Optimal Schedule of Secure Transmissions for Remote State Estimation against Eavesdropping

In this article, we investigate the privacy issue of the remote state estimation problem in cyber-physical systems. Specifically, in the presence of an eavesdropper, a sensor observes a discrete linear time-invariant process and then sends the measurements to a remote state estimator with arbitrary finite kinds of transmission options through an unreliable wireless channel. The transmission options of the sensor are in silence state or transmitting aided by injection noise with different energy levels. The eavesdropper wiretaps the channel when the sensor transmits packets to the estimator. Aiming at minimizing the remote estimation error and the cost of the sensors transmission energy while maximizing the eavesdropper state estimation error, we theoretically prove that there exist some structural properties for the optimal transmission schedule for both the known and the unknown eavesdropper's estimation errors. Numerical simulation results are provided to validate the theoretical analysis.