Minimum-Variance Recursive Filtering for Two-Dimensional Systems With Degraded Measurements: Boundedness and Monotonicity
Minimum-Variance Recursive Filtering for Two-Dimensional Systems With Degraded Measurements: Boundedness and Monotonicity
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DOI：
10.1109/tac.2019.2895245
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发表时间：
2019-01
影响因子：
6.8
通讯作者：
Jinling Liang;Fan Wang;Zidong Wang;Xiaohui Liu
中科院分区：
文献类型：
--
作者：
Jinling Liang;Fan Wang;Zidong Wang;Xiaohui Liu
研究了一类具有随机非线性和退化测量值的二维位移变系统的递推最小方差滤波问题。随机非线性受其统计特性控制，退化的测量值反映了信号的退化服从一定的概率分布。本文的主要目标是构造一个两步递归滤波器，使每一步的状态估计误差方差最小。首先利用归纳法保证了滤波器的无偏性，然后利用完全平方法设计了滤波器的参数。在此基础上，通过严格的数学分析，研究了测量信号的有界性和单调性等滤波性能。此外，还提出了一种计算算法，使所设计的滤波器能够在线实现。最后，通过数值仿真验证了所提滤波方案在电路系统中长传输线监控状态估计问题中的有效性和适用性。
This paper addresses the recursive minimum-variance filtering problem for a class of two-dimensional shift-varying systems with stochastic nonlinearity and degraded measurements. The stochastic nonlinearity is governed by its statistical characteristics and the degraded measurements reflect the signal degradation obeying certain prescribed probabilistic distributions. The main objective of this paper is to construct a two-step recursive filter that achieves the minimum error variance of the state estimation at each step. Utilizing an inductive approach, unbiasedness of the proposed filter is first ensured and the parameters of the filter are then designed by resorting to the completing squares method. Subsequently, the filtering performances including the boundedness and the monotonicity are investigated with respect to the measurement degradations through mathematically rigorous analysis. Moreover, a computational algorithm is presented to facilitate the online implementation of the designed filter. Finally, numerical simulation illustrates the effectiveness and applicability of the proposed filtering scheme in the state estimation problem for monitoring a long transmission line in circuit systems.