快速次优固定区间Wiener平滑器算法

Fast suboptimal fixed-interval Wiener smoothing algorithm

为了克服带相关噪声控制系统的最优固定区间Kalman平滑算法要求较大计算负担的缺点,应用Kalman滤波方法,基于CARMA新息模型,由稳态最优Kalman平滑器导出了带相关噪声控制系统的最优固定区间Wiener递推状态平滑器,它带有系数阵指数衰减到零的高阶多项式矩阵.用截断系数矩阵近似为零的项的方法提出了相应的快速次优固定区间Wiener平滑算法.它显著地减少了计算负担,便于实时应用,还给出了截断误差公式和选择截断指标的公式.仿真例子说明了快速平滑算法的有效性.

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.