西南交通大学测量工程系：《GPS卫星定位技术与方法（GPS技术与应用）》课程教学资源（课件讲稿）Lecture 2 Principles of the Global Positioning System

雨自文大電园地 Principles of the Global Positioning System Lecture 02 YUAN Linguo Email:lgyuan@163.com Dept of Surveying Engineering, Southwest Jiaotong University Overview GPS Basic Positioning Principle Two reference systems: Time and Coordinate Syst 9 GPS S=vt Time known 3 Coordinate System EX Principles of the Global Positioning System 2005-34(2

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

A Group of Basic Concepts 1. Sun and earth Spring 2. Earth ummer 3. Celestial body 21 12月21日 4. Ecliptic Plane Winter 5. Earth Equator Autumn 6. Celestial 7. Greenwich Meridian Principles of the Global Positioning System 2005-34(3 9. Nod 10. Pe ILA ② ■RBy像 目Mss扫描条带 NEV Principles of the Global Positioning System 2005-34(4

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12. Space-fixed Coordinate System 13. Earth-fixed Coordinate System 14. Artificial Earth Satellite 15. Orbital Plane 16. Orbital plane Coordinate System satellite perge node orbit UV Principles of the Global Positioning System Prime Meridian Equat O Degree Latitude EX Principles of the Global Positioning System 2005-34(6

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1. A uniform coordinate system 2. A three-dimensional Cartesian system The Xi -axis for the space-fixed system points towards the vernal X3=X X,-axis of the earth-fixed system defined by intersection line of the equatorial plane geocenter with the plane ted by the Greenwich vernal equinox meridian wv Principles of the Global Positioning System The angle Oo between the two systems is called Greenwich sidereal time The X-axis being orthogonal to both the x-axis and the x-axis completes a right-handed coordinate frame EX Principles of the Global Positioning System 2005-34(8

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Coordinate Systems o Definition of coordinates o Conventional"realization"of coordinates a Modern realizations using spaced based geodetic systems(such as GPS) wy Principles of the Global Positioning System 200534(9 Coordinate system definition To define a coordinate system you need to define: Its origin (3 a 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 NEV Principles of the Global Positioning System

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)

A Group of Terms Precession(Sun-Earth-Moon, Fixed! I ) Vernal Equinox moves towards west 50.26second. The difference between equinox calendar year and sidereal year 0. 014day Nutation: The oscillation withprespect to the inertial space is called nutation(Sun-Earth-Moon, Change! ! !) 1. Secular precession 2. Periodic nutation Polar motion: The oscillation with respect to the terrestrial system is named polar motion Chandler period: The period of the free motion amounts to about 430 days and is known as the Chandler period Ev Principles of the Global Positioning System 1. Conventional Celestial Reference System 1. Definition of CCRS CRF: Since this system is defined conventionally and the practical realization does not necessarily coincide with the theoretical system, it is called(conventional) Celestial Reference Frame(CRF oquasi-inertial"means a geocentric system is not rigorously inertial because of the accelerated motion of the earth around the sun o the International Earth Rotation Service (IERS) called /CRF EX Principles of the Global Positioning System

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Z-Axis PrAxis Point伸,0 Y- Axis Y-Axis ThreeDimensional Artesia Three- Dimensional Polar Coordinates X.Y.Z (中,e,r) wy Principles of the Global Positioning Syste 200534(13 Y-Axis Three- Dimensional Polar Coordinates Three- Dimensional Cartesian Coordinates x=rcos(中)c0s() 中)sin(0 rsin(中) rinciples of the Global Positioning System 2005-3-4

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Conventional Terrestrial Reference System Definition: Terrestrial Reference Frame(TRF) TRF: is defined by a set of terrestrial control stations erving as reference points. Most of the reference stations are equipped with Satellite Laser Ranging(SLR)or Very Long Baseline Interferometry (VLBD bilit o World Geodetic System 1984(WGS-84), 1500 o ITRF-94 established by the IErS, 180 points Principles of the Global Positioning System 2005-34(15 Geodetic Coordinates Geodetic Height of Point p Ellipsoid Semi Minor Axi Point p Semi Mayor Axis Equator Geodetic Longitude at Latitude at Point p Point p WE Principles of the Global Positioning System 200534(16

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Geodetic coordinates Easiest global system is Cartesian XYZ but not common outside scientific use Conversion to geodetic Lat, Long and Height X=(N+h)cos ocos/ Y=(N+h)cos sin A N+h)sin g N o+b sin o ey Principles of the Global Positioning Syste 200534(17 WGS 84 Four Defining Parameters SemI-major Axis a 6378137.0 meters Reciprocal of Flattening 1298257223563 Angular Velocity of the Earth 7292115.0 x 10-IIrad sec-I Earth's GravitationalConstant GM 3986004. m 3/s 2 Mass of Earths Atmosphere Included) a and 1/f are the same as in the original definition of WGs 84 Gv Principles of the Global Positioning System 2005-3-4

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 = ( b2 a 2 N + h)sinφ N = a 2 a 2 cos2 φ +b2 sin2 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

What is itrf The International Earth Rotation Service(IErS) has been established in 1988 jointly by the International Astronomical Union (IAU) and the Intermational Union of Geodesy and geophysics (UGG). The IErS mission is to provide to the worldwide scientific and technical community reference values for Earth orientation parameters and reference realizations of 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 wy Principles of the Global Positioning System 2005-34(19 ITRF97 and collocated techniques 8 4 Colocated tachniques> 49 8 rinciples of the Global Positioning System 2005-3-4

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