Coordinate Systems

Dinesh Manandhar Center for Spatial Information Science The University of Tokyo Contact Information: [email protected]

Training on GNSS – Course T151-40, Organized by: GIC/AIT, CSIS/UT and ICG, held at: GIC/AIT, Thailand from 6 – 10 JAN 2020 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

Training on GNSS – Course T151-40, Organized by: GIC/AIT, CSIS/UT and ICG, held at: GIC/AIT, Thailand from 6 – 10 JAN 2020 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

Training on GNSS – Course T151-40, Organized by: GIC/AIT, CSIS/UT and ICG, held at: GIC/AIT, Thailand from 6 – 10 JAN 2020 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 = 퐿푎푡𝑖푡푢푑푒 푍푎 휆 = 퐿표푛𝑔𝑖푡푢푑푒 휃 = 푎푡푎푛 H = Height above Ellipsoid 푃푏 푎 푁 휑 = 1−푒2푠푖푛2휑

Training on GNSS – Course T151-40, Organized by: GIC/AIT, CSIS/UT and ICG, held at: GIC/AIT, Thailand from 6 – 10 JAN 2020 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)

Training on GNSS – Course T151-40, Organized by: GIC/AIT, CSIS/UT and ICG, held at: GIC/AIT, Thailand from 6 – 10 JAN 2020 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

MinorAxis First Eccentricity Square = e^2 = 2f-f^2 -

= 0.00669437999013 Semi

Semi-Major Axis

Equator

Training on GNSS – Course T151-40, Organized by: GIC/AIT, CSIS/UT and ICG, held at: GIC/AIT, Thailand from 6 – 10 JAN 2020 Slide : 6 Dinesh Manandhar, CSIS, The University of Tokyo, [email protected]