A new fixed-lag smoother using recent finite observations

This paper proposes a new fixed-lag smoother for state estimation in discrete-time state space models, which is called the unbiased, fixed-lag, and optimal (UFO) smoother. The proposed UFO smoother is obtained by directly solving an optimization problem with the unbiasedness constraint using only the most recent finite observations. Therefore, the proposed UFO smoother is both unbiased and optimal by design. The proposed UFO smoother also has inherent properties such as deadbeat, time-invariance, and robustness. Via numerical simulations, the performance of the proposed UFO smoother is evaluated by the comparison with that of the existing fixed-lag Kalman smoother, which shows that the proposed UFO smoother could be appropriate for fast estimation of signals that vary relatively quickly.