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Convergence of the SMC implementation of the PHD filter
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Johansen, Adam M., Singh, Sumeetpal S. (Sumeetpal Sidhu), Doucet, Arnaud and Vo, BaNgu. (2006) Convergence of the SMC implementation of the PHD filter. Methodology and Computing in Applied Probability, Vol.8 (No.2). pp. 265291. ISSN 13875841

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Official URL: http://dx.doi.org/10.1007/s110090068552y
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 multipleobject tracking problem.
We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation
of the PHD filter converges in mean of order p ≥ 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 multipleobject filtering methodology
and generalises some results from sequential Monte Carlo theory.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Filters (Mathematics), Point processes 
Journal or Publication Title:  Methodology and Computing in Applied Probability 
Publisher:  Springer 
ISSN:  13875841 
Official Date:  2006 
Volume:  Vol.8 
Number:  No.2 
Page Range:  pp. 265291 
Identification Number:  10.1007/s110090068552y 
Status:  Peer Reviewed 
Access rights to Published version:  Restricted or Subscription Access 
References:  1. M. Abramowitz and I. A. Stegun, editors. Handbook of Mathematical Functions. 
URI:  http://wrap.warwick.ac.uk/id/eprint/37284 
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