Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Interacting particle filtering with discrete observations


Code(s) de Classification MSC:

Résumé: We give give a review of some Monte-Carlo methods for numerically solving the non-linear filtering equation associated with a discrete-time or continuous-time Markov state process and a discrete-time observation process. These methods are based on interacting particle systems, which have been introduced earlier, for example in \cite{DJP98}, \cite{DJ99} or \cite{DM99}. Here we first state again the results of these previous papers, with only very short hints for the proofs, and with emphasis on the central limit theorem obtained as the number of particles (hence the time necessary to perform the procedure) increases. We also state and prove some new results concerning the case where the setting of the dynamical system, that is the initial law, the transition probabilities and/or the mathematical description of the observation noise are unperfectly known.

Mots Clés: Filtering ; Monte-Carlo methods ; Diffusion processes ; Interacting particle systems

Date: 1999-12-10

Prépublication numéro: PMA-552

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