Distributed Tracking Stopping Time Using Average Consensus

We study the problem of tracking stopping time in a distributed circumstance. More specially, a Gaussian random walk with positive drift is observed simultaneously by multiple detectors in a noisy fashion. The goal is to estimate the first-passage time when the random walk reaches a predefined level. After characterizing the optimal estimator with mean absolute p-moment, a distributed tracking stopping time estimation algorithm is proposed, where each detector only exchanges observation with their neighbors based on the average consensus scheme. Then, we provide theoretical performance bound and testify the asymptotic optimality of proposed distributed stopping time estimator. Finally, performance analysis is depicted by the numerical simulation.