Stability and approximation of nonlinear filters: an information theoretic approach

François Le Gland 1
1 SIGMA2 - Signal, models, algorithms
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : It has recently been proved by J.M.C. Clark et al. that the relative entropy (or Kullback-Leibler information distance) between two nonlinear filters with different initial conditions is a supermartingale, hence its expectation can only decrease with time. This result was obtained for a very general model, where the unknown state and observation processes form jointly a continuous-time Markov process. The purpose of this paper is (i) to extend this result to a large class of f-divergences, including the total variation distance, the Hellinger distance, and not only the Kullback-Leibler information distance, and (ii) to consider not only robustness w.r.t. the initial condition of the filter, but also w.r.t. perturbation of the state generator. On the other hand, the model considered here is much less general, and consists of a diffusion process observed in discrete-time.
Type de document :
Communication dans un congrès
Proceedings of the 38th Conference on Decision and Control, Phoenix 1999, Dec 1999, Phoenix, United States. 2, pp.1889-1894, 1999, 〈10.1109/CDC.1999.830910〉
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https://hal.inria.fr/hal-00912069
Contributeur : Francois Le Gland <>
Soumis le : lundi 2 décembre 2013 - 00:26:16
Dernière modification le : jeudi 11 janvier 2018 - 06:20:10

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François Le Gland. Stability and approximation of nonlinear filters: an information theoretic approach. Proceedings of the 38th Conference on Decision and Control, Phoenix 1999, Dec 1999, Phoenix, United States. 2, pp.1889-1894, 1999, 〈10.1109/CDC.1999.830910〉. 〈hal-00912069〉

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