Let's bring another factor into it.
GNSS procedures require the navigation computer to use the GPS inputs provided [as such there will not be a requirement to enter a potentially incorrect QNH resulting in blunder error].
NOTE: not all in-service aircraft (like the 737) have this capability, thus are restricted to BARO-VNAV which requires higher minimums and are not authorised to fly GNSS approaches, only LNAV/VNAV using the Baro VNAV technique.
With a GPS's as part of the aircraft's navigation computers, the aircraft then requires the ANP<
RNP to be within limits, the RNP being default coded by set parameters by its provider iaw minimums set by authorities depending on phase of flight (cruise, approach, final approach, etc). More detailed requirements for this capability can be found in various websites, they include but are not limited to things like 'no single failure may..." statements, basically requring dual FMS, autopilot, etc before it can be used.
The theory is extensive and very much airframe specific whether or not it can be applied to an operation.