12.540 Principles of the Global Positioning System

 

The aim of this course is to introduce the principles of the Global Positioning System and to demonstrate its application to various aspects of Earth Sciences. The specific content of the course depends each year on the interests of the students in the class. In some cases, the class interests are towards the geophysical applications of GPS and we concentrate on high precision (millimeter level) positioning on regional and global scales. In other cases, the interests have been more toward engineering applications of kinematic positioning with GPS in which case the concentration is on positioning with slightly less accuracy but being able to do so for a moving object. In all cases, we concentrate on the fundamental issues so that students should gain an understanding of the basic limitations of the system and how to extend its application to areas not yet fully explored.

 

Basic topics to be covered

1: Coordinate and Time systems

            Definition of global and local coordinate systems

            Relationship between satellite and conventional geodetic systems

2: Satellite orbital motions

            Description of motions

            Forces acting on the satellites

            Satellite NAV messages.

3: GPS Observables

            Pseudo Ranges

            Carrier phases

            SA/AS

            Format of data (RINEX)

4: Estimation procedures

            Stochastic and mathematical models

            Propagation of covariance matrices

            Sequential estimation

            Kalman filtering

            Statistics in least-squares estimation

5: Propagation medium

            Troposphere

            Ionosphere

            multipath

6:  Mathematical model of GPS observables

            Basic theory of contributions that need be to include for millimeter level global positioning

            Use of differencing, differential position

            Wide-lanes and use in kinematic positioning

7: Methods of processing GPS data

            Available software

            Available data set, International GPS Service (IGS).

            Cycle slip fixing/Bias resolution

            Kinematic (moving receiver) GPS processing

            Relationship between satellite and conventional geodetic systems

8: Applications and examples of GPS data analysis along with other space geodetic data.

 

Text Books

 

B. Hofmann-Wellenhof, H. Lichtenegger, and J. Collins, GPS Theory and Practice, Springer-Verlag, Wein, New York, pp. 326, 1992.

Parkinson, B. W., J. Spilker, P. Axelrad and P. Enge, Global Positioning System: Theory and Applications, 793 pp., Am. Inst. Aeronaut. Astronaut., Washington D. C., 1996.

Some web sites to explore:

http://www.navcen.uscg.gov

http://www.unavco.org/

http://reason.scign.org

 

Class requirements

 

There will be homework once every few weeks.  There will be no final, but there will be an end of semester paper on a topic of your choice.  Grading will be from the homework (which will be largely the development of an GPS data analysis program) and the end of semester paper.  The paper will be a review of an area related to the applications of GPS and will developed during the semester (i.e., the paper will be revised for content several times during semester).

 

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. 

 

Class web page http://www-gpsg.mit.edu/~tah/12.540.  During semester, references and homework will be added to this area.

 

Class schedule of topics.  As semester progresses this list will be updated.

NOTE: In some weeks class will be taught on Friday as well as Monday/Wednesday

Class

Date

Topic

1

02/05/14

Introductory lecture.  Overview of the aims of the class and introduction to coordinate systems: Papers on GPS and coordinate systems (MIT certificates needed)
Herring, 1999

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736344&isnumber=15872&tag=1

Herring GGOS 2009

http://www.springerlink.com/index/mv1l4800q2l70855.pdf

2

02/10/14

Coordinate and time systems

3

02/19/14

Coordinate and time systems

4

02/24/14

Coordinate and time systems

5

02/26/14

Satellite motions

6

02/28/14

GPS Observables

7

03/03/14

GPS Observables

8

03/10/14

GPS Observables

9

03/12/14

GPS Observables

10

03/14/14

Estimation

11

03/17/14

Estimation

12

03/19/14

Estimation Paper topic and outline due April 1.

 

03/18-22/14

Fieldwork making GPS measurements.  Meet at 9:00 am in 54-820A.  We will be working on the fields near the Johnson Athletics Center.

 

 

Spring Break

13

03/31/14

Estimation: Kalman filtering

14

04/02/14

Propagation medium

15

04/07/14

Propagation medium

16

04/09/14

Propagation medium

17

04/14/14

Propagation medium

18

04/16/14

Mathematical models         

19

04/23/14

Processing methods. 

20

04/28/14

Processing methods.

21

04/30/14

IGS and data access

22

05/05/14

Kinematic processing

23

05/07/14

Applications/PBO

24

05/12/14

Applications and review

-

05/14/14

Student Presentations of GPS papers and final draft of paper.

 

The lecture notes for the course will appear here as power point, html and pdf files.  (Power point files can be down loaded from the HTML version

 

Lecture Notes: As semester progressed notes will be replaced with this years versions.

Lecture

 Date

 Links

01

02/06/13

PDF

 

PowerPoint

 

 

Class introduction and content. Papers:

(MIT certificates needed)
Herring, 1999

Herring GGOS 2009

Other web sites

http://www.navcen.uscg.gov/

http://www.unavco.org/

http://reason.scign.org

02

02/11/13

PDF

 

PowerPoint

 

 

Introduction to coordinate system definition and realization concentrating on geometric definitions.

http://sco.wisc.edu/surveying/networks.php

http://www.ngs.noaa.gov/

03

02/13/13

PDF

 

PowerPoint.

 

 

Potential fields and coordinate systems. We also used some Matlab scripts in this lecture.  The two programs are Harmonics.m, which plots low order harmonics and Sectorials.m, which plots high order sectorial harmonics.  Surface harmonic figure and code: SurfaceHarmonic.fig and SurfaceHarmonic.m

http://mathworld.wolfram.com/LegendrePolynomial.html

04

02/19/13

PDF

 

PowerPoint

 

 

Coordinate systems, rotation of the Earth, Geoid, Spherical trigonometry.

http://www.iers.org/

JB000165_online.pdf

geoid99_prompt1.prl

http://www.ngs.noaa.gov/GEOID/images/2009/geoid09conus.jpg

http://mathworld.wolfram.com/SphericalTrigonometry.html

05

02/20/13

PDF

 

PowerPoint

 

 

GPS Satellite orbits.  Homework #1 set. The Matlab program to compute eccentic and true anomalies is truea.m

 

http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm

 

The interface control document is linked on the Stellar web site.  A shortened version with just the navigation message and evaluation is also linked.

icd200cw1234.pdf

icd200cw1234.Nav.pdf

06

02/26/13

PDF

 

PowerPoint

 

 

Start analysis of GPS observables in form of carrier phase.  Initial discussion looks at how distances are measured using modulated electromagnetic waves (optical, near infared, and microwave)

07

02/27/13

PDF

 

PowerPoint

 

 

GPS codes on signals

http://www.gps.gov/systems/gps/modernization/civilsignals/

08

03/04/13

PDF

 

PowerPoint

 

 

Pseudorange and phase measurements. The data file displayed in class is etab.plt.dat

http://www.unavco.org/facility/software/teqc/teqc.html

ftp://igscb.jpl.nasa.gov/igscb/data/format/rinex2.txt  

09

03/06/13

PDF

 

PowerPoint

 

 

The data files displayed in class are ASCII tab delimited files: etab.02tab etab.07tab etab.11tab etab.26tab etab.28tab

The following files are based on 2008 homework: Data from base station with approximate XYZ coordinates

-2197259.2644 -4811601.7696  3552341.4441 (m)

Each file has a header line with column titles.  All range and phase units are meters except as noted where range differences have been converted to L1 cycles.

base.02 base.04 base.05 base.09 base.12 base.17 base.28 base.29

The site coordinates are in the rinex header shown in Lecture 8.

Sources of GPS data (main archives)

SOPAC http://sopac.ucsd.edu/

CDDIS http://cddis.gsfc.nasa.gov/cddis.html

NGS/CORS http://www.ngs.noaa.gov/CORS/

UNAVCO http://www.unavco.org/facility/data/data.html

10

03/11/13

PDF

 

PowerPoint

 

 

Start estimation looking a parametric estimation methods

http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd4.htm

http://demonstrations.wolfram.com/search.html?query=least%20squares

histograms.m generates histogram plots

11

03/13/13

PDF

 

PowerPoint

 

 

Continue estimation now examining it from a statistical point of view.

12

03/15/13

PDF

 

PowerPoint

 

 

Statistical description of process noise in parameter values. The matlab program fogm.m generates first-order Gauss Markov processes. (Note since the random number generator is not initialized, your results will differ from those in the class notes (Signal processing tool box is needed for the PSD calculation). FlickerNoise.m implements flckernoise model through PSD->Covarinace Matrix->eigenvectors and values.

 

13

03/18/13

PDF

 

PowerPoint

 

 

Kalman filter approach to estimation. Homework 2 set, due 4/17/2013

14

03/20/13

PDF

 

PowerPoint

 

 

Timing in GPS.  Examine clock estimation.

https://goby.nrl.navy.mil/IGStime/index.php

https://goby.nrl.navy.mil/IGStime/igst.php IGS Time scale

Finish up with Matlab example 04/01/2013

15

04/03/13

PDF

 

PowerPoint

 

 

Tropospheric delay estimation

http://www-das.uwyo.edu/~geerts/cwx/notes/chap01/tropo.html

http://gauss.gge.unb.ca/papers.pdf/igs97tropo.pdf

http://ggosatm.hg.tuwien.ac.at/DELAY/

 

04/05/13

Likely day for fieldwork (meet 54-820A 9:00 am).  No Classes week of Apr 8-10 (EGU meeting).

16

04/17/13

PDF

 

PowerPoint

 

 

Ionospheric delays

ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/RIDAILY.PLT
Data file (Year Month Day SunSpot number)

RIDAILY  (1811-2012/04)

17

04/22/13

PDF

 

PowerPoint

 

 

Antennas and calibrations

http://www.ngs.noaa.gov:80/ANTCAL/

http://www.geopp.de/media/docs/AOA_DM_T

18

04/24/13

PDF

 

PowerPoint

 

 

Class starts development of mathematical models needed for precise GPS positioning.  In this class we look at solid-Earth tides, ocean-tidal lloading and other types of loading effects.  The following Fortran source code was discussed in the lecture earth_tide.f and gst_jd.f.  For a complete bibliography of tidal effects see: http://www.astro.oma.be/ICET/icetdb/icetindex.html

19

04/26/13

PDF

 

PowerPoint

 

 

Models: Rank deficiencies, ambiguity resolution and differencing methods

20

04/29/13

PDF

 

PowerPoint

 

 

Processing software:
http://www-gpsg.mit.edu/~simon/gtgk/docs.htm

http://geowweb.mit.edu/~simon/gtgk/Montserrat12/  

http://geoweb.mit.edu/~simon/gtgk/tutorial/Index.html

21

05/01/13

PDF

 

PowerPoint

 

 

GPS data availability and site locations

http://www.unavco.org/

http://igscb.jpl.nasa.gov/

http://igscb.jpl.nasa.gov/images/maps/all_world.png

Networks

http://www.scign.org/

http://pbo.unavco.org/

http://www.ngs.noaa.gov/CORS/

http://quake.geo.berkeley.edu/bard/

http://www.panga.cwu.edu/

Results

sopac.ucsd.edu/cgi-bin/dbShowArraySitesMap.cgi

http://sideshow.jpl.nasa.gov/mbh/series.html

http://reason.scign.org

http://geoapp03.ucsd.edu/gridsphere/gridsphere

http://pbo.unavco.org/data/gps

22

05/01/13

PDF

 

PowerPoint

 

 

Kinematic GPS processing and results from experiment earlier class

Help file for GAMIT track program:

http://geoweb.mit.edu/~simon/gtgk/help/track.hlp.htm

Results from 2005 MIT survey

track_LC.out

track.NEU.rovr.LC

track.NEU.rovr.L1+L2

Results from the 2010 MIT survey

TR02.sum TR02.out TR02.NEU.rovr.L1+L2 TR02.NEU.rovr.LC

TR0p.sum TR0p.NEU.rovr.P1+P2

23

-

PDF

 

PowerPoint

 

 

Lectures above cover applications to tectonic problems.

Tools mentioned in last lecture and used to generate some of the figures

http://www-gpsg.mit.edu/~tah/GGMatlab

 

05/06/13

Last day of classes; Student Presentations.

 

Additional References:

The material in Lectures 2 and 3 can be found in:

Author  

Heiskanen, Weikko A. (Weikko Aleksanteri), 1895-1971.

Title  

Physical geodesy [by] Weikko A. Heiskanen [and] Helmut Moritz.

Availability  

All items

Location  

Hayden Library - Stacks | QB281.H473

 

 

Published  

San Francisco, W. H. Freeman [1967]

Description  

vi, 364 p. illus. 25 cm.

Series  

Series of books in geology.

Format  

Book BK

Bibliography  

Includes bibliographies.

Subject  

Gravity.

 

Geodesy.

Other Author  

Moritz, Helmut.

 

Author  

Lambeck, Kurt, 1941-

Title  

The earth’s variable rotation : geophysical causes and consequences / Kurt Lambeck.

Availability  

All items

Location  

Hayden Library - Stacks | QB633.L35

 

 

Published  

Cambridge ; New York : Cambridge University Press, 1980.

Description  

xi, 449 p. : ill. ; 23 cm.

Series  

Cambridge monographs on mechanics and applied mathematics.

Format  

Book BK

Note  

Includes indexes.

Bibliography  

Bibliography: p. [401]-436.

Subject  

Earth -- Rotation.

 

Geophysics.

ISBN  

0521227690

 

Author  

Stacey, F. D. (Frank D.)

Title  

Physics of the earth / Frank D. Stacey, Paul M. Davis.

Edition  

4th ed.

Online Ed. URL  

Table of contents only : http://www.loc.gov/catdir/enhancements/fy0903/2008279148-t.html 

Availability  

All items

Location  

Hayden Library - Stacks | QC806.S65 2008 - New Books Displ

 

 

Related Website  

Publisher description : http://www.loc.gov/catdir/enhancements/fy0903/2008279148-d.html 

Published  

Cambridge ; New York : Cambridge University Press, 2008.

Description  

xi, 532 p. : ill., maps ; 26 cm.

Format  

Book BK

Bibliography  

Includes bibliographical references (p. [496]-513) and indexes.

Contents  

1. Origin and history of the Solar System -- 2. Composition of the Earth -- 3. Radioactivity, isotopes and dating -- 4. Isotopic clues to the age and origin of the Solar System -- 5. Evidence of the Earth’s evolutionary history -- 6. Rotation, figure of the Earth and gravity -- 7. Precession, wobble and rotational irregularities -- 8. Tides and the evolution of the lunar orbit -- 9. The satellite geoid, isostasy, post-glacial rebound and mantle viscosity -- 10. Elastic and inelastic properties -- 11. Deformation of the crust: rock mechanics -- 12. Tectonics -- 13. Convective and tectonic stresses -- 14. Kinematics of the earthquake process -- 15. Earthquake dynamics -- 16. Seismic wave propagation -- 17. Seismological determination of Earth structure -- 18. Finite strain and high-pressure equations of state -- 19. Thermal properties -- 20. The surface heat flux -- 21. The global energy budget -- 22. Thermodynamics of convection -- 23. Thermal history -- 24. The geomagnetic field -- 25. Rock magnetism and paleomagnetism -- 26. ’Alternative’ energy sources and natural climate variations: some geophysical background -- App. A. General reference data -- App. B. Orbital dynamics (Kepler’s laws) -- App. C. Spherical harmonic functions -- App. D. Relationships between elastic moduli of an isotropic solid -- App. E. Thermodynamic parameters and derivative relationships -- App. F. An Earth model: mechanical properties -- App. G. A thermal model of the

Subject  

Geophysics.

ISBN  

9780521873628

 

0521873622