Quickest detection in coupled systems

TL;DR

This paper addresses the problem of quickest detection of signals in a coupled multi-sensor system, proposing an asymptotically optimal detection strategy based on multiple CUSUM procedures under a stochastic optimization framework.

Contribution

It introduces an asymptotic optimality result for the minimum of N CUSUMs in coupled sensor systems with different signal onset times, using an extended Kullback-Leibler divergence criterion.

Findings

Minimum of N CUSUMs is asymptotically optimal for large false alarm intervals.

The detection problem is formulated as a stochastic optimization with a divergence-based delay measure.

Signals modeled as Ito processes with coupling across sensors.

Abstract

This work considers the problem of quickest detection of signals in a coupled system of N sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled a general Ito processes, are coupled across sensors, but that their onset times may differ from sensor to sensor. The objective is the optimal detection of the first time at which any sensor in the system receives a signal. The problem is formulated as a stochastic optimization problem in which an extended average Kullback- Leibler divergence criterion is used as a measure of detection delay, with a constraint on the mean time between false alarms. The case in which the sensors employ cumulative sum (CUSUM) strategies is considered, and it is proved that the minimum of N CUSUMs is asymptotically optimal as the mean time between false alarms increases without bound.