How to Efficiently Compute Ranges Over a Difference Between Boxes, With Applications to Underwater Localization

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. c ⃝2018 World Academic Press, UK. All rights reserved.