How much is it genuine noise, and how much is it the fact that you're trying to measure a fractal? It's like the coastline measurement problem, just in the z dimension - there is no right answer, any answer between the net gain of c. 6.2k ft, and infinity (which may explain why it feels further in descent!) are possible answers depending on the resolution chosen. The more accurate the underlying map, the greater the elevation change that will be recorded.
A perfectly accurate, infinite resolution altimeter would record an apparently "noisy" signal as it measured the up and down movement of the hiker it was attached to.
