Ta, Jacquelyne Lan
The Global Positioning System (GPS) is a satellite-based navigation
system made up of a network of 24 satellites placed into orbit by the United States Department of Defense (DOD) and managed by the United States Air Force 50th Space Wing. GPS was originally intended for military applications. It was designed
to assist soldiers and military vehicles, planes, and ships in accurately determining their locations world-wide. However, in the 1980s, the government made the system available for civilian
Civilian applications are evolving and expanding constantly. Today,
the uses of GPS have extended to include both the commercial
and scientific worlds. Commercially, GPS is used as a navigation and positioning tool in airplanes, boats, cars, and most outdoor recreational activities such as hiking, fishing, and kayaking. In the scientific community, GPS plays an important role in the earth sciences. Meteorologists use GPS for weather forecasting and global climate studies. Geologists use GPS for surveying and earthquake studies to measure tectonic motions during and between earthquakes.
The GPS is vast, expensive and involves a lot of technical ingenuity,
but the fundamental concepts at work are quite simple and intuitive. The objective of this thesis paper is to give the readers a working familiarity with both the basic theoretical and practical aspects of how the GPS works. Chapter 1 introduces a condensed GPS program history that involves three competing concepts from the Transit, Timation, and Project 621B programs.
Chapter 2 examines the GPS system consisting of three segments: space segment, control segment, and user segment. The three segments contribute to overall accuracy, reliability, and functionality. Chapter 3 outlines the basic mathematical methods used to calculate user's position based on a system with no errors. Finally, Chapter 4 and 5 covers two important math theories needed to handle satellite and receiver clock errors:
Newton-Raphson Method and the Least Squares Method.
All rights reserved to author and California State University Channel Islands
Newton-Raphson interation
Least squares
Mathematics thesis
Ta2011Thesis.pdf
Mathematics [35]