OK, back to the thread! In the late '80s we flew a trial on the auto ILS mode (APP) in the Tornado GR1. There were two problems: First, the gains for the drive laws varied as a function of the rad alt signal and, as has been mentioned previously, the early rad alts locked up to the nose leg when the landing gear was down. This then resulted in the wrong gains being used by the autopilot and erratic localiser following. However, later standards of rad alt solved that problem so this was not insurmountable.
However, the bigger problem was that the system used the selected course (set on the HSI) and heading, rather than track, to maintain the localiser. Basically, when the aircraft was on the localiser the AFDS turned the aircraft to match the heading with the set course. Therefore, if there was a crosswind the aircraft flew inbound displaced downwind from the localiser. We recommended having a crosswind limit for coupled approaches (and I think that about 20 kts would have been feasible) to limit lateral displacement such that a sidestep could be flown from Decision Height and a landing could be made. However, 'the Company' solution was to adjust the course setting by a factor of the drift angle (can't remember exactly what the factor was but 1/2 comes to mind). The scope for getting it wrong was monstrous so we would not endorse this but we could not get support for the crosswind limit option. However, without any significant crosswind it worked quite well.
The F3 had the same system as the GR1 and the GR4 does also. I have tried it in the GR4 sim and it usually ends up with a divergent oscillation down the localiser but in fairness it is not cleared in the aircraft so the drive laws in the sim were never required to be refined.