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12.540 Principles of
the Global Positioning System |
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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. |
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
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B.
Hofmann-Wellenhof, H. Lichtenegger, and J. Collins, GPS Theory and Practice, Springer-Verlag, Wein, New York, pp.
326, 1992. |
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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:
Class
requirements
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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). |
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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.
NOTE: In some weeks class will be
taught on Friday as well as Monday/Wednesday
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Class |
Date |
Topic |
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1 |
02/08/12 |
Introductory
lecture. Overview of the aims of the
class and introduction to coordinate systems: Papers on GPS and coordinate
systems (MIT certificates needed) |
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2 |
02/13/12 |
Coordinate
and time systems |
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3 |
02/15/12 |
Coordinate
and time systems |
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4 |
02/17/12 |
Coordinate
and time systems |
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5 |
02/21/12 |
Satellite
motions |
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6 |
02/22/12 |
GPS
Observables |
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7 |
02/24/12 |
GPS
Observables |
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8 |
03/05/12 |
GPS
Observables |
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9 |
03/07/12 |
GPS
Observables |
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10 |
03/12/12 |
Estimation |
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11 |
03/14/12 |
Estimation |
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03/16/12
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Fieldwork
making GPS measurements. Meet at 10:30
am in 54-820A. We will be working on
the fields near the Johnson Athletics Center. |
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12 |
03/19/12 |
Estimation
Paper topic and outline due. Homework 2 set |
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13 |
03/21/12 |
Estimation:
Kalman filtering |
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14 |
03/23/12 |
Propagation
medium |
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Spring
Break |
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15 |
04/09/12 |
Propagation
medium |
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16 |
04/11/12 |
Propagation
medium |
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17 |
04/13/12 |
Propagation
medium |
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04/16/12 |
Patriots
Day, no classes |
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18 |
04/18/12 |
Mathematical
models |
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19 |
04/30/12 |
Processing
methods. |
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20 |
05/02/12 |
Processing
methods. |
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21 |
05/07/12 |
IGS
and data access |
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22 |
05/09/12 |
Kinematic
processing |
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23 |
05/14/12 |
Applications/PBO |
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- |
05/16/12 |
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
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Date
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Links
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01 |
02/08/12 |
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Class introduction and content. Papers: (MIT
certificates needed) Other web sites |
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02 |
02/13/12 |
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Introduction
to coordinate system definition and realization concentrating on geometric
definitions. |
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03 |
02/15/12 |
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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 |
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04 |
02/17/12 |
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Coordinate systems, rotation of the Earth, Geoid,
Spherical trigonometry. |
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05 |
02/21/12 |
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GPS Satellite orbits. Homework #1 set. The Matlab program
to compute eccentic and true anomalies is truea.m |
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06 |
02/22/12 |
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Start analysis of GPS observables in form of
carrier phase |
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07 |
02/24/12 |
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GPS codes on signals |
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08 |
03/05/12 |
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Pseudorange and phase
measurements. The data file displayed in class is etab.plt.dat |
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09 |
03/07/12 |
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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/ |
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10 |
03/12/12 |
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Start
estimation looking a parametric estimation methods http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd4.htm
http://www.weibull.com/LifeDataWeb/least_squares.htm histograms.m generates histogram plots |
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11 |
03/14/12 |
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Continue estimation now examining it from a
statistical point of view. |
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12 |
03/19/12 |
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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. Homework 2 set, due 4/18/2012 |
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13 |
03/21/12 |
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Kalman filter approach to estimation. |
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14 |
03/23/12 |
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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 |
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15 |
04/09/12 |
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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/ http://www.hg.tuwien.ac.at/~ecmwf1/ (older site) |
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16 |
04/11/12 |
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Ionospheric
delays ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/RIDAILY.PLT |
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17 |
04/13/12 |
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Antennas and calibrations |
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18 |
04/18/12 |
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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 |
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19 |
04/30/12 |
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Models: Rank deficiencies, ambiguity resolution and
differencing methods |
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20 |
05/02/12 |
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Processing
software: |
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21 |
05/07/12 |
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GPS data availability and site
locations http://igscb.jpl.nasa.gov/images/maps/all_world.png Networks http://quake.geo.berkeley.edu/bard/ Results sopac.ucsd.edu/cgi-bin/dbShowArraySitesMap.cgi http://sideshow.jpl.nasa.gov/mbh/series.html |
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22 |
05/09/12 |
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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 Results from the 2010 MIT survey |
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23 |
05/14/12 |
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Lectures above cover applications to tectonic
problems. Tools mentioned in last lecture and used to
generate some of the figures |
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05/16/12 |
Last day of classes; Student Presentations. |
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Additional References:
The material in Lectures 2 and 3 can be found in:
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Author |
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Title |
Physical geodesy [by] Weikko A. Heiskanen [and] Helmut Moritz. |
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Availability |
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Location |
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Published |
San
Francisco, W. H. Freeman [1967] |
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Description |
vi, 364
p. illus. 25 cm. |
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Series |
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Format |
Book BK |
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Bibliography |
Includes
bibliographies. |
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Subject |
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Other Author |
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Author |
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Title |
The earth’s variable rotation : geophysical causes and consequences / Kurt
Lambeck. |
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Availability |
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Location |
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Published |
Cambridge
; New York : Cambridge University Press, 1980. |
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Description |
xi, 449 p.
: ill. ; 23 cm. |
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Series |
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Format |
Book BK |
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Note |
Includes
indexes. |
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Bibliography |
Bibliography: p.
[401]-436. |
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Subject |
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ISBN |
0521227690 |
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Author |
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Title |
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Edition |
4th ed. |
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Online Ed. URL |
Table of
contents only : http://www.loc.gov/catdir/enhancements/fy0903/2008279148-t.html |
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Availability |
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Location |
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Related Website |
Publisher
description : http://www.loc.gov/catdir/enhancements/fy0903/2008279148-d.html |
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Published |
Cambridge
; New York : Cambridge University Press, 2008. |
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Description |
xi, 532 p.
: ill., maps ; 26 cm. |
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Format |
Book BK |
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Bibliography |
Includes
bibliographical references (p. [496]-513) and indexes. |
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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 |
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Subject |
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ISBN |
9780521873628 |
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0521873622 |
Homework for 2012:
Num Due Homework: NOTE data files will be
updated during semester once data for this year has been collected.
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03/07/12 |
web: PDF: The broadcast
ephemeris file to use is mit0090s.10n (containing
the 10 satellites visible at MIT at 15:15 GPST) and the full set of
satellites mit00900.10n. The GPS interface control document icd200cw1234.pdf will be useful
for this homework. The sub-section of ICD2000 that discusses the broadcast
ephemeris is icd200cw1234.Nav.pdf |
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Rinex Definition |
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M-file to
read Broadcast file ReadNav.m Solution 12.540_HW_01_soln.pdf HW01_2012.m |
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2 |
03/23/12 |
Class
Paper Subject and Outline due |
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3 |
04/18/12 |
web.
PDF. Homework covers estimation
methods using simple linear regression and GPS-like clock problem. Solution HW02_2012_soln.pdf HW02_2012.m |
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4 |
05/02/12 |
Draft of
paper due |
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5 |
05/16/12 |
Class
presentations of papers |
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6 |
05/16/12 |
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Data mitb076s.12o mitb0760.12n mitb0760.12o rovr0760.12o (optional
files) |
