Construction of finite-dimensional nonlinear filter via ODEs

Author

Yau, Stephen S T ; Jin, Ning ; Yan, Changlin

Author_Institution

Dept. of Math., Stat. & Comput. Sci., Chicago Univ., IL, USA

Volume

3

fYear

2003

fDate

4-6 June 2003

Firstpage

2447

Abstract

Consider the robust Duncan-Mortensen-Zakai (DMZ) equation arising from Yau filtering system which includes Kalman-Bucy filtering system and Benes filtering. The main problem of nonlinear filtering is to solve this robust DMZ equation in real time. It is shown that this equation can be solved explicitly with an arbitrary initial condition by solving a linear system of ODEs and a Kolmogorov-type equation. Furthermore, it is shown that the Kolmogorov-type equation can be solved via the Riccati-type system of ODEs. Thus the robust DMZ equation arising from Yau´s filtering system is shown to be solvable in real time.

Keywords

Riccati equations; filtering theory; linear systems; multidimensional systems; nonlinear filters; nonlinear systems; partial differential equations; Duncan-Mortensen-Zakai equation; Kalman-Bucy filtering system; Kolmogorov equation; ODE; Riccati system; Yau filtering system; finite dimensional system; nonlinear filter; nonlinear system; ordinary differential equation; Algebra; Filtering; Mathematics; Nonlinear equations; Nonlinear filters; Polynomials; Riccati equations; Robustness; Statistics; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2003. Proceedings of the 2003

ISSN

0743-1619

Print_ISBN

0-7803-7896-2

Type

conf

DOI

10.1109/ACC.2003.1243442

Filename

1243442