Recursive Multiple Wiener Integral Expansion for Nonlinear Filtering of Diffusion Processes
نویسنده
چکیده
A recursive in time Wiener chaos representation of the optimal nonlinear filter is derived for a time homogeneous 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 on-line speed of the algorithm can be increased by performing part of the computations off line.
منابع مشابه
Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time homogeneous diffusion model with correlated noise. An algorithm is proposed for computing recursive approximations of the unnormalized filtering density and filter, an...
متن کاملWiener Chaos and Nonlinear Filtering
The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the CameronMartin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process....
متن کاملStochastic Differential Equations: a Wiener Chaos Approach
A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of ordinary and partial differential equations driven by finiteor infinite-dimensional noise with either adapted or anticipating input. Existence, uniqueness, regula...
متن کاملNonlinear Filtering Revisited: a Spectral Approach, II∗
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 erro...
متن کاملNonlinear Filtering for Diffusions in Random Environments
Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X and establish a multipl...
متن کامل