The objective of this paper was to determine if recent advances in
numerical electromagnetic wave propagation modelling techniques could
be used to study the propagation of GPS signals over arbitrary terrain.
Specifically the effects of diffraction and multipath were to be modelled
accurately for propagation over arbitrary terrain surfaces defined by a
digital terrain model. Ideally the model was to be in three dimensions and
cover an area of a few square kilometres with a simulation height of a few
hundred metres. Simulations were to run on current technology PC's with
run times less than a few hours. A relatively new technique that involves a numerical solution to the
Parabolic Equations can be used to solve for two-dimensional propagation
over any type of terrain. The PE provides a direct solution of Maxwell's
wave equations by approximating the Helmholtz scalar wave equation.
This technique does not rely on the study of individual ray paths as used
in the Geometrical Theory of Diffraction (GTD). It was decided to develop a two dimensional Parabolic Equation code,
using the Fourier Split/Step method that allowed propagation over
arbitrary terrain (; ; ). The model boundary conditions assumed that the
satellite transmission was a plane wave, and that the lower boundary was
a perfect reflector. Propagation simulations from the model accurately
provide the amplitude and phase of the propagated plane wave at all
points within the model domain. The PE model was used to study the effects of diffraction and
multipath caused by various types of terrain commonly found in an open
cut mining environment. The study of diffraction errors was relatively
simple, because we are simply concerned with amplitude of the signal as
it diffracts about an obstacle. If the amplitude is above the level receivable
by a GPS receiver then the diffraction error can be obtained from the
geometry of the terrain obstacle. The study of multipath is more complex,
as the computed phase from the PE model is ambiguous and the presence
of multipath can only be inferred. Thus the absolute magnitude of the
nmltipath error is not currently determinable, though the results of some
new work is shown here. This paper shows that diffraction effects can cause significant errors in
range. It also shows the effects that multipath has on the received
amplitude of the signal and the received phase of the signal. A discussion
is made of further work that is presently underway that will allow the
direct determination of the multipath error by comparing the ambiguous
phase with a reference phase.