GPS on airplanes
Most airlines allow private use of ordinary GPS units on their flights, except during landing and take-off, like all other electronic devices. Portable GPS units do not transmit radio signals like mobile phones; however there is some concern that the local oscillator, used to match the GPS frequency to the internal receiver could cause interference to communications equipment on the aircraft. This is a concern, as stray emissions from GPS units in the aircraft are electronically shielded to prevent the energy from the oscillator from leaking into the equipment. Additionally, some airline companies disallow use of hand-held receivers for security reasons, such as unwillingness to let ordinary passengers track the flight route. On the other extreme, some airlines such as Song and JetBlue integrate GPS tracking of the aircraft into their aircraft's seat-back television entertainment systems, available even during takeoff and landing to all passengers.
GPS
As the quote says, Song and jetBlue have a built in unit in their seatback TVs...AA has this too on certain aircraft, it's called the Airshow which cycles altitude, temp, time, position. This is an approved source that the FAA/FCC/AA has approved. Personal devices AA has not authorized because of the bolded text above.
I had been on several flights pre-9/11 where the pilots were testing out their personal GPS unit and found out that we were 20 miles off course, couldn't figure out why until they turned off the device.
With a very quick Google search, I found the site above. I'm not going to argue with anyone with their personal views on the GPS rules. I'm sure you won't find any actual reports either by ATC, FAA, or ANY airline stating that a GPS personal unit interefered with navigational systems, (would create a huge panic in the flying public) I never said that AA discontinued the use because of 9/11, I know pre-9/11 they were interefering with systems because it happened on a flight or two of mine.
Because of the statement to where it could interefere, I know I wouldn't risk trying to use my device...even those people who have used it in flight, you are risking interference, and my life is much too valuable to play 'tester'.