Apparatus and methods of monitoring mooring lines of an offshore drilling rig, with the apparatus including a communication system in communication with a global positioning system, providing position coordinates of the apparatus at a first point on the line, and also includes an inertial navigation system supported by the frame, providing position coordinates of the apparatus at a second point on the line, by double integration with respect to time of inertial accelerations measured by the device as it is moved from the first point to the second point. Correction at the second point is provided by obtaining at the second point, depth, position relative to magnetic north, and deviation from vertical.