Convergence of the SMC implementation of the PHD filter

AM Johansen, SS Singh, A Doucet, B-N Vo

Research output: Contribution to journalArticle (Academic Journal)peer-review

51 Citations (Scopus)


The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges in mean of order , and hence almost surely, to the true PHD filter. We also present a central limit theorem for the SMC approximation, show that the variance is finite under similar assumptions and establish a recursion for the asymptotic variance. This provides a theoretical justification for this implementation of a tractable multiple-object filtering methodology and generalises some results from sequential Monte Carlo theory.
Translated title of the contributionConvergence of the SMC implementation of the PHD filter
Original languageEnglish
Pages (from-to)265 - 291
Number of pages27
JournalMethodology and Computing in Applied Probability
Volume8 (2)
Publication statusPublished - Jun 2006

Bibliographical note

Publisher: Springer Netherlands


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