I fly the 747-400 that is equipped with 2 GPS receivers and 3 INS units. All are tied into the FMS computer, and the FMS computes the track the airplane should follow.
In normal circumstances, the GPS position is used for primary navigation. The FMS keeps a second position as a backup, called the "IRS(3)" position, because it combines and weighs the position from each IRS (Inertial Reference System, sometimes called IMU or Inertial Measurement Unit), then updates it with DME, LOC, and/or VOR data when available. Note that the INS systems themselves are not updated -- the updating is within the FMS only. Also, GPS is not used for IRS(3) updating, to preclude excessive errors if both GPS systems go bad.
The IRS(3) position, as well as the position of each GPS and INS, can be read out from the FMS display when desired, and the individual plots can be put in the Nav Display.
GPS is the most accurate, and the Actual Navigation Precision (ANP) typically varies between 0.05 and 0.07 NM (300 and 420') -- less than 2 wingspans. Individual INS positions may be off as much as 3 or 4 miles after a 12-14 hour flight across the Pacific, and typically the errors run in the 0.1 to 0.3 NM per hour range (1 to 3 NM total). The FMS IRS(3) position is within about 0.2 NM when DME updating is available, and varies out to maybe half of the greatest individual IRS error enroute when the updates are stale.