For once, the airbus system seems to operate fairly similarly, at least in terms of IRS.
Each of the two Flight Managemant and Guidence Computers, which are normally synchronised, computes its own position from a mean weighted average of the three IRS positions, called Mix IRS and a computed radio or GPS position. If one IRS drifts abnormally, an algorithm that decreases the influence of the drifting IRS within the Mix position is used.
The overall system, FMGS (which looks after the FMGCs) selects the most accurate of these, taking into account the estimated accuracy and integrity of each positioning equipment.
Each IRS also computes an hybrid position that is a mix IRS/GPS position called GPIRS. Each FMGC receives these three hybrid positions and one is selected according to figure of merit and a priority system.
If the GPIRS data does not comply with an integrity criteria, the GPS mode is rejected and radio position updating is used, as described in earlier posts.
Each FMGC computes a vector from its Mix IRS position to the radio or GPIRS position called a bias. Each FMGC continuously updates its bias, if a radio or GPIRS postion is available. If an FMGC loses its radio/GPIRS position, it memorises the bias and uses it to compute an FM position, which equals the Mix IRS position plus the bias. The FM position is also updated on departure to the runway threshold position. The priority for updating FM position in flight is given to GPIRS, then to IRS-DME/DME, then IRS-VOR/DME, then IRS only.
For simplicity, the crew's primary check on Navigation is an accuracy level display on one of the screens, either HIGH or LOW, depending on whether the FMGS calculated Estimated Position Error is less than or greater than the Required Navigation Performance for the flight phase. Most of the time, GPS PRIMARY is displayed as the main Nav mode, with NAV ACCURACY HIGH.
IRS drift rates on my machine (A330) tend to be around 0.2 nm/h over an 8 hour flight.
Hope this helps answer the question!