That's post-processing, and it's still done. Here's why: The satellites only know their own position to a certain precision, and there are only so many bits to

That's post-processing, and it's still done. Here's why: The satellites only know their own position to a certain precision, and there are only so many bits to express it in the data packet. More bits wouldn't make sense because the measurements aren't that good in the first place. So what you get "live" is naturally limited by both of those things. Single-frequency unassisted solutions are usually good to a few meters, dual-frequency to a meter or so. But ground stations can determine, after observing the satellites for a long time, where they _were_ to a much higher accuracy. It's a complicated process involving a whole network of ground stations, whose own positions are precisely surveyed, etc. The product of that network is known as "precise ephemeris", and it's available in an "ultra-rapid" (3-9 hours later), "rapid" (24 hours later), and "final" (13 days later) version. With these data, the initial observation can be post-processed to get very good solutions. Down into the millimeters. The RTKLIB manual has a lot more detail if you're curious.