  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 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 is varied.
