12.215 Modern Navigation U (3-1-8)

Thomas Herring (tah@mit.edu), MW 10:30-12:00 Room 54-322

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, non-spherical 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. Dead-reckoning, 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 anti-spoofing) and their effects on navigation and precise positioning.

(4) Estimation procedures; Stochastic and mathematical models; statistical descriptions of dynamic systems; propagation of covariance matrices least-squares 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. Hofmann-Wellenhof, H. Lichtenegger, and J. Collins, GPS Theory and Practice, Springer-Verlag, Wein, New York, pp. 326, 1992.

G. Strang and K. Borre, Linear Algebra, Geodesy, and GPS, Wellesley-Cambridge Press, Wellesley, MA. pp. 526, 1997. (http://www-math.mit.edu/~gs)

Class Schedule

 

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 on-line

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 “read-ahead” 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

XYZ to Lat/Long/height

Geodetic Datums

Moments of Inertia

http://www.iers.org

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

US Height system

NGS Geoid site

3.         PowerPoint    PDF     HTML

 

Mon

09/28/09

Spherical trigonometry.  Derivations and examples on how to use.

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

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

http://www.usno.navy.mil/USNO/astronomical-applications/data-services/

http://www.usno.navy.mil/USNO/astronomical-applications/images_aa/Moon_phases.jpg
http://www.tecepe.com.br/scripts/AlmanacPagesISAPI.isa This is an online almanac that looks like the nautical almanac

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://geo.phys.uit.no/articl/roadto.html
http://www.earthsci.unimelb.edu.au/ES304/MODULES

http://www.ngdc.noaa.gov/geomagmodels/struts/calcDeclination Generates declination at function of time and location,
http://gsc.nrcan.gc.ca/geomag/nmp/northpole_e.php

http://www.irbs.com/bowditch/ This is the classic navigation text
http://www.phy.ntnu.edu.tw/java/ruler/vernier.html
http://www.tpub.com/math1/7e.htm  Vernier scale

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/Course-Info/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:
http://www.maptools.com/UsingUTM/
http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html
www.nationalgeographic.com/features/2000/exploration/projections/

mathworld.wolfram.com/MapProjection.html

11.       PowerPoint    PDF     HTML

 

Mon

10/21/09

Statistics and propagation of variance-covariance matrices

12.       PowerPoint    PDF     HTML

 

Mon

10/26/09

Estimation of over-determined, 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 pseudo-range 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 non-linear model that can be used to represent the measurements taken. Homework set and due 12/02/2009.

LSextant.        PowerPoint    PDF     HTML

 

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://www-das.uwyo.edu/~geerts/cwx/notes/chap01/tropo.html
http://geoweb.mit.edu/~tah/cont98g/sky.html has comparisons of NCEP and GPS estimates of atmospheric delays under the Atmosphere link.

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

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

http://igscb.jpl.nasa.gov/components/prods.html

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://gpshome.ssc.nasa.gov/

http://www.gpsworld.com/

http://www.mitre.org/technology/gps/online/gps_apps.html

http://geoweb.mit.edu/~tah/GGMatlab/

http://www.scign.org/

23        Power Point   PDF     HTML

 

 

 


HOMEWORKS for 2009:

HW 01: Due Wednesday, October 7, 2009.  HTML  PDF

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

 

HW 03: Due Wednesday, December 2, 2009           HTML  PDF

Solution           PDF File         HW03_09.m