Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


  • Coordinate systems on a deformable, non-spherical Earth. Concepts of latitude and longitude as determined by the direction of gravity (astronomical latitude and longitude) and as determined by the normal to an ellipsoidal shape (geodetic latitude and longitude). Relationships between coordinates; concepts of changes in the rotation of the Earth; rotations and translations between coordinate systems. Effects that need to be considered for different accuracy results and the accuracies that are achievable with GPS.
  • Principles of Navigation. Dead-reckoning, true and magnetic bearings; use of celestial bodies, use of secants for position fixes. Introduction to common map projections; uses of different map projections. Vector approach to spherical trigonometry.
  • Principles of GPS. Pseudorange and phase measurements. Spread spectrum signal structure; basic concepts of signal analysis. Contributions of pseudorange and phase (geometric positions, clock errors, propagation medium, cycles ambiguity for phase). Simple atmospheric and ionospheric delay models; use of dispersive properties of plasmas (ionosphere). Use of differencing techniques in the analysis of GPS data. Security systems on GPS satellites (selective availability and anti-spoofing) and their effects on navigation and precise positioning.
  • Estimation procedures; Stochastic and mathematical models; statistical descriptions of dynamic systems; propagation of covariance matrices least-squares estimation.
  • Examples of aircraft navigation using GPS (comparison with laser profiling); examination of real data to assess the limits of accuracy obtainable with GPS; applications in a variety of areas including precision farming; and intelligent vehicle navigation systems.


Buy at Amazon Wellenhof, B. Hofmann-, H. Lichtenegger, and J. Collins. Global Positioning System: Theory and Practice. New York, NY: Springer-Verlag, 1994. ISBN: 9783211825914.

Buy at Amazon Strang, G., and K. Borre. Linear Algebra, Geodesy, and GPS. Wellesley, MA: Wellesley-Cambridge Press, 1997. ISBN: 9780961408862.


It will be acceptable in this course to work together on homework with the aim of better understanding the material and to refer to other books and published material provided that these additional materials are cited appropriately in the homework. Each student should complete the homework separately. It is not acceptable to simply copy the homework of another student.


Homework 60%
Final Exam 30%
Class Participation 10%


1 Introduction and Coordinate Systems  
2 Latitude and Longitude Definition  
3 Height Definition  
4 Spherical Trigonometry  
5 Position Determination by Astronomical Methods Homework 1 due
6 Almanacs in Paper and Electronic Form  
7 Dead Reckoning and Sextants  
8 Review of Linear Algebra  
9 Sextant Measurements  
10 Map Projections  
11 Statistics and Propagation of Variance-covariance Matrices  
12 Least Squares Estimation  
13 Homework 2 Solution Homework 2 due
14 Correlations  
15 Electromagnetic Distance Measurement (EDM)  
16 Basics of GPS Pseudo Range  
17 Geometry of GPS Measurements and Accuracy  
18 GPS Carrier Phase Measurements  
19 Atmosphere Delay Effects Homework 3 due
20 Ionosphere and Dispersive GPS Delay Correction  
21 Satellite Orbit Representation and Sources of Information about Orbits  

Basics of Hand Held GPS Receivers

Class Outside Using GPS

23 Applications of GPS