This paper is concerned with the optimal state estimation for linear systems when the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. We derive the optimal linear estimation in a sequential form and for distributed fusion. They are both compared with the optimal batch fusion, suboptimal batch fusion, suboptimal sequential fusion, and the suboptimal distributed fusion where the cross-correlation between the noises are neglected. The comparison is in terms of theoretical filter mean square error and the real root mean square error. Simulation on a target tracking example is given to show the effectiveness of the presented algorithms. (C) 2013 Elsevier Ltd. All rights reserved.