Encryption scheduling for remote state estimation under an operation constraint

In remote state estimation, data transmitted by a sensor through a wireless communication channel may be overheard by an eavesdropper. One possible way to avoid information leakage is to encrypt the transmitted data all the time. However, this may impose an extra operation energy burden on the sensor. In this paper, we investigate the optimal encryption scheduling in order to protect data privacy and ensure estimation accuracy under an energy constraint. Specifically, the sensor computes its local state estimate and then quantizes it using a non-subtractively dithered quantizer. Before each transmission, the sensor determines whether encrypting the data or not in order to strike a balance between data privacy and estimation accuracy. As the information about eavesdropper is unknown to the estimator, we introduce the concept of eavesdropper-invariant schedules and derive associated structural results. In addition, we propose a practical algorithm that compares a finite number of points to obtain an ε-optimal encryption schedule. Numerical examples are provided to illustrate performance benefits of the proposed methods.