Nonlinear Filtering Stochastic Analysis and Numerical Methods.
Boris L. Rozovskii, F. LeGland · 1998
Abstract : The final report contains outline of research that was done during period 1995-98. The main objective was to develop effective numerical algorithms of optimal nonlinear filtering and prediction and (more generally), state and parameter estimation in partially observed stochastic dynamical systems. During course of project a number of fundamental results were obtained, such as: development of a Wiener type optimal nonlinear filter (complete solution of the last Wiener problem); development of spectral based approach to nonlinear filtering, which have led to spectral separating scheme (separation of parameters and observations in optimal nonlinear filter) and other effective numerical approximations for optimal nonlinear filter that include projection filter and assumed density filters. The results have been applied to specific difficult problems in target tracking, particularly, to angle only tracking in EO and IR search and track systems and track-before-detect of resolved or sub-resolved low SNR targets. Extensive simulation showed that proposed approach allows us to obtain much better performance as compared to conventional expended Kalman filter in a number of important practical situations.