Numerical solution:

The field in the shadow is very difficult and critical to calculate.
The ratio or the superposition between the direct signal and the multipath signal is even more difficult to determine.
Standard numerical methods are not really applicable in general (PO, GTD/UTD, ...).
GTD/UTD can handle only the idealized single wedge case.
The real humps cannot approximated sufficiently by a single hump in most cases.
NAVCOM Consult has introduced the adapted and optimized application of the "parabolic equation PE"
(cooperative project with the University of Stuttgart).
PE can solve in principle the wave propagation over ground of general shape and materials.
Restrictions apply also for the implementation of the PE.
PE solves the majority of the hump-site problems

Results:

A comparison of measured and numerically calculated fields 4m above the runway centerline (CATIII situation) shows
an excellent agreement (see Fig. 1 here) for the extreme modified hump at Luxemburg airport.
The integration of the verified method into a 3D-ILS-system simulation of DDM-distortions has been concluded
by NAVCOM Consult.
The method has been applied for the determination of Localizer pedestals.
Reliable numerical simulation and performance predictions are possible now for the hump-installations,
i.e. new installations, upgrading cases from CATI to CATII/II.

The referred optimized method is applicable after some minor systematic modifications for other navaids systems,
e.g. MLS, DME/TACAN, VOR/DVOR, GPS