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A uniformly convergent adaptive particle filter. (English) Zbl 1102.60037

Particle filters are Monte Carlo methods that approximate the optimal filter of a partially observed Markov chain. The author deals with the case where the transition kernel of the Markov chain depends on unknown parameters. She proposes an algorithm that is a combination of the interacting particle filter for computation of the optimal filter for fixed parameter value and a variation of the Monte Carlo particle filter described by P. Del Moral [J. Appl. Probab. 35, No. 4, 873–884 (1998; Zbl 0940.60060)] for computation of the posterior distribution of the parameter. In the case where the system is linear and Gaussian an algorithm is described that is a combination of the Monte Carlo particle filter and the Kalman-Bucy filter. Uniform convergence of the proposed algorithms is proved as time and the number of particles go to infinity.

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
93E10 Estimation and detection in stochastic control theory
93E11 Filtering in stochastic control theory
65C50 Other computational problems in probability (MSC2010)

Citations:

Zbl 0940.60060
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Full Text: DOI

References:

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