A Differential Geometric Approach to Nonlinear Filtering : the Projection Filter Damiano Brigo Bernard Hanzon, Francois Le Gland
نویسندگان
چکیده
This paper deals with a new and systematic method of approximating exact nonlinear lters with nite dimensional lters. The method used here is based on the diierential geometric approach to statistics. The projection lter is derived in the case of exponential families. A characterization of the lters is given in terms of an assumed density principle. An a posteriori measure of the performance of the projection lter is deened. Applications to particular systems, and numerical schemes which can be used to implement the projection lter are given in the nal part. The results of simulations for the cubic sensor are discussed. Une Approche du Filtrage Non{Lin eaire Fond ee sur la G eom etrie Dii erentielle : le Filtre par Projection R esum e : Cet article propose une m ethode nouvelle et syst ematique pour l'approximation d'un ltre non{lin eaire exact par un ltre de dimension nie. La m ethode repose sur l'utili-sation d'outils de g eom etrie dii erentielle en statistique. L' equation du ltre par projection est etablie dans le cas des familles exponentielles, et on en donne une caract erisation en tant que ltre de forme donn ee. On d eenit egalement une mesure a posteriori de la qualit e de l'approximation. Dans la derni ere partie, on etudie quelques exemples, et on propose un sch ema num erique pour la mise en uvre du ltre par projection. Finalement, on pr esente des r esultats de simulations pour le probl eme du senseur cubique.
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A Differential Geometric Approach to Nonlinear Filtering : the projection Filter*
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