IJPAM: Volume 10, No. 3 (2004)

OPTIMAL FILTERING FOR LINEAR
SYSTEMS WITH STATE DELAY

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
Apartado Postal 144-F, C.P. 66450, San Nicolas de los Garza
Nuevo Leon, MEXICO
$^1$e-mail: mbasin@fcfm.uanl.mx
$^2$e-mail: jgrg17@yahoo.com.mx
$^3$Department of Electrical and Mechanical Engineering
Autonomous University of Coahuila
Calle Barranquilla, S/N, Col. Guadalupe
Apartado Postal 189, C.P. 25750, Monclova
Coahuila, MEXICO
e-mail: rodolfomart62@hotmail.com


Abstract.In this paper, the optimal filtering problem for linear systems with state delay over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the optimal estimate equation similar to the traditional Kalman-Bucy one is derived; however, it is impossible to obtain a system of the filtering equations, that is closed with respect to the only two variables, the optimal estimate and the error variance, as in the Kalman-Bucy filter. The resulting system of equations for determining the error variance consists of a set of equations, whose number is specified by the ratio between the current filtering horizon and the delay value in the state equation and increases as the filtering horizon tends to infinity. In the example, performance of the designed optimal filter for linear systems with state delay is verified against the best Kalman-Bucy filter available for linear systems without delays.

Received: July 28, 2003

AMS Subject Classification: 60G35, 93C05, 93E11

Key Words and Phrases: linear time-delay system, stochastic system, filtering

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 10
Issue: 3