Efficient Employment of Non-Reactive Sensors

We consider two types of non-reactive aerial sensors, which are subject to false-positive and false-negative errors. The sensors search for threat objects such as ballistic missile launchers or improvised explosive devices. The objects are located in a certain area of interest, which is divided into a grid of area-cells. The grid is defined such that each area-cell may contain at most one object. The objective of a sensor is to determine if a certain area-cell is likely or unlikely to contain an object. An area-cell is said to be determined if the searcher can ascertain with a given high probability these events. Since definitive identification of a threat object, and subsequent handling of that threat, are done by limited number of available ground combat units, the determination of an area-cell can help field commanders better allocate and direct these scarce resources. We develop two models, one for each type of sensor, that describe the search process and maximize the expected number of determined area-cells.