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This paper presents a moving horizon algorithm with mode detection for state estimation in Markov jump systems with Gaussian noise. This state estimation scheme is a combination of the maximum-likelihood algorithm and the moving horizon approach. The maximum-likelihood algorithm provides optimal estimate of the mode sequence within a moving fixed-size horizon, and the moving horizon estimation is an optimization-based solution. As a result, a mode detection-moving horizon estimator design method is proposed. Through the stochastic observability properties of the Markov jump linear systems, sufficient conditions for stability are established.
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Sun et al. (2018) studied this question.
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