OPTIMAL LINEAR FILTERING FOR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS
Michael Basin, Edgar Nelson Sanchez, Rodolfo Martinez-Zu · 2007
In this paper, the optimal filtering problem for linear systems with multi- ple state and observation delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate, error variance, and various error co- variances. The paper treats the most general case of multiple delays in both state and observation equations, which are allowed to be different from each other. The resulting system of equations for determining the filter gain matrix consists, in the general case, of an infinite set of equations. It is however demonstrated that a finite set of the filter- ing equations can be obtained in the particular case of equal or commensurable delays in the observation and state equations. In the example, performance of the designed opti- mal filter for linear systems with state and observation delays is verified against the best Kalman-Bucy filter available for linear systems without delays. Keywords: Filtering, Stochastic system, Time-delay system