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.

Document type :

Journal articles

Domain :

Mathematics [math] / Probability [math.PR]

Complete list of metadatas

https://hal.univ-cotedazur.fr/hal-00755431
Contributor : Sylvain Rubenthaler <>
Submitted on : Wednesday, November 21, 2012 - 11:29:04 AM
Last modification on : Wednesday, November 20, 2019 - 1:47:00 AM

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

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

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