Nearly 60 years ago, in a celebrated paper of Kalman and Bucy, it was established that optimal estimation for linear Gaussian systems is dual to a linear-quadratic optimal control problem. In this paper, for the first time, a duality result is established for a general nonlinear filtering problem, mirroring closely the original Kalman-Bucy duality of control and estimation for linear systems. The main result is presented for a finite state space Markov process in continuous time. It is used to derive the classical Wonham filter. The form of the result suggests a natural generalization which is presented as a conjecture for the continuous state space case. 查看全文>>