Introduction to Global Navigation Satellite System (GNSS) Coordinate Systems, Datum, Geiod Dinesh Manandhar Center for Spatial Information Science The University of Tokyo Contact Information: [email protected] Slide : 1 Dinesh Manandhar, CSIS, The University of Tokyo, [email protected] Geodetic Coordinate System Satellite Pole Semi Minor Axis User at P(x, y, z) Ellipsoid Surface Normal Vector to Ellipsoid at Point P Semi Major Axis Geodetic Latitude at P Equator Semi Major Axis Geodetic Longitude at P Slide : 2 Dinesh Manandhar, CSIS, The University of Tokyo, [email protected] ECEF (Earth Centered, Earth Fixed) ECEF Coordinate System is expressed by assuming the center of the earth coordinate as (0, 0, 0) P (X, Y, Z) (0, 0, 0) Equator Slide : 3 Dinesh Manandhar, CSIS, The University of Tokyo, [email protected] Coordinate Conversion from ECEF to Geodetic and vice versa ECEF (X, Y, Z) to Geodetic Latitude, Longitude & Height to Geodetic Latitude, Longitude & Height ECEF (X, Y, Z) 푍+푒2푏 푠푖푛3휃 휑=atan 푝−푒2푎푐표푠3휃 푋 = 푁 + ℎ cos 휑 cos 휆 휆=atan2 푌, 푋 푌 = 푁 + ℎ cos 휑 sin 휆 푃 ℎ = − N 휑 cos 휑 Z = 푁 1 − 푒2 + ℎ sin 휑 푃 = 푥2 + 푦2 휑 = 퐿푎푡푡푢푑푒 푍푎 휆 = 퐿표푛푡푢푑푒 휃 = 푎푡푎푛 H = Height above Ellipsoid 푃푏 푎 푁 휑 = 1−푒2푠푖푛2휑 Slide : 4 Dinesh Manandhar, CSIS, The University of Tokyo, [email protected] Topographic, Ellipsoidal & Geoid Height Topographic Surface Ellipsoidal Surface h H N Geoid Surface MSL Topographic Height (H) = Ellipsoidal Height (h) - Geoid Height (N) • Geoid Model is based on Gravitation Measurement • In USA, Ellipsoid is above Geoid • Other Continents, Geoid is above Ellipsoid Slide : 5 Dinesh Manandhar, CSIS, The University of Tokyo, [email protected] Geodetic Datum: Geometric Earth Model WGS-84 Geodetic Datum Ellipsoidal Parameters Semi-Minor Axis, b = 6356752.3142m Pole Semi-Major Axis, a = 6378137.0m Flattening, f = (a-b)/a = 1/298.257223563 Minor Axis Minor First Eccentricity Square = e^2 = 2f-f^2 - = 0.00669437999013 Semi Semi-Major Axis Equator Slide : 6 Dinesh Manandhar, CSIS, The University of Tokyo, [email protected].