When using underwater autonomous vehicles, it is important to localize them. Underwater localization is very approximate. As a result, instead of a single location x, we get a set X of possible locations of a vehicle. Based on this set of possible locations, we need to find the range of possible values of the corresponding objective function f (x). For missions on the ocean floor, it is beneficial to take into account that the vehicle is in the water, i.e., that the location of this vehicle is not in a set X describing the under-floor matter. Thus, the actual set of possible locations of a vehicle is a difference set X − X. So, it is important to find the ranges of different functions over such difference sets. In this paper, we propose an effective algorithm for solving this problem.