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1、I.INTRODUCTIONThemultitargetrecursiveBayesfilterPHDFiltersofHigherOrderinisthetheoreticallyoptimalapproachtomultisensor-multitargetdetection,tracking,andTargetNumberidentification.Givenatime-sequenceZ(k):Z,:::,Z1kofmultitargetmeasurement-sets,itpropagatestheBayesmultitargetposteriorviaan
2、alternatingsequenceofpredictor(time-update)andcorrector(data-update)steps(seeSectionIIF):RONALDMAHLER¢¢¢¡!f(XjZ(k))¡!f(XjZ(k))LockheedMartinkjkk+1jkpredictor¡!f(XjZ(k+1))¡!¢¢¢:k+1jk+1correctorThemultitargetrecursiveBayesnonlinearfilteristheForapplicationsinwhichthisfilteristheoreticallyo
3、ptimalapproachtomultisensor-multitargetappropriate–i.e.,those,suchaslowSNRinwhichdetection,tracking,andidentification.Forapplicationsinconventionalapproachessuchasmulti-hypothesiswhichthisfilterisappropriate,itislikelytobetractableforcorrelation(MHC)performpoorly–itislikelytoonlyasmallnu
4、mberoftargets.Inearlierpaperswederivedbetractableonlyforasmallnumberoftargets.Consequently,itmayprovetobeoflimitedpracticalclosed-formequationsforanapproximationofthisfilterbasedinterestintheabsenceofdrasticbutprincipledonpropagationofafirst-ordermultitargetmomentcalledtheapproximationst
5、rategies.probabilityhypothesisdensity(PHD).Inarecentpaper,Erdinc,Insingle-targetproblemsthecomputationallyWillett,andBar-ShalomarguedfortheneedforaPHD-typefilterfastestapproximatefilteringapproachisthewhichremainsfirst-orderinthestatesofindividualtargets,butconstant-gainKalmanfilter,ofwh
6、ichthealpha-betawhichishigher-orderintargetnumber.Inthispaperweshowfilteristhemostfamiliarinstance.Suchfiltersthatthisisindeedpossible.Wederiveaclosed-formcardinalizedpropagateafirst-orderstatisticalmoment(thePHD(CPHD)filter,whichpropagatesnotonlythePHDbutalsoposteriorexpectation)inthepl
7、aceoftheposteriortheentireprobabilitydistributionontargetnumber.distribution.Inanearlierpaper[22]weproposedananalogousstrategyformultitargetsystems:propagationofafirst-ordermultitargetmoment.Thismoment,theprobabilityhypothesisdensity(PHD)D(xjZ(k)),isuniquelydefinedbythepr
