I've looked at this recently and just created a hn account to respond. GPS satellites broadcast their position by transmitting ephemeris parameters. You can compare the accuracy of these parameters with post-processed, high accuracy orbits from igs.org. For the last few months, the real-time ephemeris has had an RMS error of about 0.5 meters (95 percentile is about 1.3 meters). (This is the range error, which includes both satellite position error and satellite clock error)
Of course, these errors cancel out if you're doing differential GPS techniques. (Where all that matters is accuracy relative to the base station)
One thing that would be nice is to access IGS's real-time streaming orbit data over the internet and have the phone's GNSS chipset use that instead of the broadcast ephemeris. However, you might still want dGPS for single frequency receivers to help with ionospheric error.
Of course, these errors cancel out if you're doing differential GPS techniques. (Where all that matters is accuracy relative to the base station)
One thing that would be nice is to access IGS's real-time streaming orbit data over the internet and have the phone's GNSS chipset use that instead of the broadcast ephemeris. However, you might still want dGPS for single frequency receivers to help with ionospheric error.