Re: Height measurement precision
I always thought that the GPS height accuracy had more to do with the geoid model (which one you chose and how accurate it is for your local position) than absolute 3D positioning. Also, if you're using GPS to measure something on earth, you have the effects of the atmosphere to consider.
The other part to consider is that the absolute height of the satellite might not be critical, as long as the error is slow and predictable. If your measurements show that the ice cap dropped by 11cm and you also orbit over New York's Central Park and show that dropped by 11 cm, you can probably determine that your altitude has changed (I'm sure the orbital dynamics are more complicated, but you get the idea).