Qi Wenjuan, Wang Shigang
School of Mechanical and Electrical Engineering, Heilongjiang University, Harbin 150080, China.
Micromachines (Basel). 2022 Jul 29;13(8):1216. doi: 10.3390/mi13081216.
This paper addresses the robust Kalman filtering problem for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, the robust local time-varying Kalman filters are presented. Further, the batch covariance intersection (BCI) fusion and a fast sequential covariance intersection (SCI) fusion robust time-varying Kalman filters are presented. They have the robustness that the actual filtering error variances or their traces are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equations approach. The concepts of the robust and actual accuracies are presented, and the robust accuracy relations are proved. It is also proved that the robust accuracies of the BCI and SCI fusers are higher than that of each local Kalman filter, the robust accuracy of the BCI fuser is higher than that of the SCI fuser, and the actual accuracies of each robust Kalman filter are higher than its robust accuracy for all admissible uncertainties of noise variances. The corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization between the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and the correctness of the robust accuracy relations.
本文研究了噪声方差具有不确定性的多传感器时变系统的鲁棒卡尔曼滤波问题。利用极小极大鲁棒估计原理，基于具有噪声方差保守上界的最坏情况保守系统，提出了鲁棒局部时变卡尔曼滤波器。进一步，提出了批处理协方差交叉（BCI）融合和快速序贯协方差交叉（SCI）融合鲁棒时变卡尔曼滤波器。它们具有这样的鲁棒性：对于所有允许的噪声方差不确定性，实际滤波误差方差或其迹保证具有最小上界。基于所提出的李雅普诺夫方程方法证明了它们的鲁棒性。提出了鲁棒精度和实际精度的概念，并证明了鲁棒精度关系。还证明了对于所有允许的噪声方差不确定性，BCI和SCI融合器的鲁棒精度高于每个局部卡尔曼滤波器的鲁棒精度，BCI融合器的鲁棒精度高于SCI融合器的鲁棒精度，并且每个鲁棒卡尔曼滤波器的实际精度高于其鲁棒精度。还针对多传感器时不变系统提出了相应的稳态鲁棒局部和融合卡尔曼滤波器，并通过动态误差系统分析（DESA）方法和动态方差误差系统分析（DVESA）方法证明了局部和融合时变及稳态卡尔曼滤波器之间实现的收敛性。给出了一个仿真例子来验证鲁棒性和鲁棒精度关系的正确性。
