One of the fundamental problems in sensor networks is to estimate and track the target states of interest that evolve in the sensing field. Distributed filtering is an effective tool to deal with state estimation in which each sensor only communicates information with its neighbors in sensor networks without the requirement of a fusion center. However, in the majority of the existing distributed filters, it is assumed that typically all sensors possess unlimited field of view to observe the target states. This is quite restrictive since practical sensors have limited sensing range. In this article, we consider distributed filtering based on linear minimum mean square error criterion in sensor networks with limited sensing range. To achieve the optimal filter and consensus, two types of strategies based on linear minimum mean square error criterion are proposed, that is, linear minimum mean square error filter based on measurement and linear minimum mean square error filter based on estimate, according to the difference of the neighbor sensor information received by the sensor. In linear minimum mean square error filter based on measurement, the sensor node collects measurement from its neighbors, whereas in linear minimum mean square error filter based on estimate, the sensor node collects estimate from its neighbors. The stability and computational complexity of linear minimum mean square error filter are analyzed. Numerical experimental results further verify the effectiveness of the proposed methods.

传感器网络的基本问题之一是估计和跟踪在传感领域发展的目标感兴趣状态。分布式滤波是处理状态估计的有效工具，其中每个传感器只与传感器网络中的邻居进行信息通信，而不需要融合中心。然而，在大多数现有的分布式滤波器中，通常假设所有传感器都具有无限的视野来观察目标状态。这是相当严格的，因为实际传感器的感应范围有限。在本文中，我们考虑了基于线性最小均方误差准则的分布式滤波在传感范围有限的传感器网络中。为了达到最优的过滤和共识，提出了两类基于线性最小均方误差准则的策略，即基于测量的线性最小均方误差滤波器和基于估计的线性最小均方误差滤波器，根据传感器接收到的相邻传感器信息的差异。传感器。在基于测量的线性最小均方误差滤波器中，传感器节点从其邻居那里收集测量值，而在基于估计的线性最小均方误差滤波器中，传感器节点从其邻居那里收集估计值。分析了线性最小均方误差滤波器的稳定性和计算复杂度。数值实验结果进一步验证了所提方法的有效性。基于测量的线性最小均方误差滤波器和基于估计的线性最小均方误差滤波器，根据传感器接收到的相邻传感器信息的差异。在基于测量的线性最小均方误差滤波器中，传感器节点从其邻居那里收集测量值，而在基于估计的线性最小均方误差滤波器中，传感器节点从其邻居那里收集估计值。分析了线性最小均方误差滤波器的稳定性和计算复杂度。数值实验结果进一步验证了所提方法的有效性。基于测量的线性最小均方误差滤波器和基于估计的线性最小均方误差滤波器，根据传感器接收到的相邻传感器信息的差异。在基于测量的线性最小均方误差滤波器中，传感器节点从其邻居那里收集测量值，而在基于估计的线性最小均方误差滤波器中，传感器节点从其邻居那里收集估计值。分析了线性最小均方误差滤波器的稳定性和计算复杂度。数值实验结果进一步验证了所提方法的有效性。传感器节点从其邻居收集测量值，而在基于估计的线性最小均方误差滤波器中，传感器节点从其邻居收集估计。分析了线性最小均方误差滤波器的稳定性和计算复杂度。数值实验结果进一步验证了所提方法的有效性。传感器节点从其邻居收集测量值，而在基于估计的线性最小均方误差滤波器中，传感器节点从其邻居收集估计。分析了线性最小均方误差滤波器的稳定性和计算复杂度。数值实验结果进一步验证了所提方法的有效性。