Discrete search with multiple sensors

Abstract

A stationary object is hidden in location i , i =1,2,..., K , with probability p i . There are M sensors available and each location can be searched by at most one sensor at each instant of time. Each search of a location takes one unit of time and is conducted independently of previous searches, so that a search of location i finds the object, if it is in that location, with probability α i . After each search of a location a sensor may either continue to search the same location or switch without any delay to another location. We determine optimal search strategies that maximize the total probability of successful search in N units of time, discuss an implementation of an optimal search strategy, and specify conditions under which the solution can be obtained by a forward induction argument. Finally, we discuss the relationship to multi-armed bandits with multiple plays.