Older A320s that I previously flew had tripple Inertial Reference System (IRS) but the newer A321 had that plus dual GPS. The GPS automatically updated the IRS position, unlike the older system that relied on a passing DME for updating. Single DME updating was used on the very much older INS often installed in B707, B727 and probably earlier B747 and original B52 etc.
I believe the modern civil standards will be similar to the A321 system described.