一种新的带白噪声估值器的固定滞后Kalman平滑器

NEW FIXED-LAG KALMAN SMOOTHERS WITH WHITE NOISE ESTIMATORS

本文基于经典 Kalm an滤波器和 Mendel的输入白噪声估值器 ,应用射影理论 ,提出了一种新的带白噪声估值器的最优固定滞后 Kalm an平滑器 ,且给出了平滑增益阵和平滑误差方差阵新算法 ,避免了计算滤波和预报误差方差阵的逆矩阵 ,减少了计算负担 .还提出了相应的稳态次优固定滞后 Kalm an平滑器 ,它具有渐近稳定性 .仿真例子说明了所提出的结果的有效性 .

Based on classical Kalman filter and Mendel's input white noise estimators, using the projection theory, this paper presents the new optimal fixed lag Kalman smoothers with white noise estimators, and gives new algorithms for the smoother gain matrix and the variance matrix of the smoothing error. They avoid the inverses of the variance matrices of the filtering and prediction errors, so that the computational burden is reduced. The corresponding steady state suboptimal fixed lag Kalman smoothers are also presented, which have the asymptotic stability. A simulation example shows the effectiveness of the proposed results.