New Nonlinear Filters and Exact Solutions of the Fokker-Planck Equation

A new nonlinear filter is derived for continuous time processes with discrete time measurements. The filter is exact, and it can be implemented in real-time with a computational complexity that is comparable to the Kalman filter. This new filter includes both the Kalman filter and the discrete time version of the Bene¿ filter as special cases. Moreover, the new theory can handle a large class of nonlinear estimation problems that cannot be solved using the Kalman or discrete time Bene¿ filters. A new approximation technique is suggested for problems that do not satisfy the theoretical conditions exactly. This approximation is simple and straightforward, analogous to the extended Kalman filter.