Optimal Privacy-aware Estimation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

1 Scopus Citations
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Original languageEnglish
Pages (from-to)2253-2266
Journal / PublicationIEEE Transactions on Automatic Control
Issue number5
Online published6 May 2021
Publication statusPublished - May 2022


This article studies the design of an optimal privacy-aware estimator of a public random variable based on noisy measurements, which contain private information. The public variable carries also nonprivate information, but its estimate will be correlated with the private information due to the estimation process. The objective is to design an optimal estimator of the public random variable such that the leakage of private information, via the estimation process, is kept below a certain level. The privacy metric is defined as the discrete conditional entropy of the private variable given the output of the estimator. We show that the optimal privacy-aware estimator is the solution of a (possibly infinite-dimensional) convex optimization problem when the estimator has access to either the measurement or the measurement together with the private information. We study the optimal perfect-privacy estimation problem that ensures the estimate of the public variable is independent of the private information. A necessary and sufficient condition is derived guaranteeing that an estimator satisfies the perfect-privacy requirement. It is shown that the optimal perfect-privacy estimator is the solution of a linear optimization problem. A sufficient condition for its existence is derived. The impact of the distribution mismatch on the perfect-privacy condition is studied. Numerical examples are used to illustrate the privacy-accuracy tradeoff.

Research Area(s)

  • Estimation, Noise measurement, Optimization, Privacy, Random variables, Sensors, Temperature measurement

Citation Format(s)

Optimal Privacy-aware Estimation. / Nekouei, Ehsan; Sandberg, Henrik; Skoglund, Mikael; Johansson, Karl H.

In: IEEE Transactions on Automatic Control, Vol. 67, No. 5, 05.2022, p. 2253-2266.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review