Abstract:
We consider a nonlinear filtering problem where a signal process is modeled by a stochastic differential equation and the observation is perturbed by a white noise. The goal of nonlinear filtering is to find the best estimation of the signal process based on the observation. Some well known approaches include the Kalman filter, particle filter and Zakai filter. In this talk, we shall present two new numerical algorithms to solve nonlinear filtering problems. The first one is an implicit Bayesian filter method and the second one is a hybrid sparse grid Zakai filter method. Both theoretical results and numerical experiments will be presented.