FAA has published an update to the AIM, effective 26 May 2016, and it includes a big change if you have an IFR-approved GPS [i.e., a “suitable navigation system” as defined in AC 20-138 and AIM 1-2-3 (b).]
Now, if you fly a conventional approach based on a VOR or NDB (but not a localizer), you can fly the procedure entirely with the GPS, provided you can monitor (using a separate CDI or a bearing pointer) the VOR or NDB facility specified for the approach.
The new language is in section 1?2?3. Use of Suitable Area Navigation (RNAV) Systems on Conventional Procedures and Routes.
The summary of changes to this AIM update notes that:
This change allows for the use of a suitable RNAV system as a means to navigate on the final approach segment of an instrument approach procedure (IAP) based on a VOR, TACAN, or NDB signal. The underlying NAVAID must be operational and monitored for the final segment course alignment.
The new text in the AIM is in paragraph 5 of AIM 1-2-3:
5. Use of a suitable RNAV system as a means to navigate on the final approach segment of an instrument approach procedure based on a VOR, TACAN or NDB signal, is allowable. The underlying NAVAID must be operational and the NAVAID monitored for final segment course alignment.