Remote State Estimation over Packet Dropping Links in the Presence of an Eavesdropper
For control systems security, this work provides theoretical guarantees on estimation and secrecy trade-offs, though the results are incremental extensions of known threshold policies.
This paper addresses remote state estimation over packet-dropping links with an eavesdropper, deriving optimal transmission policies that minimize estimation error at the remote estimator while keeping the eavesdropper's error above a threshold. For unstable systems, they show that bounded estimation error can coexist with unbounded eavesdropper error, but information-theoretic security constraints impose a lower bound on leaked information.
This paper studies remote state estimation in the presence of an eavesdropper. A sensor transmits local state estimates over a packet dropping link to a remote estimator, while an eavesdropper can successfully overhear each sensor transmission with a certain probability. The objective is to determine when the sensor should transmit, in order to minimize the estimation error covariance at the remote estimator, while trying to keep the eavesdropper error covariance above a certain level. This is done by solving an optimization problem that minimizes a linear combination of the expected estimation error covariance and the negative of the expected eavesdropper error covariance. Structural results on the optimal transmission policy are derived, and shown to exhibit thresholding behaviour in the estimation error covariances. In the infinite horizon situation, it is shown that with unstable systems one can keep the expected estimation error covariance bounded while the expected eavesdropper error covariance becomes unbounded. An alternative measure of security, constraining the amount of information revealed to the eavesdropper, is also considered, and similar structural results on the optimal transmission policy are derived. In the infinite horizon situation with unstable systems, it is now shown that for any transmission policy which keeps the expected estimation error covariance bounded, the expected amount of information revealed to the eavesdropper is always lower bounded away from zero. An extension of our results to the transmission of measurements is also presented.