Masters Theses

Date of Award


Degree Type


Degree Name

Master of Science


Electrical Engineering

Major Professor

Paul B. Crilly

Committee Members

Aly E. Fathy, Seddik M. Djouadi


A model for the phase of a ground wave propagating over irregular and forested terrain has been developed and tested for a transmission system operating at 3.315 MHz.

In this model, the time delay induced beyond that of the standard velocity of radio waves in air is modeled as a combination of 3 effects: the finite conductivity of the earth, the irregularity of the terrain over which the wave is propagating, and the forestation of the terrain.

The finite conductivity model is based on a small curvature formula developed by Van Der Pol and Bremmer. The terrain irregularity model models additional delay as a perturbation of the surface impedance and is a function of the slope angle.

The additional delay due to forestation is modeled as a dissipative dielectric slab which introduces a velocity factor. The foliage on the range was quantized into three levels of density: open, thin, and thick. The foliage thickness was determined manually from commercial satellite imagery.

The ground based network used to measure propagation times consists of 5 perimeter transmitter sites and 5 receiver sites. Results for 1 of the 5 receiver sites have already been obtained. The results accurately predict the additional delay time introduced. The additional delays predicted over the 5 paths vary widely, ranging from 400 to almost 1000 nanoseconds. The lengths of these paths vary between 2 and 3 miles. The relative permittivity of each grade of forest density along each path was found to be in agreement.

The significance of this work revolves around navigating in GPS denied environments, areas of chronic GPS unavailability, such as urban areas, canyons, under dense foliage, or when a GPS signal is being unintentionally or intentionally jammed. In order to provide a path forward to a robust augmentation to GPS, the propagation phenomena associated with ground-based navigation must be understood, and more effectively modeled.

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