Originally Posted by SiempreTuna
Given that civilian GPS is specified as being accurate "to 7.8 meters at a 95% confidence
", getting to within a couple of metres is rather better than you could realistically expect.
You are quite right that it is better than you could expect (although the link you posted, which was interesting, says that this is "worst case") and I certainly wouldn't claim that it will always be this accurate but I have checked several times when I have been in my bedroom and I can clearly see on the satellite view on Google Maps whether I am on my bed or at my desk and they are only 2-3m apart. I am now sitting by my sitting room window and it says I am in my front garden but it's still less than 3m out although it is wandering around slightly but only by about 2m.
All in all, I think it's pretty impressive that something as small as an S4 can be as accurate as it is. It's a shame the compass isn't as good - I have found that to be wildly inaccurate.