IJPAM: Volume 12, No. 3 (2004)


Michael V. Basin$^1$, Jesus Rodriguez-Gonzalez$^2$
Rodolfo Martinez-Zuniga$^3$
$^{1,2}$Department of Physical and Mathematical Sciences
Autonomous University of Nuevo Leon
Apdo Postal 144-F, Cd. Universitaria, C.P. 66450
San Nicolas de los Garza
Nuevo Leon, MEXICO
$^1$e-mails: mbasin@fcfm.uanl.mx, jgrg17@yahoo.com.mx
$^2$e-mail: jgrg17@yahoo.com.mx
$^3$Department of Electrical and Mechanical Engineering
Autonomous University of Couahuila
Calle Barranquilla, S/N, Col. Guadalupe
Apdo Postal 189, C.P. 25750, Monclova
Coahuila, MEXICO
e-mail: rodolfomart62@hotmail.com

Abstract.In this paper, the optimal filtering problem for nonlinear systems over linear observations with time delay is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for a polynomial state over linear observations with delay is then established, which yields the explicit closed form of the filtering equations in the particular case of a bilinear system state. In the example, performance of the designed optimal filter for bilinear states over linear observations with delay is verified against the best filter available for bilinear states over linear observations without delays and the conventional extended Kalman-Bucy filter.

Received: February 16, 2004

AMS Subject Classification: 93E11, 93C10, 60G35

Key Words and Phrases: filtering, stochastic system, nonlinear system, time delay system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 3