Finite-dimensional filters with nonlinear drift. III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for the linear filtering system and the Benes filtering system

Author

Shing-Tung Yau ; Yau, Stephen S T

Author_Institution

Dept. of Math., Harvard Univ., Cambridge, MA, USA

Volume

33

Issue

4

fYear

1997

Firstpage

1277

Lastpage

1294

Abstract

We consider the Duncan-Mortensen-Zakai (DMZ) equation for the Kalman-Bucy filtering system and Benes filtering system. We show that this equation can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a Kolmogorov-type equation, Let n be the dimension of state space. We show that we need only n sufficient statistics in order to solve the DMZ equation.

Keywords

differential equations; filtering theory; multidimensional systems; probability; Benes filtering; Duncan-Mortensen-Zakai equation; Kalman-Bucy filtering; Kolmogorov-type equation; arbitrary initial condition; finite-dimensional filters; linear filtering; nonlinear drift; ordinary differential equations; statistics; Algebra; Differential algebraic equations; Differential equations; Filtering; Maximum likelihood detection; Nonlinear equations; Nonlinear filters; Partial differential equations; State-space methods; Statistics; Stochastic processes;

fLanguage

English

Journal_Title

Aerospace and Electronic Systems, IEEE Transactions on

Publisher

ieee

ISSN

0018-9251

Type

jour

DOI

10.1109/7.625127

Filename

625127