The AIM contains the information required to operate under IFR using GPS1.
To summarize the requirements, WAAS (but not "traditional" GPS) may be used stand-alone without an alternate means of navigation provided:
- Installation requirements:
- The WAAS navigation equipment is approved in accordance with TSOC145 or TSOC146
- The installation is done in accordance with AC 20-138
- Operational Requirements:
- The WAAS AFM procedures are followed
- It is not be used by a commercial operator
- Preflight Requirements:
- The GPS database is current
- The GPS database provider does not have any notices prohibiting the use of any fix or procedure that you are going to use
- GPS NOTAMs/Aeronautical Information is reviewed prior to each flight
- A RAIM prediction for the time and route is done that shows no loss of RAIM
- The flight plan navigation equipment is listed as RNAV
Note that commercial operators are required to have redundant systems or ground based backups in order to use it, and while not required for you, it's a pretty good idea.
1 More specifically, see:
AIM Chapter 1, Section 1 - Navigation Aids
- 1-1-18. Global Positioning System (GPS)
- d. General Requirements
- e. Use of GPS for IFR Oceanic, Domestic En Route, Terminal Area, and Approach
Operations
- f. General Database Requirements
- 1-1-19. Wide Area Augmentation System (WAAS)