Privacy-Preserving Distributed Estimation Over Sensor Networks With Multistrategy Injection Attacks: A Chaotic Encryption Scheme

This article explores the distributed set-membership state estimation problem over sensor networks (SNs) with chaotic encrypted privacy-preserving scheme and multistrategy injection attacks (MIAs). Since potential eavesdroppers in communication networks may intercept the transmitted measurement signals, chaotic encryption is adopted as a privacy-preserving scheme to protect the system state information from being revealed. The measurement signals are encrypted before transmission and decrypted upon reception by the remote estimator. A newly devised attack model is developed to characterize the injection attacks, which occur randomly and involve a combination of multiple attack strategies. By employing matrix inequality techniques, a unified set-membership estimation scheme is developed when both the privacy-preserving scheme and the MIAs coexist. Subsequently, based on the sufficient condition of constraining the estimation error within an ellipsoidal range, an optimization problem is formulated to achieve the optimal estimation performance at each time step, along with the development of a recursive algorithm for computing the required estimator parameters. Finally, simulation is provided to verify the set-membership estimation approach under the chaotic encryption scheme.