Accuracy and precision are words that do not mean the same thing. The fact that your GPS will report altitude to 10 cm (0.1m) does not mean that it is correct. It just means that a number was calculated and truncated to the nearest 0.1.
In fact, your commercial GPS is unable to give measurements of your true altitude any closer than perhaps +- 20 meters. Although horizontal positions can be within +- 6m of truth, the vertical (altitude) position is often an order of magnitude worst. This is due to the geometry of the satelites. You can sometimes get good results if you have a satelite directly overhead.
I have had an antenna mounted to a roof for the last five years. The connected GPS has reported altitudes between -50 meters to +350 meters over this time period, but its horizontal position has always been within a 20 meter radius.
Them be the physics.
(As in the other thread you started, radar or lidar altimeters is the way you need to go if you want altitudes that match reality).
