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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, 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. doi:10.1007/s11009-006-8552-y ISSN 1387-5841.
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Official URL: http://dx.doi.org/10.1007/s11009-006-8552-y
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 ≥ 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: | 1387-5841 | ||||
Official Date: | 2006 | ||||
Dates: |
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Volume: | Vol.8 | ||||
Number: | No.2 | ||||
Page Range: | pp. 265-291 | ||||
DOI: | 10.1007/s11009-006-8552-y | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Restricted or Subscription Access |
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