Exactly what kind of radios are prohibited for passengers inside an aircraft?
There is actually a simple answer, but it probably isn't exactly what you are looking for:  Refer all questions about what is allowed to your specific airline.  

Each airline has to come up with their own list of allowable electronic devices, and submit that list to the FAA with appropriate documentation in order to gain approval to allow passengers to use them during flight.  

Some airlines allow almost everything as long as it can be put into a non transmitting mode (airplane mode), while some still require ALL electronic devices to be completely powered down at all points during the flight.

Because of this, every airline is a little different and you are required to follow their rules while on their flights.

The GPS receiver would not cause problems, but this doesn't mean that you are necessarily allowed to use it, and there are other things in your phone that could cause a problem though.

In general, no electronic device that has a transmit function may be used because of possible interference though, unless specifically approved.