That connector is a BNC connector, and is pretty standard to GPS antennas. If you have a few days for
delivery you can probably find a GPS antenna with 3m cable and BNC connector online for $10 or less. Connect that to your GPS and run the cable out a
hatch or port. If it all works then you can start
tracking things back and get a proper
marine antenna/connection.
If you just want to replace the connector on your existing cable then search for a BNC connector, you can probably get one for a couple of bucks at Digi-Key or Mouser (or
Radio Shack if any are still open).