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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 other original particle filters.
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https://hal.inria.fr/inria-00072404
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 9:52:13 AM
Last modification on : Friday, February 12, 2021 - 3:33:15 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:06:14 PM

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  • HAL Id : inria-00072404, version 1

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François Le Gland, Nadia Oudjane. Stability and Uniform Approximation of Nonlinear Filters using the Hilbert Metric, and Application to Particle Filters. [Research Report] RR-4215, INRIA. 2001. ⟨inria-00072404⟩

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