mansfield,
The systems are set up to keep you within a certain containment area. The HIL is an estimation of the position error of where the aircraft thinks it should be. Where the aircraft thinks it should be is based on several factors, all of which have estimated error built in. As an example. it really is not a waypoint, but a waysphere. The waypoint, just in the coordinates, has a sphere, the waypoint horizontal res is 60 feet. (You can be 60 feet to the left of the coordinate, and it still thinks it is dead on) Vertical res is much different.
In addition, flyby waypoints are used and the resolution value is adjusted, well, it has to be, to get the procedure to connect, especially with S curves and inherent latency in the GPS system.
Here are some variables to consider (this is VEB, but you get some of the horizontal estimates as well such as ANPE, waypoint res, and wingspan. (note they are additive)
In regards to GPS sats, I think you will find that at least 5 are required, usually it is 7 I believe. This is so that horizontal and vertical positioning can take place, error trapping, and latency. A GPS signal is about 3 seconds long, so when you are tracking multiple sats, it takes a while for all of the signals to get there and be processed.
Per the US Govt, SPS GPS has the following accuracy
military uses PPS GPS
It is recognized that the ac knows where it was, not where it is, as the kalman filter and inertial systems estimate where the ac is.
As you can see, all of the estimated values start to add up. In short, the RNP value is a based on where the aircraft thinks it should be, but where it thinks it should be has error estimation built in as well. (ie 99.9% of being within 95%)