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Reduction of the Zakai equation by invariance group techniques

Abstract : A general procedure, inspired from that used for deterministic partial differential equations, is presented to reduce the Zakai stochastic Pde of filtering on Rn to a stochastic Pde on a lower-dimensional space Rn, with m < n. The method is based upon invariance group techniques. We show how the existence of invariant solutions of the Zakai equation is related to geometric properties of the infinitesimal generator of the signal process. An illustration of the method to a two-dimensional tracking problem with bearings-only measurements is presented. With a specific choice of the bearings-dependent output function, we obtain a continuous model for which the Zakai equation has solutions which can be computed from a one-dimensional stochastic Pde instead of a two-dimensional Pde for the general solution. © 1998 Elsevier Science B.V. All rights reserved.
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Soumis le : mardi 22 janvier 2013 - 13:03:21
Dernière modification le : vendredi 11 juin 2021 - 14:12:02


  • HAL Id : hal-00779557, version 1



Michel de Lara. Reduction of the Zakai equation by invariance group techniques. Stochastic Processes and their Applications, 1998, 73 (1), pp.119. ⟨hal-00779557⟩



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