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In this paper, we consider a remote state estimation problem in the presenceof an eavesdropper. A smart sensor takes measurement of a discrete lineartime-invariant (LTI) process and sends its local state estimate through awireless network to a remote estimator. An eavesdropper can overhear the sensortransmissions with a certain probability. To enhance the system privacy level,we propose a novel encryption strategy to minimize a linear combination of theexpected error covariance at the remote estimator and the negative of theexpected error covariance at the eavesdropper, taking into account the cost ofthe encryption process. We prove the existence of an optimal deterministic andMarkovian policy for such an encryption strategy over a finite time horizon.Two situations, namely, with or without knowledge of the eavesdropperestimation error covariance are studied and the optimal schedule is shown tosatisfy the threshold-like structure in both cases. Numerical examples aregiven to illustrate the results.

Finite Time Encryption Schedule in the Presence of an Eavesdropper with Operation Cost