This paper is concerned with the estimation of correlated noise and packet dropout for information fusion in distributed sensing networks. By studying the problem of the correlation of correlated noise in sensor network information fusion, a matrix weight fusion method with a feedback structure is proposed to deal with the interrelationship between multi-sensor measurement noise and estimation noise, and the method can achieve optimal estimation in the sense of linear minimum variance. Based on this, a method is proposed using a predictor with a feedback structure to compensate for the current state quantity to deal with packet dropout that occurs during multi-sensor information fusion, which can reduce the covariance of the fusion results. Simulation results show that the algorithm can solve the problem of information fusion noise correlation and packet dropout in sensor networks, and effectively reduce the fusion covariance with feedback.