Least and most favorable distributions for the design of randomly deployed sensor detection systems

When designing a system in which sensors are randomly deployed in a circular region to detect a signal emitter in a random location, the system designer may consider the least favorable distribution for the emitter location. The adoption of the least favorable distribution is conservative, solves the composite hypothesis issue, and makes the measurements conditionally i.i.d., as shown in our previous work. It may be argued, however, that the adoption of least favorable distributions generally leads to designs that are too conservative. In order to provide bounds for the loss in detection performance due to the least favorable distribution approach, we determine the most favorable distribution for the emitter location; then, using large sample theory, we determine how many additional sensors a design based on the least favorable distribution would require in comparison with a design based on the most favorable distribution. We also provide analytical bounds and examples.