Several GPS applications, like this one, or this one, acquire multiple (lat,lon) samples of a given location, assuming that the GPS unit is not moving, and then take an average of the samples in order to compute a "more precise" 2D location.
(We do not care about the elevation/altitude position here!)
The second app (GPS Averaging) uses the accuracy value associated to each sample as a weight for the current location, and then calculates the weighted average accordingly. It also provides an estimate of the accuracy of the averaged location.
1) While common sense pushes us to believe that averaging should lead to increased accuracy, how much sense does it make for handheld units like phones (i.e. simple devices that do not use differential GPS)?
2) Would you recommend another method than GPS Averaging's method to compute the average location?
3) How to compute an estimate of the accuracy of the averaged location?
4) Is there a way different than averaging to get a better 2D positioning by acquiring multiple (lat,lon) samples of a given location?
UPDATE 1: results of my preliminary study with 2 handheld GPS units (Sony phone models ST15i and ST17i) acquiring 3m accuracy fixes at the same position during 4.5 hours gave the following data:
=> It is quite interesting to note that even though the supposed accuracy of the fixes was 3 meters, the ST17i model had lots of points further than 3 meters from the median/average.
=> Also remarkable is the monotone drift of the longitude on the ST15i model.
(Note that the ST15i seems to have a more sensitive antenna than the ST17i as I could analyse it used on average 3 more satellites for its fixes than the ST15i!)
UPDATE 2: some further stats and numbers, still from the same datasets
=> The data is definitely not normal
=> I also computed the distance between the median location of the ST15i and the median location of the ST17i: it is 3 meters, as if the study was playing with us, since all fixes used had an accuracy of 3 meters or better. This definitely validates the suggestion below of using a known reference in order to derive meaningful conclusions about the accuracy of each GPS unit!