Wow, now I have a headache this early on this one!
but here goes,
RAIM is built into the GPS system on the aircraft, and is part of what is balancing all the the different sat connections and detecting faults the pseudorange measurements.
When you look at RAIM predictions,they are configured with 3 modes, Fault Detection, FD(5 sats req'd), Fault detection and exclusion, FDE (6 sats req'd), and if Selective Avail, SA is turned on.
For 3D navigation, you need a min of 4 sats, but will have no RAIM fault detection.
The RAIM function that you will see in the box is represented with the HIL number. Depending on your box, and RNP level set, the box will alarm when the HIL number reaches a certain threshold, the HAL, telling you that you horizontal integrity is getting near the limit Horizontal Alarm Limit of the RNP level.
The HIL, HAL, and HPL numbers are some voodo combination of the secret sauce inside each box, and given the potential combinations of algorithms and factors, I have no idea how alarm limits are decided.
As an example, during flight validation testing, with the Smiths box, RNP level 0.3, I had the box alarm at HIL of .51 in a 737, while in a 320,with a Honeywell box on RNP 0.1 it alarmed at .67....
Hope that helps!
RAIM prediction tools