GPS altitude tracking tends to lag severely, and with the rate of change we go through, it would be less than ideal.
some sort of inertial/accelerometer based system would be far better, but that would pose it's own issues since we are working around a hemisphere rather than an "open space" condition.
we use inertial, GPS, and barometric tracking in model rockets to track everything from flight events, x/y/z position, velocity, etc.... they work pretty good. but, all three sets of data must be combined and filtered to get the "best" reading. we are also working in a (hopefully) linear fashion on the way up, and a very gentle descent with some drift due to wind.
I don't think barometric would be ideal in our case, as there isn't much pressure difference between ground level and 60', and there are other challenges associated with that as a result of the plane passing through the air, propellers throwing air all over the place, flaps and elevators causing all sorts of pressure changes in addition to the speed changes, it all turns in to a pretty crazy circle. the same happens with rockets as well, but it only gets really bad in the transonic realm, and it's easier to filter the data (going back to the linear thing and all of the real crazy thrust stuff is coming out of the back).