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This paper is concerned with the distributed fusion estimation problem for a class of multi-sensor asynchronous sampling systems with correlated noises. The state updates uniformly and the sensors sample randomly. Based on the measurement augmentation method, the asynchronous sampling system is transformed to the synchronous sampling one. Local filter is designed by using an innovation analysis approach. Then, the filtering error cross-covariance matrix between any two local filters is derived. Finally, the optimal distributed fusion filter is proposed by using matrix-weighted fusion algorithm in the linear minimum variance sense. Simulation results show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]