Journal of Applied Probability

A uniformly convergent adaptive particle filter

Anastasia Papavasiliou

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Abstract

Particle filters are Monte Carlo methods that aim to approximate the optimal filter of a partially observed Markov chain. In this paper, we study the case in which the transition kernel of the Markov chain depends on unknown parameters: we construct a particle filter for the simultaneous estimation of the parameter and the partially observed Markov chain (adaptive estimation) and we prove the convergence of this filter to the correct optimal filter, as time and the number of particles go to infinity. The filter presented here generalizes Del Moral's Monte Carlo particle filter.

Article information

Source
J. Appl. Probab. Volume 42, Number 4 (2005), 1053-1068.

Dates
First available in Project Euclid: 14 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.jap/1134587816

Digital Object Identifier
doi:10.1239/jap/1134587816

Mathematical Reviews number (MathSciNet)
MR2203822

Zentralblatt MATH identifier
1102.60037

Subjects
Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 93E10: Estimation and detection [See also 60G35] 93E11: Filtering [See also 60G35] 65C50: Other computational problems in probability

Keywords
Nonlinear filtering particle filter Bayesian estimation

Citation

Papavasiliou, Anastasia. A uniformly convergent adaptive particle filter. J. Appl. Probab. 42 (2005), no. 4, 1053--1068. doi:10.1239/jap/1134587816. https://projecteuclid.org/euclid.jap/1134587816.


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