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

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.