Zheng Jie, Cui Wenxia, Sun Sian
School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China.
Sensors (Basel). 2023 Aug 5;23(15):6968. doi: 10.3390/s23156968.
Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov's equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators.
本文研究了在多种噪声、测量缺失、一步测量延迟和数据包丢失影响下的多传感器描述符系统（MSDS）的鲁棒卡尔曼估计问题。此外，所建立的MSDS模型描述了不确定方差噪声、乘性噪声、时间延迟和数据包丢失现象。不同类型的噪声和数据包丢失使得构建MSDS的估计器变得更加困难。首先，通过应用奇异值分解（SVD）方法、增广状态和虚拟噪声方法将MSDS转换为新的系统模型。此外，基于极小极大鲁棒估计原理和卡尔曼滤波理论为新推导的增广系统构造鲁棒卡尔曼估计器。另外，给定的估计器由四部分组成，即通常的卡尔曼滤波器、预测器、平滑器和白噪声反卷积估计器。然后，根据增广状态与原始系统状态的关系得到MSDS的鲁棒融合卡尔曼估计器。同时，利用数学归纳法和李雅普诺夫方程证明了MSDS实际卡尔曼估计器的鲁棒性。此外，对于所有允许的不确定噪声方差，所获得的卡尔曼估计器的误差方差保证在其上界以内。最后，通过一个电路系统的仿真例子来说明鲁棒估计器的性能和有效性。
