In the Mediterranean Sea, the KM3NeT Collaboration is constructing a the deep-sea research infrastructure hosting next generation neutrino telescopes. In the KM3NeT telescopes the Cherenkov radiation induced by the secondary charged particles produced in the interaction of cosmic and atmospheric neutrinos within an effective volume between megaton and several cubic kilometers of water are detected by an array of thousands of photomultipliers. The capability of the telescope to determine the direction of secondary charged particles and to point back to the neutrino source is strongly connected to the accuracy on photomultipliers positions. In KM3NeT, the photomultiplier positions are continuously monitored by an acoustic positioning system, ...