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

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

Optimal quantization methods for nonlinear filtering with discrete-time observations

Auteur(s):

Code(s) de Classification MSC:

Résumé: We develop an optimal quantization approach for numerically solving nonlinear filtering problems associated with discrete-time or continuous-time state process and discrete-time observations. Two quantization methods are proposed~: a marginal quantization and a Markovian quantization of the signal process. The approximate filters are explicitly solved by a finite-dimensional backward or forward procedure. A posteriori error bounds are stated and we show that the approximate error terms are minimal at some specific grids that may be computed by stochastic gradient descent methods based on Monte-Carlo simulations.

Mots Clés: Nonlinear filtering ; Markov chain ; Euler scheme ; vector quantization ; stochastic gradient descent ; stationary process ; numerical approximation

Date: 2002-12-05

Prépublication numéro: PMA-778