Privacy against state estimation:An optimization framework based on the data processing inequality

Information about the system state is obtained through noisy sensor measurements. This data is coded and transmitted to a trusted user through an unsecured communication network. We aim at keeping the system state private; however, because the network is not secure, opponents might access sensor data, which can be used to estimate the state. To prevent this, before transmission, we randomize coded sensor data by passing it through a probabilistic mapping, and send the corrupted data to the trusted user. Making use of the data processing inequality, we cast the synthesis of the probabilistic mapping as a convex program where we minimize the mutual information (our privacy metric) between two estimators, one constructed using the randomized sensor data and the other using the actual undistorted sensor measurements, for a desired level of distortion-how different coded sensor measurements and distorted data are allowed to be.