State Estimation with Protecting Exogenous Inputs via Cram\'er-Rao Lower Bound Approach

TL;DR

This paper develops a privacy-preserving state estimation method for dynamic systems that uses the Cramér-Rao lower bound to protect exogenous inputs from adversaries, ensuring privacy with low computational complexity.

Contribution

It introduces a novel CRLB-based constrained optimization framework for privacy-preserving state estimation, with a low-complexity solution and differential privacy guarantees.

Findings

Effective privacy protection demonstrated in building occupancy scenario

Low-complexity algorithm maintains real-time performance

CRLB-based approach ensures specified privacy levels

Abstract

This paper addresses the real-time state estimation problem for dynamic systems while protecting exogenous inputs against adversaries, who may be honest-but-curious third parties or external eavesdroppers. The Cram\'er-Rao lower bound (CRLB) is employed to constrain the mean square error (MSE) of the adversary's estimate for the exogenous inputs above a specified threshold. By minimizing the MSE of the state estimate while ensuring a certain privacy level measured by CRLB, the problem is formulated as a constrained optimization. To solve the optimization problem, an explicit expression for CRLB is first provided. As the computational complexity of the CRLB increases with the time step, a low-complexity approach is proposed to make the complexity independent of time. Then, a relaxation approach is proposed to efficiently solve the optimization problem. Finally, a privacy-preserving state estimation algorithm with low complexity is developed, which also ensures $(\epsilon, \delta)$-differential privacy. Two illustrative examples, including a practical scenario for protecting building occupancy, demonstrate the effectiveness of the proposed algorithm.