I'm writing on an Android app that tracks the distance and bearing between two GPS location (each from a different device).
Finding the mean distance and angle between the devices is quite easy, and seems to work well. But since my locations are rather close, and I really need the results to be as reliable as possible, I'm also trying calculating the uncertainty of the calculations, and here I need some help.
I'm using the accuracy parameter I get from android as my error estimation for the GPS readings (Android docs say this parameter gives a circular radius that the location has a 68% certainty to be within, so I assume the result is normally distributed, and that this parameter is the SD).
I know how to officially calculate the propagated uncertainty (using partial derivatives) if I ignore the covariance (which I have no idea if I could even theoretically find) - But this gives me a tremendous uncertainty, since both GPS readings have a very large uncertainty.
The thing is, all I'm looking for is the relative distance (or angle) between these location, and I don't care where they really are compared to earth. And since I know that at lest some of this uncertainty is the same for both devices (for instance, Ionospheric effects), I could safely ignore them and get much more precise results. Even better, if part of the uncertainty comes from random errors, I could filter most of it out even before comparing the locations (Although I suspect that that the location Android provides is already filtered).
The thing is, I don't know what part of the uncertainty is random and what part is constant, and I obviously have to deal with them separately...
So, to sum up my problem - given two sets of GPS reading, plus their 'accuracy', how can I tell apart the uncertainty that is the same for both sets, from the part the varies between them? I'm sure there is a good mathematical way to do this, I just can't think of one...