12.540 | Spring 2012 | Graduate

Principles of the Global Positioning System

Lecture Notes

LEC # TOPICS NOTES, SUPPORTING FILES AND LINKS
1 Overview of the aims of the class (PDF)

Class introduction and content

U.S. Coast Guard Navigation Center Website 
University NAVSTAR Consortium Website 
SCIGN Data Portal Website

2 Coordinate and time systems (PDF) Introduction to coordinate system definition and realization concentrating on geometric definitions 
SCO Web: Control Networks 
National Geodetic Survey
3 Potential fields and coordinate systems (PDF) Potential fields and coordinate systems. We also used some Matlab scripts in this lecture. The two programs are Harmonics.m (M), which plots low order harmonics and Sectorials.m (M), which plots high order sectorial harmonics. Surface harmonic figure and code: SurfaceHarmonic.fig (FIG) and SurfaceHarmonic.m (M
Legendre Polynomial
4 Coordinate types (PDF - 1.7MB) Coordinate systems, rotation of the Earth, Geoid, Spherical trigonometry 
International Earth Rotation and Reference Systems Service 
Modeling of Nutation-Precession: Very long baseline interferometry results (PDF
Computation of Geoid99 Geoid Height 
Spherical Trigonometry
5 GPS satellite orbits (PDF) GPS satellite orbits. The MATLAB program to compute eccentic and true anomalies is truea.m (M
The GPS interface control document (PDF
Unclassified (PDF - 1.3MB)
6 GPS observables (PDF) Start analysis of GPS observables in form of carrier phase
7 Specifics of GPS signal (PDF) GPS codes on signals
8 Pseudorange measurements (PDF) Pseudorange and phase measurements. The data file displayed in class is etab.plt.dat (DAT
TEQC—The Toolkit for GPS/GLONASS/Galileo/SBAS Data 
RINEX: The Receiver Independent Exchange Format Version 2 (TXT)
9 Range and phase data (PDF - 1.3MB) The data files displayed in class are ASCII tab delimited files: etab.02tab (TXT) etab.07tab (TXT) etab.11tab (TXT) etab.26tab (TXT) etab.28tab (TXT
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 (TXT) base.04 (TXT) base.05 (TXT) base.09 (TXT) base.12 (TXT) base.17 (TXT) base.28 (TXT) base.29 (TXT
The site coordinates are in the rinex header shown in Lec #8 
Sources of GPS data (main archives) 
SOPAC 
CDDIS 
NGS/CORS 
UNAVCO
10 Estimation: introduction (PDF)

Start estimation looking a parametric estimation methods 
Data Analysis for Process Modeling 
Least Squares Parameter Estimation (Regression Analysis)

histograms.m (M) generates histogram plots

11 Statistical approach to estimation (PDF) Continue estimation now examining it from a statistical point of view
12 Estimation: correlations (PDF) Statistical description of process noise in parameter values. The MATLAB program fogm.m (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 (M) implements flckernoise model through PSD->Covarinace Matrix->eigenvectors and values
13 Estimation (PDF) Kalman filter approach to estimation
14 Propagation medium: propagation (PDF - 2.3MB) Timing in GPS. Examine clock estimation 
IGS Clock Products Working Group 
IGS Time Scale
15 Propagation medium: neutral atmosphere (PDF) Tropospheric delay estimation 
The Height of the Tropopause 
Effects of the Troposheric Mapping Function on Space Geodetic Data (PDF - 1.0MB
Index of /DELAY
16 Propagation: ionospheric delay (PDF - 1MB) Ionospheric delays 
National Geophysical Data Center 
Data file (Year Month Day SunSpot number) 
RIDAILY (1811-2012/04)
17 Basic antenna operation (PDF - 1.7MB) Antennas and calibrations 
NGS/Antenna Calibrations
18 Mathematical models in GPS (PDF) Class starts development of mathematical models needed for precise GPS positioning. In this class we look at solid-Earth tides, ocean-tidal loading and other types of loading effects. The following Fortran source code was discussed in the lecture earth_tide.f (F) and gst_jd.f (F)
19 GPS models and processing (PDF - 1.4MB) Models: Rank deficiencies, ambiguity resolution and differencing methods
20 Processing software (PDF) Processing software: 
GAMIT/GLOBK Web Tutorial
21 GPS groups/IGS (PDF)

GPS data availability and site locations 
UNAVCO 
International GNSS Service 
International GNSS Service—All world map (PNG)

Networks 
SCIGN 
UNAVCO 
NGS/CORS 
Bay Area Regional Deformation Network 
Pacific Northwest Geodetic Array

Results 
Permanent GPS Site Arrays 
GPS Time Series 
SCIGN Data Portal 
GPS Explorer 
UNAVCO

22 Kinematic GPS (PDF)

Kinematic GPS processing and results from experiment earlier in semester 
Results from MIT survey 
track_LC.out (TXT
track.NEU.rovr.LC (TXT
track.NEU.rovr.L1+L2 (TXT)

Results from the 2010 MIT survey

TR02.sum (TXT) TR02.out (TXT) TR02.NEU.rovr.L1+L2 (TXT) TR02.NEU.rovr.LC (TXT
TR0p.sum (TXT) TR0p.NEU.rovr.P1+P2 (TXT)

23 Applications, High-rate GPS results, and Tools (PDF - 6.4MB) Applications to tectonic problems 
Tools used to generate some of the figures 
GAMIT/GLOBK MATLAB Tools

Course Info

As Taught In
Spring 2012
Level
Learning Resource Types
Problem Sets with Solutions
Lecture Notes
Programming Assignments with Examples