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This paper furthers current research into the notion of guaranteed privacy,which provides a deterministic characterization of the privacy of outputsignals of a dynamical system or mechanism. Unlike stochastic differentialprivacy, guaranteed privacy offers strict bounds on the proximity between theranges of two sets of estimated data. Our approach relies on synthesizing aninterval observer for linear time-invariant (LTI) bounded-error systems. Thedesign procedure incorporates a bounded noise perturbation factor computationand an observer gain synthesis. The observer simultaneously provides guaranteedprivate and stable interval-valued estimates for the desired variable. Wedemonstrate the optimality of our design by minimizing the$\mathcal{H}_{\infty}$ norm of the observer error system. Lastly, we assess theaccuracy of our proposed mechanism by quantifying the loss incurred whenconsidering guaranteed privacy specifications, and illustrate our approachoutperformance to differential privacy through simulations.

Guaranteed Privacy-Preserving $\mathcal{H}_{\infty}$-Optimal Interval Observer Design for Bounded-Error LTI Systems