GPS can only tell you how fast you're moving over the ground. It can't tell you how fast you're moving through an airmass that might be moving with or against you, this is far more important to keeping a plane in the air than how fast you're moving between point a and point b.
I wonder if GPS could be used to estimate the air speed by means of a permanently refining mathematical model? E.g. If I know I have heading X, ground speed Y, weight Z, thrust A, you should be able to work out your predicted ground speed. Any variation in real ground speed and estimated ground speed is got to me made up of wind direction and velocity right??? Just a thought.
(Disclaimer: I know nothing about aerodynamics so this may be nonsense)