The Kalman type recursive state estimator with a finite-step correlated process noises

This paper consider the Kalman type recursive filter with finite-step correlated process noises. We propose a modified Kalman type filtering for such dynamic system. More importantly, unlike the previous result on the Kalman filtering with color noises, no process noise correlation model is required. What we need is only the correlation of process noises of two different time instants. We analyze its local optimality and demonstrate via several examples that the proposed recursive filter can significantly increase the performance over the standard Kalman filter when dynamic system with finite-step correlated process noises.