ALTERNATIVE OPTIMAL FILTER FOR LINEAR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS

作者：Basin Michael^*; Calderon Alvarez Dario

来源：International Journal of Innovative Computing Information and Control, 2008, 4(11): 2889-2898.

• Filtering
• Linear stochastic system
• Multiple state
• Observation delays

In this paper, the optimal filtering problem for linear systems with multiple state and observation delays is treated using the optimal estimate of the state transition matrix. As a result, the alternative optimal filter is derived in the form similar to the traditional Kalman-Bucy one, i.e., consists of only two equations, for the optimal estimate and the estimation error variance. Thus, this paper designs the optimal mean-square finite-dimensional filter for linear time-delay systems with arbitrary, even non-commensurable delays, in both state and observation equations. This presents a significant advantage in comparison to the previously obtained optimal filter [1], which includes infinite or variable number of covariance equations, unboundedly growing as the filtering horizon tends to infinity. Performances of the two optimal filters are compared in example; the obtained results are discussed.

• 出版日期2008-11