I don't think couloimann's post is the definitive answer. Definitely interesting and true for HIS GPS, but it can very well be that different GPS' have different software implementations.
Incidentally, I am an embedded software engineer working on various GPS units. Indeed, 'normal' GPS' are extremely inaccurate in vertical position. Normal being most consumer GPS. Aviation GPS have a new feature called WAAS which improves vertical accuracy drastically. However, due to consumer GPS' vertical inaccuracy I would think most, if not all, are implemented to compute X-Y speeds only.
I am working on a small private project, implemting and proramming a circuit board with GPS, Accelerometer, and Pressure sensors. The GPS sensor I'm using has the new WAAS feauture and will by itself be much more accurate in the vertical direction. Accuracy will be further improved by error-checking the data against readings from the prsesure sensors. This should give me EXTREMELY accurate position and speed measurements in 3D space.
I'll let everyone know how it goes on my first run.
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