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Nonlinear filters for linear models (a robust approach). (English) Zbl 0837.93071

The paper deals with the filtering problem when there are unknown noises. In general, these noises may be quite arbitrary, nonwhite, but they are assumed to be stationary and ergodic. The main contribution consists in showing how to use diffusion approximation methods for constructing nonlinear filtering schemes for a large class of linear models with observation noises of rather complicated nature. It is shown that it is possible to develop robust nonlinear filters, which are asymptotically efficient when the observation noise is not exactly known, but belongs to a finite family of possible noises. A theorem which shows how to use the diffusion approximation method for obtaining the best possible filter error is proven. The paper is addressed to scientists working in the field of nonlinear filtering theory.

MSC:

93E11 Filtering in stochastic control theory
93C10 Nonlinear systems in control theory
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