Optimal filtering for linear systems with multiple observation delays

In this paper, the optimal filtering problem for a linear system over observations with multiple delays is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and its variance. As a result, the optimal filtering equations similar to the traditional Kalman-Bucy ones are obtained in the form dual to the Smith predictor, commonly used for robust control design in time delay systems. In the example, the obtained optimal filter over observations with multiple delays is verified for a sample system and compared with the best Kalman-Bucy filter available for delayed measurements.