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.
Yeah, like I mentioned above, you can analyze gpx files yourself very easily. The fractal concept is fun to think about (I've had the same thought myself) but with typical GPS receivers (dunno about super high-end ones) the noise is really just noise.
Below is data from a ~4 mile hike in the Angeles National Forest that I manually extracted the numbers from the .gpx, loaded into a spreadsheet, and then ran two filtering passes on.
It's only when you get to the third image that the total accumulated elevation gain and loss matches expected numbers. The raw elevation gain/loss in the first image is 2x higher thanks to all the noise. i.e. if you sum up the delta between every sample it says I climbed ~4000 feet instead of what should be closer to 2000.
Intuitively speaking, the third picture feels the most accurate to what it was like to walk the trail. There was a little bit of noisy up and down but not nearly as much as in the second pic.
