Skip to Main content Skip to Navigation
Journal articles

Stability and uniform approximation of nonlinear filters using the Hilbert metric, and application to particle filters

François Le Gland 1 Nadia Oudjane 2
1 SIGMA2 - Signal, models, algorithms
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal filter of several particle filters, such as the interacting particle filter and some other original particle filters.
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/hal-00912081
Contributor : Francois Le Gland <>
Submitted on : Sunday, December 1, 2013 - 11:19:29 PM
Last modification on : Tuesday, June 15, 2021 - 4:22:39 PM

Links full text

Identifiers

Citation

François Le Gland, Nadia Oudjane. Stability and uniform approximation of nonlinear filters using the Hilbert metric, and application to particle filters. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2004, 14 (1), pp.144-187. ⟨10.1214/aoap/1075828050⟩. ⟨hal-00912081⟩

Share

Metrics

Record views

397