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For the multisensor systems with correlated noises and identical measurement matrices, based on linear unbiased minimum variance (LUMV) criterion, a weighted measurement fusion (WMF) Kalman filter is presented, where the optimal weights is given by the Lagrange multiplier method. By using the information filter, it is proved that it is functionally equivalent to the centralized fusion Kalman filter, i.e. it is numerically identical to the centralized fusion Kalman filter, so that they have the global optimality. In order to reduce the computational burden, another simple algorithm for computing the optimal weights is also derived, and comparison of computational counts of two algorithms for computing optimal weights is given. A numerical simulation example verifies their functional equivalence. The proposed results can be applied to solve the information fusion filtering problem for the autoregressive moving average (ARMA) signals.