%0 Journal Article %T How to Efficiently Compute Ranges over a Difference Between Boxes, with Applications to Underwater Localization %+ Lab-STICC_ENSTAB_CID_PRASYS %+ University of Texas [El Paso] (UTEP ) %A Jaulin, Luc %A Ceberio, Martine %A Kosheleva, Olga %A Kreinovich, Vladik %< avec comité de lecture %@ 1752-8909 %J Journal of Uncertain Systems %I World Academic Press %V 12 %P 190 - 199 %8 2018 %D 2018 %K underwater localization %K interval uncertainty %Z Engineering Sciences [physics]/AutomaticJournal articles %X 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. %G English %2 https://ensta-bretagne.hal.science/hal-01867533/document %2 https://ensta-bretagne.hal.science/hal-01867533/file/jusVol12No3paper05.pdf %L hal-01867533 %U https://ensta-bretagne.hal.science/hal-01867533 %~ UNIV-BREST %~ INSTITUT-TELECOM %~ ENSTA-BRETAGNE %~ CNRS %~ UNIV-UBS %~ ENSTA-BRETAGNE-STIC %~ ENIB %~ LAB-STICC %~ TDS-MACS %~ INSTITUTS-TELECOM