Optimal search and detection of clustered hidden targets under imperfect inspections

We formulate and solve a discrete-time search-optimization problem where a single searcher or several searchers (for example, unmanned aerial vehicles UAVs or robots) operate and move in a discretized 3-dimensional airspace, looking for static or moving targets in a finite set of locations. Prior probabilities of target location are known for each target, and each searcher (UAV) has to sequentially inspect the locations. The inspections are imperfect: a probability of overlooking the target (that is, a false-negative outcome) and a probability of a "false alarm" (that is, a false-positive outcome) exist. The objective is to find the targets as effectively as possible within a given level of confidence. Common measure of effectiveness for the search/detection process are: the expected time of the search; the expected cost of the search; the expected losses; and the expected averted risk. An effective index-based search algorithm is developed. An example for an automatic device (UAV or robot) searching for a target moving along a highway is discussed.