In the present study, a higher-order moment state estimation problem in a finite time interval for the discrete-time Markov jump linear systems (MJLS) is investigated. Moreover, time-correlated noise in measurements is considered. Initially, the measruement differencing approach is applied to convert the time-correlated measurement noise to an uncorrelated noise. Then the cumulant generating function is utilized to solve the stochastic jumping problem of MJLS, by which the discrete-time MJLS is transformed into a deterministic system. In this way, the transformed deterministic system has the same norm with a higher-order moment of the original state. Finally, a finite-time state estimation algorithm is proposed to guarantee that the higher-order moment of error trajectory remains within a pre-specified bound over a given time interval. In order to evaluate the performance of the proposed method, some test cases are applied. Obtained results prove the accuracy and efficiency of the proposed method.
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