Compressive Privacy for a Linear Dynamical System

TL;DR

This paper introduces a method for compressing measurements in linear dynamical systems to balance accurate public state estimation with privacy protection of private states, applicable in centralized and decentralized sensor networks.

Contribution

It formulates an optimization framework for designing measurement compression matrices that optimize utility-privacy tradeoff in both centralized and decentralized settings.

Findings

Effective compression matrices improve public state estimation accuracy.

The approach successfully limits private state estimation.

Decentralized algorithms enable local optimization without message exchange.

Abstract

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 separately 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. We consider the cases where there is no message exchange between the sensors; and where each sensor takes turns to transmit messages to the other sensors. Simulations and empirical experiments demonstrate the efficiency of our proposed approach in allowing the fusion center to estimate the public states with good accuracy while preventing it from estimating the private states accurately.