This article tackles the recursive filtering problem for an array of 2-D systems over sensor networks with a given topology. Both the measurement degradations of the network outputs and the stochastic perturbations of network couplings are modeled to reflect engineering practice by introducing some random variables with given statistics. The goal of the addressed problem is to devise the distributed recursive filters capable of cooperatively estimating the true state in order to ensure locally minimal upper bound (UB) on the second-order moment of the filtering error (also viewed as the general error variance). For this purpose, the general error variance regarding the underlying target plant is first provided to facilitate the subsequent filter design, and then a certain UB on the error variance is constructed by exploiting the stochastic analysis and the induction approach. Furthermore, in view of the inherent sparsity of the sensor network, the gain parameters of the desired distributed filters are determined, and the proposed recursive filtering algorithm is shown to be scalable. Finally, an illustrative example is given to demonstrate the validity of the established filtering strategy.

中文翻译：

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具有测量退化的传感器网络上二维系统的局部最小方差滤波：一种分布式递归算法

本文解决了具有给定拓扑的传感器网络上的二维系统阵列的递归过滤问题。通过引入一些具有给定统计数据的随机变量，对网络输出的测量退化和网络耦合的随机扰动进行建模以反映工程实践。解决问题的目标是设计能够协同估计真实状态的分布式递归滤波器，以确保滤波误差（也被视为一般误差方差）的二阶矩的局部最小上界（UB） . 为此，首先提供有关潜在目标植物的一般误差方差，以方便随后的滤波器设计，然后利用随机分析和归纳法构造误差方差上的一定UB。此外，鉴于传感器网络固有的稀疏性，确定了所需分布式滤波器的增益参数，并证明了所提出的递归滤波算法具有可扩展性。最后，给出一个说明性的例子来证明所建立的过滤策略的有效性。