Differentially Private Set-Based Estimation Using Zonotopes

Abstract: For large-scale cyber-physical systems, the collaboration of spatially distributed sensors is often needed to perform the state estimation process. Privacy concerns naturally arise from disclosing sensitive measurement signals to a cloud estimator that predicts the system state. To solve this issue, we propose a differentially private set-based estimation protocol that preserves the privacy of the measurement signals. Compared to existing research, our approach achieves less privacy loss and utility loss using a numerically optimized truncated noise distribution. The proposed estimator is perturbed by weaker noise than the analytical approaches in the literature to guarantee the same level of privacy, therefore improving the estimation utility. Numerical and comparison experiments with truncated Laplace noise are presented to support our approach. Zonotopes, a less conservative form of set representation, are used to represent estimation sets, giving set operations a computational advantage. The privacy-preserving noise anonymizes the centers of these estimated zonotopes, concealing the precise positions of the estimated zonotopes.