Numerical Modelling of GPS Signal Propagation

Rodney A. Walker, Kurt Kubik

Abstract:	The objective of this paper was to determine if recent advances in numerical electromagnetic wave propagation modelhng 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 Equation’ 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 (Levy, A4. F. (1990); Clarke, R. H. and Brown, John (I 980); Kuttler, James R. and Dockev, G. Daniel (1991)). 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 multipath 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 furthur work that is presently underway that will allow the direct determination of the multipath error by comparing the ambiguous phase with a reference phase.
Published in:	Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996) September 17 - 20, 1996 Kansas City, MO
Pages:	709 - 717
Cite this article:	Walker, Rodney A., Kubik, Kurt, "Numerical Modelling of GPS Signal Propagation," Proceedings of the 9th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1996), Kansas City, MO, September 1996, pp. 709-717.
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