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

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

Stability and Uniform Particle Approximation of Nonlinear Filters in Case of Non Ergodic Signals


Code(s) de Classification MSC:

Résumé: In this paper, we propose a new approach to study the stability of the optimal filter w.r.t. its initial condition in introducing a "robust filter'" which approximates the optimal filter uniformly in time. This approach allows us to prove, in some cases when the signal is non ergodic, the stability of the optimal filter in mean over the observations and the uniform convergence in mean over the observations of a special interacting particle filter to the optimal filter.

Mots Clés: nonlinear filter ; particle filter ; stability ; total variation norm ; mixing

Date: 2003-01-15

Prépublication numéro: PMA-786

Pdf file: PMA-786.pdf