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This paper is concerned with the state estimation problem of discrete-time Markov jump linear systems where the noises influencing the systems are assumed to be arbitrarily correlated Gaussian noises. As a result, two algorithms are proposed. The first algorithm is an optimal algorithm of state estimate in the sense of minimum mean-square error estimate, which can exactly compute the minimum mean-square error estimate of systems state given an observation sequence. The second algorithm is a suboptimal algorithm which is proposed to reduce the computation and storage load of the proposed optimal algorithm. A numerical example is given to evaluate the performance of the proposed suboptimal algorithm.