Deterministic Nonlinear Filtering

A model for nonlinear filtering is considered in which errors in state dynamics and observations are modelled deterministically. Mortensen's deterministic estimator and a minimax estimator are considered. A risk sensitive stochastic filter model with small state and observation noise intensities is also considered. The minimax estimator is obtained in the zero noise intensity limit, using asymptotic properties of a pathwise interpretation of the Zakai stochastic partial differential equation. 1 Introduction. In general terms, the filtering problem can be stated as follows. Let x T denote a state (or signal) at time T and y T an observation at time T . The observation depends on both x T and certain measurement errors. Estimates Research partially supported by NSF grant DMS-9531276 through Brown University and by ONR grant N0014-96-1-0267 through North Carolina State University. e T for x T are allowed which depend on past observations y t for 0 t T . The goal of filtering is t..