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.

翻译：针对大规模信息物理系统，往往需要空间分布式传感器的协同来实现状态估计过程。将敏感测量信号透露给预测系统状态的云端估计器会引发隐私问题。为解决该问题，我们提出一种差分隐私的集值估计协议，可保护测量信号的隐私性。与现有研究相比，本方法通过采用数值优化的截断噪声分布，实现了更低的隐私损失与效用损失。与文献中的解析方法相比，所提出的估计器在保证同等隐私水平的前提下受到更弱噪声的扰动，从而提升了估计效用。通过截断拉普拉斯噪声的数值实验与对比实验验证了本方法的有效性。采用保守性更低的集值表示形式——Zonotopes（多面体带状域）表示估计集，使集合运算具有计算优势。隐私保护噪声对估计Zonotopes的中心进行匿名化处理，隐藏了估计Zonotopes的精确位置。