Optimal filtering for linear state delay systems

Michael Basin

doi:10.1109/TAC.2005.846599

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Optimal filtering for linear state delay systems

2005-05-01

PRE

Michael Basin

Jesús Rodríguez-González

Rodolfo Martinez‐Zuniga

DOI：10.1109/TAC.2005.846599

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Abstract

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In this note, 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 and two versions of the extended Kalman-Bucy filter for time-delay systems.

Keywords:

filtering

stochastic system

time delay state

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