Optimal Search with Uncertain Sweep Width

This paper considers file problem of optimal search for a stationary target when the detection capability of the search sensor, as characterized by its sweep width, is fixed but not known in advance. Most of the results are confined to the assumption of a gamma prior sweep-width distribution and to the cases of normal and uniform prior target-location distributions. Explicit formulas are obtained for the optimal search plans, the probability of detection versus time, the expected time to detection, and the posterior marginal distributions for target location and sweep width. In the case of a normal prior target-location distribution, expected time to detection is compared for the optimal plan and search plans based on the assumption of a known value for sweep width; this includes a sensitivity analysis treating actual sweep width as a parameter. For a target of value, the search plan that maximizes expected net return is determined. This plan requires specification of a rule for terminating an unsuccessful search. Explicit results are given assuming a nonincreasing target value and a nondecreasing search-cost rate.