A SVD-based optimal filtering for multi-channel system with correlated multiplicative noises

An optimal filtering recursive algorithm was proposed for multi-channel system with correlated multiplicative noises among observation channels. The system is under the condition that the multiplicative noises are general stochastic matrix and correlated in each observation channel at the same time. Considering the numerical stability of the algorithm, an equivalent algorithm based on singular value decomposition (SVD) was given for the same system. The SVD algorithm, as well as the previous algorithm, is optimal in the sense of linear minimum-variance. Simulation examples to demonstrate the performance of both algorithms show that the algorithm based on SVD has higher computational precision and numerical stability.