Questions About GPS Measurements

[Jens Noriʇzsɔɥ]

What exactly do Horizontal Accuracy and Vertical Accuracy mean / where do these values come from? 
It seems unrealistic to assume there is a guarantee that my actual position is within x meters of the measured position. My guess is the accuracy expresses an uncertainty that perhaps can be given by a distribution where, say, I can be 95% confident my actual position is within x meters of the measured position. Is that the case?

It is just 68% on Android, see https://developer.android.com/reference/...Accuracy(), I could not find similar information for iOS…

In addition, I have found  https://stackoverflow.com/questions/2846...confidence and keep it here just for my reference…

How is Distance (km) data computed? 
A simple way would be to compute the straight-line distance between two (measured) positions. However, given the uncertainty in the measurement, I think this tend to overstate the actual distance traveled in the time delta t. Is any correction applied for an expected overstatement based on the accuracy values?

We use a simple way with spherical coordinates. You could check the exact formula in https://github.com/phyphox/phyphox-exper...ps.phyphox (see phyphox file format). So, an overestimate of 5…10% would not be unexpected and I have received a report where phyphox in fact has overshot a distance in this margin.

We have briefly though about improving the algorithm, however, it is rather low priority on our list at the moment.