Mathematical Modeling of the Global Positioning System GPS

Abstract

The Global Positioning System (GPS) is a space-based radio navigation system that provides consistent positioning, navigation and timing services to users on a continuous worldwide basis. The objective of this thesis research is to give the readers a working familiarity with both the basic theoretical and practical aspects of how the GPS works. In this research, we have addressed the most important issues related to GPS, such as the transmission of information through it, the mechanism used by GPS receiver to determine our position depending on satellite information, we also studied the factors that led to errors in determining the location. This thesis is divided into 5 sections. First, it introduces a condensed GPS program history, the main components of a GPS receiver (hardware) and some useful applications for the GPS. Second, the nature of the signal, the transmission of the signal, and the mechanisms involved in its transmission are discussed. It also shows how the receiver obtains the signal with the best accuracy, where the receiver basically corrects the frequency of the signal (the carrier plus the well-known PRN code). Third, the wave transmission in its three-dimensional form is discussed and how to deal with this shape mathematically. Fourth, we provide the basic mathematical methods used to calculate user’s position with the help of Matlab program. Finally, we focused on how to model a mathematical expression for GPS signal tracking using a phase-locked loop filter receiver in order to obtain a zero steady state error. Then the Z-transform is used to build a phase-locked loop in software for digitized data.