State-Secrecy Codes for Stable Systems

摘要

In this paper, we study the problem of remote state estimation, in the presence of a passive eavesdropper. An authorized user estimates the state of a stable linear plant, based on the packets received from a sensor, while the packets may also be intercepted by the eavesdropper. Our goal is to design a coding scheme at the sensor, which encodes state information, in order to impair the eavesdropper's estimation performance, while enabling the user to successfully decode the sent messages. We introduce a novel class of codes, termed State-Secrecy Codes. By using acknowledgment signals from the user, they apply linear time-varying transformations to the current and previously received states, imposing artificial unstable dynamics to the eavesdropper's Riccati recursive estimation scheme. By exploiting the process noise, the channel randomness and the artificial dynamics, these codes manage to be fast and efficient for real-time dynamical systems. Under minimal conditions they achieve perfect secrecy, namely the eavesdropper's estimation error covariance matrix converges to the open-loop prediction one, which is the same as not intercepting any messages at all; meanwhile, the user's estimation performance is optimal. Those conditions only require that at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. The theoretical results are illustrated in simulations.