AN ANALYSIS OF THE SEARCH AND DETECTION PROBLEM

A modification of the Koopman framework for search and detection problems is proposed to account for nonuniform probabilities of target arrival. It essentially consists in determining various physical quantities relevant to the search and detection game for any of a family of simple target paths, each one of which is assigned a given probability of having been chosen from the family. The actual value of the physical quantity of interest is then obtained by averaging over the family parameters. We developed this idea to provide probability densities of target arrival and detection environment. The mathematical structure of the problem is shown to reduce a system of iterative equations that are easily amenable to numerical as well as analytical handling. The most appealing quality of our formal structure is the capability it has to account for such realistic features of the search and detection game as partial knowledge of target track and correlations along the path of the searcher.