Convergence of the SMC Implementation of the PHD Filte

Adam Johansen, Sumeetpal S. Singh (), Arnaud Doucet () and Ba-Ngu Vo ()
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Sumeetpal S. Singh: Department of Engineering
Arnaud Doucet: University of British Columbia
Ba-Ngu Vo: University of Melbourne

Methodology and Computing in Applied Probability, 2006, vol. 8, issue 2, 265-291

Abstract: Abstract 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 $$p \geq 1$$ , 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.

Keywords: Central limit theorem; Filtering; Sequential Monte Carlo; Finite random sets; Primary 60F05; Secondary 60F25; 62P30; 93E11 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s11009-006-8552-y

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