Abstract: By modern time series analysis method, based on ARMA innovation model, under the linear minimum variance optimal information fusion criterion, the distributed fusion steady-state optimal Kalman predictors weighted by matrices, scalars, and diagonal matrices are presented for multisensor systems with correlated input and observation noises, and with correlated observation noises, respectively. Based on the Lyapunov equations, the formulas of computing local predicting error variances and covariances are given, which are applied to compute optimal weights. Compared to the single sensor case, the accuracy of the fused predictor is improved. A simulation example for tracking systems shows its effectiveness, and shows that the accuracy distinction of the predictors weighted by three ways is not obvious, but the predictor weighted by scalars can obviously reduce the computational burden, and provides a fast real time information fusion estimation algorithm.