Optimal state estimation for sampled-data systems with randomly sampled and delayed measurements

The optimal state estimation problem for sampled-data systems with randomly sampled and delayed measurements is addressed in this paper. An optimal filter is presented first for the sampled-data system with randomly sampled and delay-free measurements from multiple sensors. The filter, which has been proved to be optimal in the sense of minimum estimation variance, updates the state estimation once new measurements are available. The result is applicable to a wide range of sampling cases of which the corresponding state estimation procedures are formulated separately. Discrete-time equivalent of the filter is also derived rigorously which makes it feasible for computer implementation. Furthermore, we extend the optimal filter and develop a sliding time window estimator through the measurement reorganization technique to deal with the situation of delayed measurements. Monte-Carlo simulations are carried out to demonstrate the effectiveness of the proposed approach.

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