This paper studies the distributed secure estimation problem of sensor networks (SNs) in the presence of eavesdroppers. In an SN, sensors communicate with each other through digital communication channels, and the eavesdropper overhears the messages transmitted by the sensors over fading wiretap channels. The increasing transmission rate plays a positive role in the detectability of the network while playing a negative role in the secrecy. Two types of SNs under two cooperative filtering algorithms are considered. For networks with collectively observable nodes and the Kalman filtering algorithm, by studying the topological entropy of sensing measurements, a sufficient condition of distributed detectability and secrecy, under which there exists a code–decode strategy such that the sensors’ estimation errors are bounded while the eavesdropper’s error grows unbounded, is given. For collectively observable SNs under the consensus Kalman filtering algorithm, by studying the topological entropy of the sensors’ covariance matrices, a necessary condition of distributed detectability and secrecy is provided. A simulation example is given to illustrate the results.

本文研究了存在窃听者的传感器网络（SN）的分布式安全估计问题。在SN中，传感器通过数字通信通道相互通信，窃听者会监听传感器在衰落的窃听通道上发送的消息。传输速率的提高在网络的可检测性中起着积极的作用，而在保密性方面则起着消极的作用。考虑两种协同过滤算法下的两种类型的SN。对于具有可共同观察节点和卡尔曼滤波算法的网络，通过研究传感测量的拓扑熵，分布式可检测性和保密性的充分条件，在这种情况下，给出了一种编码-解码策略，以使传感器的估计误差有界，而窃听者的误差则无限制地增长。对于共识卡尔曼滤波算法下的集体可观测序列，通过研究传感器协方差矩阵的拓扑熵，为分布式可检测性和保密性提供了必要条件。给出了一个仿真例子来说明结果。