On the Mortensen equation for maximum likelihood state estimation

Author

Aihara, Shin Ichi ; Bagchi, Arunabha

Author_Institution

Dept. of Manage. & Syst. Sci., Sci. Univ. of Tokyo, Japan

Volume

44

Issue

10

fYear

1999

fDate

10/1/1999 12:00:00 AM

Firstpage

1955

Lastpage

1961

Abstract

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

Keywords

continuous time systems; dynamic programming; filtering theory; functional equations; maximum likelihood estimation; nonlinear systems; recursive estimation; state estimation; stochastic systems; Mortensen equation; Onsager-Machlup functional; continuous-time nonlinear stochastic dynamical system; maximum likelihood state estimation; recursive filtering; Additive white noise; Dynamic programming; Filtering; Filters; Maximum likelihood estimation; Nonlinear equations; Probability; State estimation; Stochastic processes; Stochastic systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.793785

Filename

793785