Dead reckoning plotters have been around for a long time. You input course, revolutions, etc. from the log and gyro compass, and the plotter moves a lighted "bug" under the top of a glass plot table. You need to start at a known position, and they weren't accurate enough for precise navigation, but they helped. For confirmation, you had to surface and take celestial sights, or Loran (or equivalent) fixes, after which you would reset the plotter.

Inertial navigation systems were developed for nuclear boats. Much simplified, you take the basic idea of the old dead reckoning plotter, but with far more accurate inputs from accelerometers and other equipment. Since nukes rarely surfaced the system had to be a lot more accurate. And one of the major factors behind the development of GPS was to provide a quick, highly accurate way of obtaining a precise position fix for missile boats in the event they should fail in their mission and actually have to launch.

Most WWII era boats really didn't get deep enough to worry too much about running into anything except in coastal areas, or in shallow seas. There are things you can run into in the central Atlantic, but most of them are deeper than you'd want to be for safety reason.

J.T. McDaniel