Optimal linear filtering over observations with multiple 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. Copyright (C) 2004 John Wiley Sons, Ltd.