Probabilistic Transmission Scheme for Distributed Filtering Over Randomly Lossy Sensor Networks in the Presence of Eavesdropper

This article studies distributed secure estimation in sensor networks with packet losses and an eavesdropper. The message is transmitted through communication channels between sensors, which can be overheard by the eavesdropper with a certain probability. Two types of sensor networks under two cooperative-filtering algorithms are considered, and probabilistic transmission schemes to defend against the eavesdropper are proposed. For collectively detectable sensor networks under a consensus Kalman filter, a sufficient distributed detectability condition on the transmission probabilities is identified to guarantee that the estimation errors of the sensors are statistically bounded. Furthermore, a necessary and sufficient security condition is obtained to guarantee unboundedness of the eavesdropper's estimation error. For neighborhood-detectable nodes under a standard Kalman filter, a sufficient distributed detectability condition and a necessary security condition are provided on the transmission probabilities. Simulation examples are given to illustrate the results.