Nonlinear filtering revisited: a spectral approach. II

For pt. I see SIAM Journal on Control and Optimization (1997). A recursive in time Wiener chaos representation of the optimal nonlinear filter is derived for a continuous time diffusion model with uncorrelated noises. The existing representations are either not recursive or require a prior computation of the unnormalized filtering density, which is time consuming. An algorithm is developed for computing a recursive approximation of the filter, and the error of the approximation is obtained. When the parameters of the model are known in advance, the online speed of the algorithm can be increased by performing part of the computations off line