Discrete-time linear estimation with correlated noises

Most of the existing recursive state estimation algorithms for discrete-time linear system with correlated noises assume that process and measurement noises are correlated at the same instant. Via sampling discretization to the continuous-time linear system with uncorrelated process and measurement noises, it is shown that the neighbouring process and measurement noises are correlated in its discretized counterpart. In the sense of linear unbiased minimum variance estimation, a global optimal recursive state estimation algorithm for this discretized linear system is proposed. Monte-Carlo simulation results are provided to compare the new algorithm with the Kalman filter with uncorrelated process and measurement noises, which demonstrates the validity of the new algorithm.