One shot schemes for decentralized quickest change detection

TL;DR

This paper analyzes decentralized quickest change detection using one shot communication schemes where sensors signal only once, showing that such schemes are asymptotically optimal and perform as well as centralized methods in large false alarm regimes.

Contribution

It demonstrates that one shot schemes with distributed CUSUM sensors are asymptotically optimal, matching centralized detection performance in a minimal communication setting.

Findings

One shot schemes are asymptotically optimal in extended Lorden sense.

Performance loss compared to centralized detection is negligible at high false alarm thresholds.

Distributed CUSUM sensors can effectively detect changes with minimal communication.

Abstract

This work considers the problem of quickest detection with N distributed sensors that receive continuous sequential observations from the environment. These sensors employ cumulative sum (CUSUM) strategies and communicate to a central fusion center by one shot schemes. One shot schemes are schemes in which the sensors communicate with the fusion center only once, after which they must signal a detection. The communication is clearly asynchronous and the case is considered in which the fusion center employs a minimal strategy, which means that it declares an alarm when the first communication takes place. It is assumed that the observations received at the sensors are independent and that the time points at which the appearance of a signal can take place are different. It is shown that there is no loss of performance of one shot schemes as compared to the centralized case in an extended Lorden min-max sense, since the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound.