Abstract: The invention concerns acoustic under-water measurement apparatus for determining the location with respect to a surface vessel of objects such as submersible vessels, pipe-riders, mining apparatus, or the like, including tethered submersible vessels. A receiver hydrophone set located on the tethered vehicle receives acoustic reply pulses from sea bottom transponders, telemetering the times of reception to a surface support ship via conductors in the tether cable. Signals obtained at the surface ship directly from the transponders and indirectly via the tether cable conductors are combined aboard the surface ship for computing the positions of both vessels with respect to a base line established by the sea bottom transponders. The system is self-calibrating, so that an expensive survey to determine the actual locations of the bottom transponders is no longer required.