This concerns post-processing via base station correction in Pathfinder Office. I understand the base station is a known location and the GPS receiver's location is corrected relative to the base. I'm trying to better understand how the post-processing process works. Does the correction application use the base station's location data to do a bias correction of the uncorrected data or does it redo the trilateration somehow?
Pathfinder Office (or other post-processing software) knows the position of the base station, Almanac and Emphemeris (downloaded from Internet) allow PFO to work out the position of each of the satellites every second, and the base data provides pseudo-range (code) measurements) and Carrier measurements. From the base location and satellite positions, PFO can work out theoretical pseudo-range and carrier measurements (what should be measured per epoch per satellite at the base station), and PFO subtracts these theoretical values from the actual base data measured pseudo-range and carrier measurement values. This gives pseudo-range and carrier correction values for each satellite for each epoch. These correction values are added to the GPS Receiver pseudo-ranges or carrier values for the various satellites to give corrected values. And the corrected pseudo-ranges or carrier values are then used to calculate the corrected position of the GPS receiver using trilateration or whatever method (same techniques as a GPS receiver uses but with corrected pseudo-range and / or carrier values).
This explanation is simplified - since base data is usually only supplied every 15 or 30 seconds, there's some extrapolation but the corrections don't change very fast.