12.215
Modern Navigation U (318) Thomas
Herring (tah@mit.edu), MW 10:3012:00 Room
54322 http://chandler.mit.edu/~tah/12.215 2009 Accessibility 
The development of the Global Positioning System
(GPS) started in the 1960s, and the system became operational in 1992. The
system has seen many diverse applications develop in the last few years with
the accuracy of positioning ranging from a few meters to less than 1
millimeter. In this course we
will apply many of basic principles of science and mathematics learnt at MIT
to explore the applications and principles of GPS. We also use GPS and other
equipment in the class (and outside on Campus) to demonstrate the uses of
this system. 
Topics to be covered in the course are: 
(1) Coordinate systems
on a deformable, nonspherical Earth. Address concepts of latitude and
longitude as determined by the direction of gravity (astronomical latitude
and longitude) and 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. 
(2) Principles of
Navigation. Deadreckoning, true and magnetic bearings; use of celestial
bodies, use of secants for position fixes. Introduction common map
projections; uses of different map projections. Vector approach to spherical
trigonometry. 
(3) 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 antispoofing) and their effects on navigation and precise
positioning. 
(4) Estimation
procedures; Stochastic and mathematical models; statistical descriptions of
dynamic systems; propagation of covariance matrices leastsquares estimation.

(5) 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. 
We will have some lab
sessions during the course and there will be homework once every few weeks.
There will be an open book final exam. Grading will be from the homework
(70%), final exam (20%) and class participation (10%). 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. 
Texts

B. HofmannWellenhof, H.
Lichtenegger, and J. Collins, GPS
Theory and Practice, SpringerVerlag, Wein, New York, pp. 326, 1992. G. Strang and K. Borre, Linear
Algebra, Geodesy, and GPS, WellesleyCambridge Press, Wellesley, MA. pp.
526, 1997. (http://wwwmath.mit.edu/~gs) 
The class schedule is
approximate and will evolve during the semester depending on developments in
the class. 
Class 
Topic 
1 
Introduction 
2 
Latitude and Longitude
definition 
3 
Height Definition 
4 
Spherical trigonometry 
5 
Motion of Sun/Earth and
astronomical position determination 
6 
Almanacs paper and
online 
7 
Dead reckoning and
conventional navigation 
8 
Use of sextant and
measurements 
9 
Linear algebra 
10 
Analysis of Sextant
results 
11 
Map projections 
12 
Basic statistics and
Propagation of variances 
13 
Least squares estimation 
14 
Correlations 
15 
Electronic distance
measurement 
16 
Basics of GPS pseudo
range 
17 
Geometry of GPS
measurements and accuracy 
18 
GPS carrier phase
measurements 
19 
Neutral atmosphere
propagation 
20 
Dispersive propagation
delays 
21 
Satellite motions 
22 
Class before
Thanksgiving will be informal question and answer time 
23 
Basics of hand held GPS 
24 
GPS outside the
classroom 
25 
Practical Aspects of GPS
and Applications of GPS in different fields 
26 
Final class review and
enquiry session 
Lecture Notes:
Lecture notes are
updated during the semester. For
those students wishing a “readahead” in the notes previous years notes are
keep online. They will evolve
during the semester, boxes will be shaded as notes are updated. 
Wed 
09/09/09 
Introduction
and coordinate systems 
1. PowerPoint PDF HTML
Mon 
09/21/09 
Definitions of the types of latitude and longitude; mathematical
relationship between these and Cartesian XYZ; motion of the rotation axis,
which effects determination of latitude and longitude. Web sites used in this
lecture 
2. PowerPoint PDF HTML
Wed 
09/23/09 
Height definitions, methods for determining heights, spirit
leveling and trigonometric leveling; geoid heights and their determination.
Web sites used in this lecture 
3. PowerPoint PDF HTML
Mon 
09/28/09 
Spherical trigonometry.
Derivations and examples on how to use. 
4. PowerPoint PDF HTML
Wed 
09/30/09 
Determination of latitude and longitude using astronomical
methods. http://www.nmm.ac.uk/ Equation of time site. http://www.bipm.org/jsp/en/kcdb_data.jsp#nohref
web site points to tables that contain adjustments to all of world’s cesium
national standard clocks (Bureau International des Poids et Measures (BIPM). 
5. PowerPoint PDF HTML
Mon 
10/05/09 
Almanacs in
both paper and electronic forms http://www.fourmilab.ch/earthview/moon_ap_per.html http://www.usno.navy.mil/USNO/astronomicalapplications/dataservices/
http://www.usno.navy.mil/USNO/astronomicalapplications/images_aa/Moon_phases.jpg 
6. PowerPoint PDF HTML
Wed 
10/07/09 
Dead
reckoning and sextants. The
following web sites are used in the notes. (These links appear in the web page and power point notes
but not in the PDF file. http://www.ngdc.noaa.gov/geomagmodels/struts/calcDeclination
Generates declination at function of time and location, http://www.irbs.com/bowditch/ This is
the classic navigation text 
7. PowerPoint PDF HTML
Wed 
10/13/09 
Sextant
measurements 
8. PowerPoint PDF HTML
Wed 
10/14/09 
Review of
linear algebra covering vectors and matrices, solving linear equations,
vector spaces, eigenvalues and vectors, rotation matrices. http://web.mit.edu/18.06/www/CourseInfo/Mfiles/slu.m 
9. PowerPoint PDF HTML
Mon 
10/19/09 
Map
Projections of different types and the mathematics behind some projections.
Web pages used in class: 
11. PowerPoint PDF HTML
Mon 
10/21/09 
Statistics
and propagation of variancecovariance matrices 
12. PowerPoint PDF HTML
Mon 
10/26/09 
Estimation
of overdetermined, nearly linear systems including least and weighted least
squares. 
13. PowerPoint PDF HTML
Wed 
10/28/09 
Finish
estimation with sequential estimation and error ellipses; Examine
correlations between random time series. (The time series and correlation values plotted in this
lecture were generated with cross.f 
14 PowerPoint PDF HTML
Mon 
11/02/09 
Electromagnetic
Distance Measurement (EDM).
Conventional instruments and theory of their operation. 
15 PowerPoint PDF HTML
Wed 
11/04/09 
GPS
pseudorange measurements and basic principals of GPS. We also use the Matlab code GPSSim.m and xcor.m in this class. 
16 PowerPoint PDF HTML
Wed 
11/18/09 
GPS signal
tracking, orbit geometry, specific signal structure, phase measurements and
data. 
17. PowerPoint PDF HTML
Mon 
11/23/09 
Examined HW
02 solution and the nonlinear model that can be used to represent the measurements
taken. Homework set and due 12/02/2009. 
Wed 
11/25/09 
GPS pseudo
range and phase measurements, basic processing methods, dilution of precision
measures. 
18. PowerPoint PDF HTML
Mon 
11/30/09 
Atmosphere
delay effects. Links in this lecture http://wwwdas.uwyo.edu/~geerts/cwx/notes/chap01/tropo.html 
19. PowerPoint PDF HTML
Wed 
12/02/09 
Ionosphere
and dispersive GPS delay correction (dual frequency ionospheric delay
corrections.) 
20. PowerPoint PDF HTML 
Mon 
12/07/09 
Satellite
orbit representation and sources of information about orbits http://geoweb.mit.edu/~tah/icd200c123.pdf

21 Power Point PDF HTML 
Wed 
12/09/09 
Basics of
hand held GPS receivers. 
22 Power Point PDF HTML 
Wed 
12/09/09 
Applications
of GPS http://www.mitre.org/technology/gps/online/gps_apps.html 
23 Power Point PDF HTML 
HOMEWORKS for 2009: 
Solution PDF File 

HW
02: Due Wednesday,
November 4, 2009. HTML PDF data file (Note: To copy the data file, display it
in your browser and then select all the text and copy to a working
document. A direct save the data
file may not look like a text file depending on the system you are
using). The data file has UTC hr
min seconds data deg minutes. 
Solution PDF File HW02_Sextant_09.m 
