Innovation-Based Remote State Estimation Secrecy with no Acknowledgments

Abstract: Secrecy encoding for remote state estimation in the presence of adversarial eavesdroppers is a well studied problem. Typical existing secrecy encoding schemes rely on the transmitter's knowledge of the remote estimator's current performance. This performance measure is often shared via packet receipt acknowledgments. However, in practical situations the acknowledgment channel may be susceptible to interference from an active adversary, resulting in the secrecy encoding scheme failing. Aiming to achieve a reliable state estimate for a legitimate estimator while ensuring secrecy, we propose a secrecy encoding scheme without the need for packet receipt acknowledgments. Our encoding scheme uses a pre-arranged scheduling sequence established at the transmitter and legitimate receiver. We transmit a packet containing either the state measurement or encoded information for the legitimate user. The encoding makes the packet appear to be the state but is designed to damage an eavesdropper's estimate. The pre-arranged scheduling sequence and encoding is chosen psuedo-random. We analyze the performance of our encoding scheme against a class of eavesdropper, and show conditions to force the eavesdropper to have an unbounded estimation performance. Further, we provide a numerical illustration and apply our encoding scheme to an application in power systems.