Optimal filtering for linear systems with state and multiple observation delays

This article solves the optimal filtering problem for linear systems with state and multiple observation delays. The optimal estimate equation similar to the traditional Kalman-Bucy one is derived, and the system of equations for determining the filter gain matrix consists of an infinite set of equations. It is then demonstrated that a finite set of the filtering equations can be obtained in case of commensurable delays. In the example, the designed optimal filter is compared to the traditional Kalman-Bucy filter.