I've written some software for an Air traffic Control program, which tracks a flight against its flight plan, using the radar track/plot (much the same thing as you are asking), in order to update the progress of the ATC flight plan.
The logic I applied was to identify whether the distance to the next navigatoin point was decreasing or increasing.
If decreasing, was the flight within a reasonable proximity circle (e.g. 1n.m. ) to indcate it had passed close to the point. If so, once the distance began increasing it was assumed the point had been crossed.
If the flight never reached a close proximity circle, then a check was made of the track (over the ground) and the relative bearing of the navigation point from the aircraft position. Once the relative bearing exceeded a parameter (e.g. 60 degrees) and the distance was increasing, this was taken as passing the point.
I would imaging the GPS does something similar, but with greater precision, perhaps.
(edited fro the last part of the question).
If you have passed (or been deemed to have passed) the navigation point, it is no longer the next point, so if you turn around, then you are flying AWAY from the next point - so go to point 2 above.
GB
Last edited by GroundBound; 13th Apr 2005 at 11:02.