Optimal distributed fusion of two-channel observation systems with correlated noises

State fusion problems are discussed for two-channel observation systems with correlated observation noises. An optimal recursive algorithm is presented. The performance of the algorithm is equal to that of centralized Kalman filtering. Different from the existing one based on information filters and matrix transformations, our algorithm directly uses the projection theorem in Hilbert space. Therefore, the algorithm has the practical advantages of flexibility and simplicity.