Privacy-Aware State Estimation: From Coarse to Precise Privacy Protection

2026-06-28

AI Summary

This work addresses the challenge of simultaneously achieving coarse- and fine-grained privacy in state estimation by proposing a novel privacy-preserving framework. It introduces, for the first time, the formal notion of “exact directional privacy” and establishes its intrinsic connection to the system’s unobservable subspace. By designing an analytical state transformation, a randomized intermittent encryption mechanism, and tailored manipulation of the observable subspace, the proposed method ensures high estimation performance for legitimate users while driving both the eavesdropper’s total mean squared error (MSE) and the MSE along sensitive directions to infinity. Theoretical analysis provides a lower bound on the encryption probability guaranteeing divergence of the total MSE and rigorously proves necessary and sufficient conditions for unbounded directional MSE, thereby demonstrating that the framework simultaneously fulfills both privacy objectives.

Abstract

This paper addresses the problem of achieving both coarse and precise privacy in state estimation. Coarse privacy forces the eavesdropper's total mean-square error (MSE) to infinity, but errors along certain confidential directions may remain bounded. This motivates precise privacy, which additionally drives the MSE along any prescribed direction to infinity. For coarse privacy, an analytical transformation is established, preserving the user's optimality and driving the eavesdropper's total MSE to infinity at a polynomial-exponential rate. A stochastic intermittent encryption scheme is further developed, and an explicit lower bound on the encryption probability is derived to guarantee divergence. For precise privacy, by analyzing the behavior of the Riccati equation on the unobservable subspace, we prove that the eavesdropper's directional MSE becomes unbounded if and only if the direction's unstable component lies outside the observable subspace. Finally, a systematic method is proposed to exclude target vectors from the observable subspace, forcing the directional MSE to infinity.

Problem

• privacy-aware state estimation
• coarse privacy
• precise privacy
• mean-square error
• directional privacy

Innovation

• privacy-aware state estimation
• coarse privacy
• precise privacy
• directional MSE divergence
• unobservable subspace