It's definitely not alternator noise. (too constant and occurs when the engine is off.)
Try to run without the GPS attached to see if that helps. (In theory, the GPS wire could act as an antenna to pick up electromagnetic interference.)
As already suggested, run it outside (and away from) the car. (Try this both with and without the GPS attached.)
If the issue doesn't occur outside the vehicle regardless of GPS, inspect the ground contacts on your car battery. In most vehicles, the battery, alternator and chassis are all connected to form "ground." If any of those connections are bad, it can cause "hum" (or hissing) in electronics.
If the issue doesn't occur in the car with the GPS disconnected, try adding or removing the little extension cable supplied with the camera kit to the GPS wire. (The idea is to change the length of the wire.) That wouldn't REMOVE the noise, but if it CHANGES the noise, then you know something is going on with the GPS wire acting as an antenna.
If the GPS is picking up noise, there are two Bad Things happening. The first is that the GPS wire is picking up noise. The second is that the EMI exists to begin with. (Which, ironically, can exist also because of bad grounding. Troubleshooting that, however, can be a royal PITA.)