Detection and track of a stochastic target using multiple measurements

The authors are interested in search and tracking problems. In a search, the target might be located among a number of hiding places. Multiple measurements from various locations might be used to determine the likelihood that a particular hiding place is occupied. An obvious example would be a search for a weak radiation source in a building. Search teams might make many measurements with radiation detectors and analyze this data to determine likely areas for further searching. In this paper the authors present a statistical interpretation of the implications of measurements made on a stochastic system, one which makes random state transitions with known average rates. Knowledge of the system is represented as a statistical ensemble of instances which accord with measurements and prior information. The evolution of ratios of populations in this ensemble due to measurements and stochastic transitions may be calculated efficiently. Applied to target detection and tracking, this approach allows a rigorous definition of probability of detection and probability of false alarm and reveals a computationally useful functional relationship between the two. An example of a linear array of simple counters is considered in detail. For it, accurate analytic approximations are developed for detection and tracking statistics as functions of system parameters. A single measure of effectiveness for individual sensors is found which is a major determinant of system performance and which would be useful for initial sensor design