The set-based estimation has gained a lot of attention due to its ability to guarantee state enclosures for safety-critical systems. However, collecting measurements from distributed sensors often requires outsourcing the set-based operations to an aggregator node, raising many privacy concerns. To address this problem, we present set-based estimation protocols using partially homomorphic encryption that preserve the privacy of the measurements and sets bounding the estimates. We consider a linear discrete-time dynamical system with bounded modeling and measurement uncertainties. Sets are represented by zonotopes and constrained zonotopes as they can compactly represent high-dimensional sets and are closed under linear maps and Minkowski addition. By selectively encrypting parameters of the set representations, we establish the notion of encrypted sets and intersect sets in the encrypted domain, which enables guaranteed state estimation while ensuring privacy. In particular, we show that our protocols achieve computational privacy using the cryptographic notion of computational indistinguishability. We demonstrate the efficiency of our approach by localizing a real mobile quadcopter using ultra-wideband wireless devices.

翻译：集值估计因其能够为安全关键系统提供状态包络保证而备受关注。然而，从分布式传感器收集测量结果通常需要将集值操作外包给聚合节点，这引发了诸多隐私问题。针对这一问题，本文提出采用部分同态加密的集值估计协议，保护测量值及状态估计边界的隐私。我们考虑具有有界建模和测量不确定性的线性离散时间动态系统。集值通过zonotopes和约束zonotopes表示，因其能紧凑表征高维集值，且在线性映射和闵可夫斯基加法下封闭。通过选择性加密集值表示参数，我们建立了加密集的概念，并在加密域中进行集值交集运算，从而在保障隐私的同时实现确定性状态估计。特别地，我们证明该协议基于密码学中的计算不可区分性概念实现了计算隐私。通过使用超宽带无线设备对真实移动四旋翼飞行器进行定位，验证了所提方法的有效性。