How conservative is a sensor detection system with the scan statistic designed using the union bound?

摘要

In a sensor system to detect an emitter in a large region of interest, only a subset of sensors collects strong measurements, motivating fusion rules based on the scan statistic. Determining the false alarm probability for the scan statistic is however difficu and using simple bounds such as the union bound would presumably result in too conservative designs. This paper argues that, at typical configurations, the design obtained with the union bound is not as conservative as expected. In fact, for a large class of distributions, the resulting design becomes less and less conservative as the system size grows.