An optimal two-stages search plan for a random walk target motion in the plane

This paper addresses the problem of searching for a moving target in the plane by a single autonomous sensor platform unmanned air vehicle (UAV). This sensor consists of a search team from two-searchers. The target moves in the plane with autocollimator linear motion (one-dimensional random walk) either for x-axis or y-axis. The search consists of two stages, the broad search and investigating search. In a broad search the sensor wishes to find the target's initial position, which is given by the value of the two independent random variables (X, Y ) and they have joint symmetric probability density function f(x, y). In an investigation search stage, the search team will be unmanned to detect the target on one of two real lines intersected at the target's initial position. It is desired to search in an optimal manner in each stage to minimise the expected value of the first meeting time between one of the searchers and the target, assuming circular normal distributed estimates of its initial position.