State Estimation for Linear Dynamic System With Multiple-Step Random Delays Using High-Order Markov Chain

To cope with the large state estimation error due to sensor delay, a novel flexible model is explored to describe a linear dynamic system with multiple-step random delays in this paper. Compared with existing models, this model is more consistent with the actual situation. Based on the new model, the main difficulty, which is to determine the probability of any number of steps delayed, is overcome by applying techniques of high-order Markov chain. Then, the Kalman filtering problem with measurement delays is converted to random parameter matrices Kalman filtering(RKF), the new approximate state estimators are proposed. For a <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-step random delay model, we prove that it can be treated as a <inline-formula> <tex-math notation="LaTeX">$(2n-1)th$ </tex-math></inline-formula>-order Markov chain, making it theoretically feasible to apply the method in this paper to deal with any multiple-step delay model. Some illustrative numerical examples are presented to demonstrate the efficiency of the new model and superiority over existing algorithms.

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