The sub uses GPS for positioning on and near the surface. The rest of the way it's using inertial navigation.
USL@NOC is also working on multibeam sonar so that the robot can assess its position using geologic features on the bottom (up to about 200m away I expect) for position keeping in a current.
I'm not sure why they'd use a multi-beam for station keeping when they already have an ADCP (Acoustic Doppler Current Profiler) on board. The particular ADCP they're using here was made by a company I used to work for (in fact, I wrote a lot of the firmware in that sucker) and is accurate to within a few tenths of a percent and can track the bottom out to 200m.
Work without a vision is slavery, Vision without work is a pipe dream, But vision with work is the hope of the world.