Convergence of the SMC implementation of the PHD filter
Johansen, Adam M., Singh, Sumeetpal S. (Sumeetpal Sidhu), Doucet, Arnaud and Vo, Ba-Ngu. (2006) Convergence of the SMC implementation of the PHD filter. Methodology and Computing in Applied Probability, Vol.8 (No.2). pp. 265-291. ISSN 1387-5841
jWRAP_Johansen_johansen_singh_doucet_vo_phdfilterclt.pdf - Submitted Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://dx.doi.org/10.1007/s11009-006-8552-y
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 ≥ 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.
|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|
|Page Range:||pp. 265-291|
|Access rights to Published version:||Restricted or Subscription Access|
1. M. Abramowitz and I. A. Stegun, editors. Handbook of Mathematical Functions.
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