Analysis of randomly deployed sensor detection systems under least favorable distributions

Consider the design of a system in which multiple sensors are randomly deployed in a circular region to detect the presence of a signal emitter in a random location. If the distribution of the emitter location is unknown, the design is difficult because the detection problem involves a composite hypothesis and the sensor measurements may be conditionally dependent. In this paper, we show that using the least favorable distribution for the emitter location not only is a robust design approach that solves the composite hypothesis issue, but also helps in dealing with the conditional dependency issue. We show that there are conditions under which the least favorable distribution for the emitter location causes the sensor measurements to become conditionally i.i.d. when using either the maximin or other practical fusion functions. Motivated by the form of the least favorable distribution, we also explore an alternative random sensor deployment strategy.