In order to get accurate coordinates, a GPS system should listen to at least 4 sattelites of the GPS constellation. Also, those sattelites broadcast messages that are 30 seconds long.
Since most users nowadays have some level of ADHD, a 30 seconds time to get the first fix (and a further 30 seconds more for every other fix after that) would make many project managers and device designers scream. They also want your cell phone to divine where you are even with only two or three sattelites in view - theoretically possible, but you get results with poor accuracy doing that. With three sattelites you can get an approximation, but with only two you're no better than if you were using a compass and an astrolabe.
So that's what happens: your device doesn't wait to get the whole message from the sattelites, and keeps approaching a more accurate result as more and more of the GPS message pours through. After a while, some time after the first few messages, it gets the correct fix and its stops trying to guess your coordinates.