An optimal distribution of searching effort relaxing the assumption of local effectiveness

In this paper, taking account of the detectability of a sensor for a target being in the neighborhood of a searching point, an optimal distribution of searching effort maximizing detection probability for a stationary target is investigated. Defining a function of extended effect of searching effort, the problem is formulated as a variational problem and theorems of the optimal distribution of searching effort are derived. By this model, the assumption of local effectiveness for searching effort in Koopman's model is removed and reality of the model is improved. A procedure for calculating the optimal (or suboptimal) solution is presented, and applying it, an optimal search plan for the datum search situation is analyzed in detail. Meaning of the conditions of the optimal solution and its properties are elucidated. Generalizations of the model, and problems to be investigated in future are also discussed.