Compressive Privacy for a Linear Dynamical System
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We consider a linear dynamical system in which the state vector consists of both public and private states. One or more sensors make measurements of the state vector and sends information to a fusion center, which performs the final state estimation. To achieve an optimal tradeoff between the utility of estimating the public states and protection of the private states, the measurements at each time step are linearly compressed into a lower dimensional space. Under the centralized setting where all measurements are collected by a single sensor, we propose an optimization problem and an algorithm to find the best compression matrix. Under the decentralized setting where measurements are made independently at multiple sensors, each sensor optimizes its own local compression matrix. We propose methods to separate the overall optimization problem into multiple sub-problems that can be solved locally at each sensor. Three message schedules are considered: 1) no message exchange between the sensors; 2) all sensors transmit messages simultaneously; 3) each sensor takes turns to transmit messages to the other sensors. Simulations demonstrate the efficiency of our proposed approaches in allowing the fusion center to estimate the public states with good accuracy while preventing it from estimating the private states accurately.
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