In regards to GPS location, keep in mind that GPS lets the aircraft know where it was, not where it is.
The estimate of the current location of the aircraft is from the Kalman filter.
As noted, the minimum requirement for GPS system update is 2 seconds, and the typical GPS system on a commercial aircraft is about 0.6 seconds.
What this means is the location of the aircraft can be 2 seconds off, which at 500 kts, is a good bit.
The Kalman filter is the predictive part of the GPS system, which indicates to the FMS where the aircraft is.
Final approach maneuvers, such as turns on final, are difficult to predict, hence the reported position accuracy will go down...