On the Mortensen equation for maximum likelihood state estimation
Shin Ichi Aihara, Amitava Bagchi · IEEE Transactions on Automatic Control · 1999
The main purpose of the paper is to formulate the maximum likelihood state estimation problem correctly for a continuous-time nonlinear stochastic dynamical system. By using the Onsager-Machlup functional, a modified likelihood is introduced. The basic equation for the maximum likelihood state estimate is derived with the aid of a dynamic programming approach. The numerical procedure for realizing the recursive filtering is also proposed with some numerical results.