As I'm studying, I found that GPS has to have 5 satellites or 4 satellites with "blind encoders" to use RAIM.
What is a blind encoder and what is its purpose?
A blind encoder is an altimeter that encodes pressure altitude and outputs it on a databus. They are "blind" in that they do not display data to the pilot. Most general aviation units use a parallel bus with Gillham encoding. More expensive units and air data computers use serial bus output, commonly ARINC 429.
Historically, the blind encoder existed to provide pressure altitude data to the transponder to enable Mode C reporting.
When it was proposed to use GPS as a primary means of navigation in the early 1990's, the FAA deemed that a means of ensuring the integrity of the signal was essential. The longer term solution was to establish WAAS which provided both augmentation and an integrity channel. The short term solution was to have the receivers include an internal monitor, which took on the name RAIM for Receiver Autonomous Integrity Monitor.
RAIM algorithms have evolved several times over the years. Since early GPS receivers were often single or 3 channel receivers, the use of altitude as a substitute for an additional satellite was common. (Altitude is just another range in the rho-rho computation.)
Later GPS receivers moved to 6 and 12 channel receivers, thus enabling RAIM algorithms that don't need altitude data except in extreme cases.
So yes, the number of satellites needed for a RAIM calculation can be reduced by one when pressure altitude is available from a blind encoder.
Receiver autonomous integrity monitoring Receiver autonomous integrity monitoring (RAIM) is a technology developed to assess the integrity of global positioning system (GPS) signals in a GPS receiver system. It is of special importance in safety-critical GPS applications, such as in aviation or marine navigation
Check out the GPS article in this FAA newsletter to start with: http://www.faa.gov/news/safety_briefing/2010/media/JanFeb2010.pdf
RAIM prediction is what is of primary concern for Non-WAAS equipped GPSs. If you are WAAS equipped then you are good to go without doing prediction.