In this talk we will consider a secure estimation problem in the form of a remote state estimation task 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 remote 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. Furthermore, for unstable systems, it is shown that in the infinite horizon situation there exist transmission policies, which can keep the expected remote estimation error covariance bounded while the expected eavesdropper error covariance is driven unbounded.
Welcome to everyone!