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This paper addresses localization of autonomous underwater vehicles (AUVs) from acoustic time-of-flight measurements received by a field of surface floating buoys. It is assumed that measurements are corrupted by unknown-but-bounded errors, with known bounds. The localization problem is tackled in a set-membership framework and an algorithm is presented, which produces as output the set of admissible AUV positions in a three-dimensional (3-D) space. The algorithm is tailored for a shallow water situation (water depth less than 500 m), and accounts for realistic variations of the sound speed profile in sea water. The approach is validated by simulations in which uncertainty models have been obtained from field data at sea. Localization performance of the algorithm are shown comparable with those previously reported in the literature by other approaches who assume knowledge of the statistics of measurement uncertainties. Moreover, guaranteed uncertainty regions associated to nominal position estimates are provided. The proposed algorithms can be used as a viable alternative to more traditional approaches in realistic at-sea conditions.