1 Principles of the Global Positioning System Lecture 02 YUAN Linguo Email: lgyuan@163.com Dept. of Surveying Engineering, Southwest Jiaotong University Principles of the Global Positioning System 2005-3-4 2 2 Principles of the Global Positioning System 2005-3-4 3 Principles of the Global Positioning System 2005-3-4 4 3 Principles of the Global Positioning System 2005-3-4 5 Principles of the Global Positioning System 2005-3-4 6 4 Principles of the Global Positioning System 2005-3-4 7 Principles of the Global Positioning System 2005-3-4 8 5 Principles of the Global Positioning System 2005-3-4 9 Coordinate Systems ? Definition of coordinates ? Conventional “realization” of coordinates ? Modern realizations using spaced based geodetic systems (such as GPS). Principles of the Global Positioning System 2005-3-4 10 Coordinate system definition To define a coordinate system you need to define: ? Its origin (3 component) ? Its orientation (3 components, usually the direction cosines of one axis and one component of another axes, and definition of handed-ness) ? Its scale (units) 6 Principles of the Global Positioning System 2005-3-4 11 Principles of the Global Positioning System 2005-3-4 12 7 Principles of the Global Positioning System 2005-3-4 13 Principles of the Global Positioning System 2005-3-4 14 8 Principles of the Global Positioning System 2005-3-4 15 Principles of the Global Positioning System 2005-3-4 16 Geodetic Coordinates 9 Principles of the Global Positioning System 2005-3-4 17 Geodetic coordinates Easiest global system is Cartesian XYZ but not common outside scientific use Conversion to geodetic Lat, Long and Height X = (N + h)cosφ cosλ Y = (N + h)cosφ sinλ Z = ( b 2 a 2 N + h)sinφ N = a 2 a 2 cos 2 φ +b 2 sin 2 φ Principles of the Global Positioning System 2005-3-4 18 Parameter Notation Magnitude Semi-major Axis a 6378137.0 meters Reciprocal of Flattening 1/f 298.257223563 Angular Velocity of the Earth ω 7292115.0 x 10 -11 rad sec -1 Earth’s GravitationalConstant GM 3986004.418 x 10 8 m 3 /s 2 (Mass of Earth’s Atmosphere Included) WGS 84 Four Defining Parameters a and 1/f are the same as in the original definition of WGS 84 10 Principles of the Global Positioning System 2005-3-4 19 What is ITRF ? ? The International Earth Rotation Service (IERS) has been established in 1988 jointly by the International Astronomical Union (IAU) and the International Union of Geodesy and Geophysics (IUGG). The IERS mission is to provide to the worldwide scientific and technical community reference values for Earth orientation parameters and reference realizations of internationally accepted celestial and terrestrial reference systems ? In the geodetic terminology, a reference frame is a set of points with their coordinates (in the broad sense) which realize an ideal reference system ? The frames produced by IERS as realizations of ITRS are named International Terrestrial Reference Frames (ITRF). ? Such frames are all (or a part of) the tracking stations and the related monuments which constitute the IERS Network, together with coordinates and their time variations. Principles of the Global Positioning System 2005-3-4 20 11 Principles of the Global Positioning System 2005-3-4 21 Principles of the Global Positioning System 2005-3-4 22 12 Principles of the Global Positioning System 2005-3-4 23 Principles of the Global Positioning System 2005-3-4 24 13 Principles of the Global Positioning System 2005-3-4 25 Principles of the Global Positioning System 2005-3-4 26 14 Principles of the Global Positioning System 2005-3-4 27 Principles of the Global Positioning System 2005-3-4 28 15 Principles of the Global Positioning System 2005-3-4 29 Principles of the Global Positioning System 2005-3-4 30 Behavior 1993-2001 -10.0 -5.0 0.0 5.0 10.0 0.05.010.015.020.0 Pole Position X Pole (m) Y Pole (m) 1993 2001 16 Principles of the Global Positioning System 2005-3-4 31 Principles of the Global Positioning System 2005-3-4 32 17 Principles of the Global Positioning System 2005-3-4 33 Principles of the Global Positioning System 2005-3-4 34 18 Principles of the Global Positioning System 2005-3-4 35 Principles of the Global Positioning System 2005-3-4 36 19 Principles of the Global Positioning System 2005-3-4 37 Principles of the Global Positioning System 2005-3-4 38 20 Principles of the Global Positioning System 2005-3-4 39 Principles of the Global Positioning System 2005-3-4 40 21 Principles of the Global Positioning System 2005-3-4 41 UT1-UTC -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1993.0 1994.0 1995.0 1996.0 1997.0 1998.0 1999.0 2000.0 2001.0 UT1-UTC (discontinuities are leap-seconds) UT1-UTC (s) UT1-UTC (s) Year Principles of the Global Positioning System 2005-3-4 42 22 Principles of the Global Positioning System 2005-3-4 43 Principles of the Global Positioning System 2005-3-4 44 Web Resources ? International Earth Rotation and Reference Systems Service (IERS) http://www.iers.org/ ? U.S. Naval Observatory (USNO) GPS Operations http://tycho.usno.navy.mil/gps.html ? The GPS Toolbox http://www.ngs.noaa.gov/gps- toolbox 23 Principles of the Global Positioning System 2005-3-4 45 Assignment 1. What are space-fixed and earth-fixed coordinate 2. systems? Give the examples. 3. What is sidereal time and solar time? 4. What is GPS time? Convert March 4, 2005 to JD and MJD 5. Convert geodetic position 290 deg Long 42 deg latitude ellipsoidal height 0 m into Cartesian and geocentric coordinates. What would be the error in position if geocentric coordinates were confused with geodetic coordinates at this latitude? 6. Please program to realize 4 and 5.