themulti-targetCRLBisalsocomparedwiththeerrorperformanceofamulti-targetstatemaximumlikelihoodestimator;aremarkableagreementisobservedforhighsignal-to-noiseratio.1Introductionmainideainthisapproachistouserawdatabeforedetec-tionthresholdingasmeasurements,asi

4、tisdoneintheTracking(dataprocessing)involvestheestimationoftargettrack-before-detectparadigm[5].Thresholdingingeneralstates(positions,velocities,attributes)usingtheoutputisperformedtoreducethecomputationalloadofthefromasignalprocessingunitofasurveillancesystem,tracker,andinevitablycaus

5、essomelossofinformation.suchastheradar.Forafewdecades,therehavebeenThenthemultipletargettrackingcanbeformulatedasaattemptstoderivethetheoreticallybestachievabletrackingnonlinearfilteringproblemandtheCRLBcomputedviaerrorperformance[asafunctionofsensoraccuracy,theTichavskysrecursiveformul

6、a[6].Theresultingsignal-to-noiseratio(SNR),sensorresolutionandsoon],CRLBforunthresholdeddatawasreferredtoastheultimateintheformoftheCrame´rRaolowerbound(CRLB).CRLBintheworkofRisticetal.[4],sinceitrepresentstheSuchaboundwouldbeextremelyimportantasitcouldtrulybestachievabletrackingerrorp

7、erformance.Itturnsoutbeusedformanypracticalpurposes:trackingalgorithmthatthisCRLBdependsonpracticalengineeringparametersassessment,performanceprediction,trackingsystemofsurveillancesystemssuchasthesensorresolution,design,sensorallocationandscheduling[1],tonameafew.SNRandpoint-spreadf