Secure State Estimation for Cyber-Physical Systems Against Active Eavesdropping Attacks: A Stochastic Encryption-Based Method

This article is concerned with the problem of remote state estimation for cyber-physical systems (CPSs) in the presence of an active eavesdropper. To prevent information leakage, a novel stochastic encryption scheme is proposed to protect the data transmitted via packet loss channel. The scheme can guarantee the user’s privacy and force the estimation error of the eavesdropper to diverge by using a predefined scheduling sequence to transmit raw data or an encrypted version randomly. In this case, two types of data are considered: raw measurements and local estimates. Aiming at these two transmission scenarios, the expected estimation error recursions with respect to encryption mechanisms, channel parameters, and the system dynamics are derived in the minimum mean error estimation sense. Further, we show the conditions that require the expected estimation error covariance of the user to be bounded, while the active eavesdropper’s expected estimation error grows unbounded by mathematical induction and matrix theory methods. Finally, an application example is illustrated to verify the performance of the encryption scheme. Note to Practitioners—This paper addresses the secure state estimation for a class of CPSs in the presence of eavesdropping attacks, which plays a vital role in many critical infrastructures, such as unmanned aerial vehicle (UAV) and smart grids. The system’s confidential information is transmitted over the wireless channel to a remote estimator that is likely to be overheard by a malicious eavesdropper. Most existing privacy protection methods not only constrain the capabilities of eavesdroppers, such as packet reception rate, but also have limited ability to disrupt the estimated performance of eavesdroppers. Besides, few studies have been conducted on the impact of active eavesdroppers who may have a higher packet reception rate. To overcome these difficulties, based on control-theoretic approaches, we propose two alternative encryption schemes for two different transmission scenarios. Note that our scheme can guarantee that the user’s estimation error is bounded, while the estimation error of the eavesdropper goes to unbounded. Accordingly, the privacy and estimation performance of the system can be ensured by our encryption scheme, and the encryption schemes can be conveniently applied to practical systems.