FlightPath... I might state some things you already know, sorry!
I am curious in reading through the thread, about the RAIM requirement or indication on the ac. The pilot is required to verify RAIM prior to departure, at least at midpoint of en-route, and before approach before considering the procedure, or which procedure to use.
I am wondering what is checked or how this is accomplished?
For C129 there is a requirement for the pilot to check approach level RAIM (0.3NM) before commencing an approach. There should be an approach level RAIM prediction feature in the GPS unit itself. Under the TSO, the GPS unit will not go into the ACTV (Active) mode unless there is approach level RAIM available from the FAF to the MAP - RAIM is auto calculated at 2.0NM from the FAF. So it basically won't work if you don't have approach level RAIM at the FAF and MAP but you're still required to check approach level RAIM before commencing an approach.
If you're C145/146 you don't have a requirement to check approach level RAIM, as long as you have WAAS available at the time. If there are no WAAS NOTAMs and you currently have WAAS while in the air, you don't need to check approach level RAIM before commencing an approach.
RRR... I have used that AUGUR tool a number of times but I just noticed that it will be restricted to ECAC airspace starting 1 July 2012.
FlightPath...
The different boxes have different features with a hybridized HIL that estimates when GPS integrity falls below certain limits, creating an 'equivalent' HIL, but for short amounts of time, which differs depending on equipment.
From what I've seen, Horizontal Figure of Merit (HFOM) and Horizontal Integrity Limit (HIL) both related to the Total System Error (as calculated by RAIM - RAIM calculates Navigation System Error and Flight Technical Error; assuming that the Path Definition Error is negligible, which it generally is, the NSE and FTE add up to the TSE) for the aircraft. Garmin seems to use HFOM for the 95% requirement and from what I've seen HIL relates to the 99.999% requirement.
PDE - Desired path vs defined path
FTE - Estimated position vs defined path
NSE - True position vs estimated position
TSE - True position vs desired path
During all phases of flight, the HFOM must be equal to or less than the level required for the airspace you're flying in. If it's enroute airspace (2.0NM) then as long as the HFOM is equal to or less than 2.0NM, you will "have RAIM". If your HFOM is 1.5NM and you enter Terminal airspace (1.0NM) you will receive a RAIM alert. The GPS will still provide a position solution but you have to discontinue IFR use. But HFOM is not the same as checking approach level RAIM. HFOM is current and RAIM prediction is used for the future. Also, the RAIM prediction is for approach level RAIM so you might find that when you're enroute or in terminal airspace, if you calculated RAIM for your current position, it might say that you don't have RAIM but your GPS wouldn't alert you because you still have either enroute or terminal level RAIM.
The airspace designated as RNAV 1.0 is virtually the same as airspace designated as RNP 1.0. The difference is that for RNP airspace, the equipment must have on-board performance monitoring and alerting. The whole concept behind RAIM satisfies this RNP requirement and that's why you'll see GPS being used to help satisfy the requirements for RNP airspace. However, there are different types of RNP and certification is somewhat complicated so you can't just fly a RNP procedure because you've got approach level RAIM on your GPS. The number is the accuracy required and means that the TSE must not exceed 1.0NM in this case, 95% of the time. The containment limit is 2x the RNAV or RNP - 2.0NM in this case and the TSE must not exceed the 2.0NM limit 99.999% of the time. ICAO Doc 9613 - PBN Manual (Implementing RNAV and RNP) provides some good information on this.
There are so many requirements and they differ (especially with commercial ops) that the best way to figure this out is to read the manual for the system in question. For example, here is a manual I found online for Universal Avionics -
HORIZONTAL INTEGRITY LIMIT (HIL) for Universal FMS Training Manual
What I was also looking at was some of the rest of the posts that were talking about "PRIMARY LOST" or "GPS UNAVAIL", if the pilot was looking at the page for the explanation.
All those messages will be explained in the GPS manual for the GPS system in use.