Optimal Search for a Moving Target in Discrete Time and Space with an Exponential Detection Function

Abstract

Consider search for a target which occupies one of a finite number of cells during each of a finite number of time intervals. We allocate a limited supply of search effort at each time interval to maximize the overall probability of detection. Call this an optimal search plan. Under the hypotheses stated below, a plan is optimal if and only if it cannot be improved by reallocating the search effort at any interval. The problem of optimally reallocating effort at interval i is equivalent to optimal search for a stationary target which occupies cell c with probability equal to the joint probability that the original target occupies cell c at time i and is not detected by the original search at another time interval.