As has been said before, GPS cannot give you airspeed - it gives you ground speed. It's airspeed that makes aeroplanes fly.
KISS - there can be nothing more basic and therefore reliable for measuring airspeed than an air pressure monitor sticking out into the air itself (pitot tube). The only thing that could affect this would be to obstruct the air to it. Apart from a physical object (bird?) which would possibly only effect one pitot then ice seems to be the only other thing that can cause obstruction.
As a pilot of smaller aircraft, I cannot believe that in this day and age it is beyond the wit of engineers to be able to eliminate any chance of ice build up on a pitot head of a large aircraft and for there to be a doubt about a pitot being able to resist ice (as seems to be the case) seems unbelievable considering the importance of the information from this item.