Sparse Wiener Chaos approximations of Zakai equation for nonlinear filtering

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 parameters and to shift the latter off-line. The sparse truncation can reduce the number of the WCE coefficients dramatically while keeping the same asymptotic convergence rate as the simple truncation.