Sriramya Bhamidipati, University of Illinois at Urbana-Champaign; Grace Xingxin Gao, Stanford University

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To address PMU vulnerability against spoofing, we propose a set-valued state estimation technique known as Stochastic Reachability-based Distributed Kalman Filter (SR-DKF) that computes secure GPS timing across a network of receivers. Utilizing stochastic reachability, we estimate not only GPS time but also its stochastic reachable set, which is parameterized via probabilistic zonotope (p-Zonotope). While requiring known measurement error bounds in only non-spoofed conditions, we design a two-tier approach: We first perform measurement-level spoofing mitigation via deviation of measurement innovation from its expected p-Zonotope, and second perform state-level timing risk analysis via intersection probability of estimated pZonotope with an unsafe set that violates IEEE C37.118.1a-2014 standards. We validate the proposed SR-DKF by subjecting a simulated receiver network to coordinated signal-level spoofing. We demonstrate an improved GPS timing accuracy and successful spoofing mitigation via our SR-DKF. We validate the robustness of the estimated timing risk as the number of receivers are varied.