Least favorable distributions to facilitate the design of detection systems with sensors at deterministic locations

The design of a sensor detection system to detect an emitter at a random location is difficult because of two issues: the conditional dependence among sensors´ measurements and the composite hypothesis caused by the lack of knowledge regarding the emitter location distribution. When sensor locations are also random, it was recently shown that it is possible to circumvent these issues by using a least favorable distribution for the emitter location; however, such results do not apply when sensors are at deterministic known locations. In this paper, it is shown that a least favorable distribution for the emitter location can also facilitate the design of sensor detection systems when sensors are at deterministic known locations. It is further shown that, in several cases of interest, the problem of finding a least favorable distribution for the emitter location is equivalent to the obnoxious facility location problem from the field of operations research; and it is shown how the techniques of this field can be used to find the least favorable distribution and facilitate the system design.