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

Sylvain Rubenthaler; Nadia Oudjane

doi:10.1081/SAP-200056643

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

Sylvain Rubenthaler ¹ Nadia Oudjane ^{2, 3}

1 JAD - Laboratoire Jean Alexandre Dieudonné

2 LAGA - Laboratoire Analyse, Géométrie et Applications

3 EDF - EDF

Abstract : 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 nonergodic, 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.

Keywords : Total variation norm Mixing Nonlinear filter Particle filter Stability Total variation norm.

Type de document :

Article dans une revue

Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2005, 23 (3), p. 421-448. 〈10.1081/SAP-200056643〉

Domaine :

Mathématiques [math] / Probabilités [math.PR]

Liste complète des métadonnées

https://hal.univ-cotedazur.fr/hal-00755431
Contributeur : Sylvain Rubenthaler <>
Soumis le : mercredi 21 novembre 2012 - 11:29:04
Dernière modification le : jeudi 7 février 2019 - 17:49:14

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

Identifiants

Collections

Citation

Exporter

Métriques

270

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

Identifiants

Collections

Citation

Exporter

Partager

Métriques

270