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This paper studies remote state estimation in the presence of aneavesdropper. A sensor transmits local state estimates over a packet droppinglink to a remote estimator, while an eavesdropper can successfully overheareach sensor transmission with a certain probability. The objective is todetermine when the sensor should transmit, in order to minimize the estimationerror covariance at the remote estimator, while trying to keep the eavesdroppererror covariance above a certain level. This is done by solving an optimizationproblem that minimizes a linear combination of the expected estimation errorcovariance and the negative of the expected eavesdropper error covariance.Structural results on the optimal transmission policy are derived, and shown toexhibit thresholding behaviour in the estimation error covariances. In theinfinite horizon situation, it is shown that with unstable systems one can keepthe expected estimation error covariance bounded while the expectedeavesdropper error covariance becomes unbounded. An alternative measure ofsecurity, constraining the amount of information revealed to the eavesdropper,is also considered, and similar structural results on the optimal transmissionpolicy are derived. In the infinite horizon situation with unstable systems, itis now shown that for any transmission policy which keeps the expectedestimation error covariance bounded, the expected amount of informationrevealed to the eavesdropper is always lower bounded away from zero. Anextension of our results to the transmission of measurements is also presented.

Remote State Estimation over Packet Dropping Links in the Presence of an Eavesdropper