I think you might find that this is where P-RNAV (equivalent to RNP-1 but not identical) is coming in to harmonise this situation. There are numerous standards such BRNAV, FMS, BRNAV, PRNAV, RNP, BRNAV+, etc.
There will hopefully be two main high accuracy RNAV standards in the future, BRNAV (RNP5 i.e. Enroute) and then PRNAV (RNP1 i.e. Terminal). These will be probably replaced by RNP RNAV in the coming 10 years. RNP RNAV is designed to eliminate the dependency on particular sensors and concentrates on the navigational performance of the aircraft.
Hope this helps
DTG