Surveillance Search for a Moving Target

The surveillance search problem is a generalization of the detection search problem studied by Brown and Stone, among others. In the surveillance version of the problem, the search terminates only if the time and location of a detection satisfy certain problem specific conditions; the objective is to maximize the expected value of a payoff received during and at the end of the search. For instance, we may wish to maximize the probability of finding the target in a specified subset of the state space or at a specified time. Consequently, we might detect the target several times before the search terminates. A search strategy, i.e., an allocation of the available search effort, must account for this possibility. In this paper, we formulate the surveillance search problem for applications in which the target moves according to a (not necessarily time-homogeneous) Markov process. We then derive a set of necessary conditions for the optimality of a search strategy, and develop algorithms, based on the algorithm of Brown for the detection search problem, to find strategies that satisfy these necessary conditions for problems in which the search effort is infinitely divisible.