A receding horizon Kalman filter with the estimated initial state on the horizon

In this paper, we propose a discrete-time receding horizon Kalman filter with the estimated initial state on the horizon. The proposed filter employs the conventional Kalman filter with the receding horizon strategy. The initial state on the horizon is estimated from a maximum likelihood criterion and then initiates the Kalman filter. It turns out that the proposed filter is independent of any a priori information on the state over the horizon while the previous filters assume that the stochastic information on the initial state at the starting time is available. The proposed filter is shown to have the same form as an optimal FIR filter, which leads to having the optimality and the unbiasedness.