Optimal Offline Privacy Schedule for Remote State Estimation under an Eavesdropper

Privacy preserving is an important emerging issue in Cyber-Physical Systems (CPSs). This paper considers a privacy problem for a remote state estimation system in the presence of an eavesdropper. In the system, an energy-constrained sensor sends its local estimation to a remote estimator through a wireless channel, where the eavesdropper is able to wiretap the sensor-estimator communications. There are three transmission options for the sensor, i.e., keeping in silence and plaintext or encrypted transmission. Because of limited energy, the sensor cannot transmit packets through encryption all the time during each period of the infinite horizon. Our aim is to decide the optimal transmission schedule for the sensor to maximize the eavesdropper's state estimation error. We theoretically derive the optimal privacy schedule and analyze the divergence probability of the eavesdropper's estimation error. Numerical results are presented to validate the proposed schedule.