This paper is concerned with the distributed filtering problem for a class of two-dimensional shift-varying systems over sensor networks subject to stochastic communication protocol (SCP) over a finite horizon. The communication between the sensor nodes and the filters is implemented through shared channels of limited capacity. To avoid data collisions, the SCP is applied to determine the transmission order of the signals/packets for each sensor. The considered scheduling behavior is characterized by mutually uncorrelated random variables with known probability distributions. Recursive distributed filters are proposed to estimate the system state through available information from both individual and neighboring nodes in the sensor network according to a given topology. Attention is focused on the design of distributed filters in order to ensure the locally minimal upper bound on the error variance of the state estimation. Sufficient conditions are first established, via intensive stochastic analysis and mathematical induction, on the existence of an upper bound of the estimation error variance. Then, by means of a matrix simplification technique, the desired filter gains are designed to optimize the obtained upper bound at each shift step. Finally, a practical example is given to verify the effectiveness of the proposed filter strategy.

本文关注的是在有限范围内服从随机通信协议（SCP）的传感器网络上一类二维变变系统的分布式滤波问题。传感器节点和过滤器之间的通信是通过容量有限的共享通道实现的。为了避免数据冲突，SCP用于确定每个传感器的信号/数据包的传输顺序。所考虑的调度行为的特征是具有已知概率分布的互不相关的随机变量。提出了递归分布式滤波器，以根据给定的拓扑通过来自传感器网络中各个节点和相邻节点的可用信息来估计系统状态。为了确保状态估计的误差方差的局部最小上限，注意力集中在分布式滤波器的设计上。首先，通过大量的随机分析和数学归纳，在估计误差方差的上限存在的情况下，建立充分的条件。然后，借助矩阵简化技术，设计所需的滤波器增益，以优化在每个移位步骤获得的上限。最后，给出一个实际的例子来验证所提出的过滤策略的有效性。通过矩阵简化技术，可以将所需的滤波器增益设计为在每个移位步长优化所获得的上限。最后，给出一个实际的例子来验证所提出的过滤策略的有效性。通过矩阵简化技术，可以将所需的滤波器增益设计为在每个移位步长优化所获得的上限。最后，给出一个实际的例子来验证所提出的过滤策略的有效性。