线性离散随机系统最优和稳态Kalman平滑器

对于带非零均值相关噪声的线性离散随机系统,基于Kalman 滤波器和射影理论,提出了新的最优固定点、固定区间和固定滞后 Kalman 平滑器。它们避免了计算估计误差方差阵的逆矩阵,且具有通用性。推广和改进了带零均值的不相关噪声系统的经典结果。还提出了相应的稳态 Kalman 平滑器和极点配置 Kalman平滑器,并证明它们的局部或全局渐近稳定性。

Optimal and Steady-State Kalman Smoothers for Linear Discrete Stochastic Systems

Based on the Kalman filter and projection theory,the new optimal fixed-point,fixed-interval and fixed-lag Kalman smoothers are presented for systems with correlated noises having non- zero means.They avoid to calculate the inverse of the estimation error variance matrices,and have the generality.The classical results for systems with uncorrelated noises having zero means are extended and modified.The corresponding steady-state Kalman smoothers and pole- assignment Kalman smoothers are also presented,and their local or global asymptotic stability is proved.