On the use of least favorable distributions to facilitate the design of randomly deployed sensor detection systems

Sensor detection systems with a fusion center are being considered to detect a low-power signal emitter in an unknown location within a region of interest. For example, multiple radiation sensors can be distributed in a region to detect the presence of an unauthorized radioactive material. When designing such a system, the designer faces the problem that the measurements are conditionally dependent in general. Designs for conditionally dependent measurements are significantly more difficult to achieve than designs for conditionally independent measurements. Furthermore, the distribution of measurements depends on variables with unknown distributions, such as the emitter location, which means that the alternative hypothesis is composite. Although it is possible to use the theory of least favorable distributions to deal with a composite hypothesis, many of the results in this theory require conditionally independent measurements. If the designer assumes that measurements are conditionally independent, then any performance analysis may be invalid because such an assumption is generally considered unrealistic and only justified by convenience.;How can the designer deal with the difficulties associated with conditionally dependent measurements and the composite hypothesis? It is shown in this dissertation that there are conditions that allow a designer to deal with these problems by assuming a least favorable distribution for the emitter location that not only makes the hypothesis simple and ensures detection performance, but also causes the measurements to become conditionally independent and identically distributed. It is shown that under certain conditions, any distribution that places the emitter on a subset of the boundary of the region of interest with probability one is least favorable for various systems of interest. This result may be considered intuitive; however, it does not hold in general.;Since a design based on a least favorable distribution may be considered too conservative, this dissertation proposes the use of a most favorable distribution for the emitter location and uses the theory of asymptotic relative efficiency (ARE) to evaluate how conservative the design based on a least favorable distribution is. The ARE theory is further used to, under a least favorable distribution, compare different systems and different sensor deployment strategies.