Designing Conservative Sensor Detection Systems With the Scan Statistic Under Emitter Location Uncertainty

When designing a sensor system to detect a target emitter in a region of interest, a fusion rule based on the scan statistic can provide improved detection performance when the emitter is uniformly distributed in the region; however, in many applications, the distribution of the emitter location is unknown. In these cases, a possible approach is to design the system considering a least favorable distribution for the emitter location. It is however difficult to find such a distribution because of the difficulty in computing the probabilities of false alarm (P
_FA
) and detection (P
_D
) of the scan statistic. To circumvent this difficulty, this paper proposes both lower and upper bounds for P
_D
, and presents a procedure to obtain a tight lower bound. With these bounds and procedure, systems that ensure a minimum P
_D
under a P
_FA
constraint can be designed.