Exact finite dimensional nonlinear filters

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 simple approximation technique is suggested for practical applications in which the dynamics do not satisfy the required conditions exactly. This approximation is analogous to the so-called "extended Kalman filter" [10], and it represents a generalization of the standard linearization method.