Fast suboptimal fixed-interval Wiener smoothing algorithm
快速次优固定区间Wiener平滑器算法

In order to overcome the drawback that the optimal fixed-interval Kalman smoothing algorithms require a large computational burden for control systems with correlated noise, by using the Kalman filtering method based on the controlled au-toregressive moving average (CARMA) innovation model, the optimal fixed-interval Wiener recursive state smoother is derived from the steady-state optimal Kalman smoother. The obtained smoother contains the high-order polynomial matrix whose coefficient matrices exponentially decay to zero. A fast sub-optimal fixed-interval Wiener smoothing algorithm is proposed by means of truncating terms with coefficient matrices approximately equal to zero. Thus, the computational burden is obviously reduced and the method is suitable for real time application. Both the formula for truncation error and the formula for selecting truncation index are given. A simulation example shows the effectiveness of the proposed algorithm.