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The nonlinear filtering problem is considered for the time homogeneous diffusion model with correlated noise. A numerical approach is proposed for computing approximations of the unnormalized filtering density (UFD) and the nonlinear filtering. This approach is based on the Wiener chaos expansion (WCE) of the solution of Zakai equation. A Sparse truncation method of WCE is introduced to simplify calculation,...
Sparse Wiener chaos approximations of Zakai equation is considered. The objective is to optimize an approach to nonlinear filtering based on the Cameron-Martin version of Wiener chaos expansion (WCE). The error of the approximation is obtained. The main feature of Wiener chaos expansion is that it allows one to separate the computations involving the observations from those dealing only with the system...
A comparative study related to the approximate methods of nonlinear filtering for chaotic signals is presented in this paper. In the following, we considered chaos models given as the output signals of three well known strange attractors: Lorenz, Chua and Rossler. From the implementation point of view for real time applications of the approximate nonlinear filtering algorithms, the extended Kalman...
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