Privacy Preserving Set-Based Estimation Using Partially Homomorphic Encryption

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.