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Optimal linear filtering over observations with multiple delays. (English) Zbl 1057.93055

Summary: 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.

MSC:

93E11 Filtering in stochastic control theory
93C23 Control/observation systems governed by functional-differential equations
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