Applying a smoothing criterion to the Kalman filter

A performance measure is suggested for evaluating the performance of a given optimal estimator at other lags than the design lag. Applying this idea, suboptimal smoothers are found for both continuous-and discrete-time systems, combining low complexity and good performance. Several examples are considered. Suboptimal-smoothing improvement is related to optimal improvement and interpreted in terms of input-output transfer-function properties. A special class of discrete-time systems is also discussed where the optimal smoother is of the same complexity as the zero-lag filter.