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Mathematical Modeling in Industry-A Workshop for Graduate
Students

Mathematics in GPS

Mathematics in GPS

Tutor: **Craig Poling**, Lockheed Martin

On day 1, 7/22/98, we will briefly survey the wide range of commercial, defense and scientific applications where the Global Satellite Positioning System GPS has had a major impact. Following the introduction we will develop the mathematical notation, definitions and framework necessary to describe: 1) conventional, 2) differential and 3) interferometric, or real time kinematic, positioning and attitude determination. Following the development of the mathematical framework necessary to understand GPS we will pose selected challenging mathematical problems which arise from attempts to determine ultra high precision interferometic position and attitude. GPS workshop participants will then be given selected reading material to aid in the mathematical modeling and solution of the problems that are posed.

During the course of the workshop GPS antenna and receivers will be used to collect pseudorange and integrated carrier phase data. This data can be used by the workshop participants to evaluate their mathematics models and approaches to achieving high precision position and attitude estimates. Some exposure to classical mechanics, numerical analysis, and stochastic processes would be helpful, although the workshop is designed to be self-contained.

By the end of the GPS workshop, participants will have learned how to resolve positions anywhere on the earth to subcentimeter accuracy and to determine orientation in space with accuracy comparable to that achieved byVLBI methods using quasars (e.g. 1.4 x 10-8 degrees). In addition, workshop participants will have been exposed to some of the principal research questions which arise in high precision GPS position and attitude applications.

Recommended GPS reference:

Global Positioning System: Theory and Applications; Volumes 1 and 2, edited by Bradford W. Parkenson, James J. Spilker Jr., Associate Editors, Penina Axelrod and Per Enge, Volume 164; Progress in Astronautics and Aeronautics, Paul Zarchan Editor-in-chief, published by AIAA 1996.