《全球定位系统原理》（英文版）Lecture 2 Coordinate Systems

12.540 Principles of the Global Positioning System Lecture 02 Prof. Thomas Herring 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 1 12.540 Principles of the Global Positioning System Lecture 02 Prof. Thomas Herring

Coordinate Systems Today we cover Definition of coordinates Conventional "realization "of coordinates Modern realizations using spaced based geodetic systems(such as GPS) 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 2 Coordinate Systems • Today we cover: – Definition of coordinates – Conventional “realization” of coordinates – Modern realizations using spaced based geodetic systems (such as GPS)

Coordinate system definition To define a coordinate system you need to define Its origin③3 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) 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 3 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)

Coordinate system definition In all 7 quantities are needed to uniquely specify the frame In practice these quantities are determined as the relationship between two different frames How do we measure coordinates How do we define the frames 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 4 Coordinate system definition • In all 7 quantities are needed to uniquely specify the frame. • In practice these quantities are determined as the relationship between two different frames • How do we measure coordinates • How do we define the frames

Measuring coordinates Direct measurement( OK for graph paper) Triangulation Snell 1600s: Measure angles of triangles and one-distance in base triangle Distance measured with calibrated chain"or steel band(about 100 meters long) Baseline was about 1 km long Triangles can build from small to larges ones Technique used until 1950s 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 5 Measuring coordinates • Direct measurement (OK for graph paper) • Triangulation: Snell 1600s: Measure angles of triangles and one-distance in base triangle • Distance measured with calibrated “chain” or steel band (about 100 meters long) • “Baseline” was about 1 km long • Triangles can build from small to larges ones. • Technique used until 1950s

Measuring coordinates Small errors in the initial length measurement, would scale the whole network Because of the earth is " nearly flat, measuring angles in horizontal plane only aoWs“ horizonta| coordinates”tobe determined Another technique is needed for heights 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 6 Measuring coordinates • Small errors in the initial length measurement, would scale the whole network • Because of the Earth is “nearly” flat, measuring angles in horizontal plane only allows “horizontal coordinates” to be determined. • Another technique is needed for heights

Measuring coordinates In 1950s electronic distance measurement(EDM)became available (out growth of radar Used light travel times to measure distance(strictly, travel times of modulation on either radio, light or near- infrared signals) 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 7 Measuring coordinates • In 1950s, electronic distance measurement (EDM) became available (out growth of radar) • Used light travel times to measure distance (strictly, travel times of modulation on either radio, light or near￾infrared signals)

Measuring coordinates Advent of edm allowed direct measurements of sides of triangles Since all distances measured less prone to scale errors However, still only good for horizontal coordinates 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 8 Measuring coordinates • Advent of EDM allowed direct measurements of sides of triangles • Since all distances measured less prone to scale errors. • However, still only good for horizontal coordinates

Accuracies Angles can be measured to about 1 arc second(5×106 radians) EDM measures distances to 1X10-(1 part-per-million, ppm) Atmospheric refraction 300 ppm Atmospheric bending can be 60(more effect on vertical angles) 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 9 Accuracies • Angles can be measured to about 1 arc second (5x10-6 radians) • EDM measures distances to 1x10-6 (1 part-per-million, ppm) • Atmospheric refraction 300 ppm • Atmospheric bending can be 60” (more effect on vertical angles)

Height coordinates Two major techniques Measurement of vertical angles (atmospheric refraction) Leveling measurement of height differences over short distances(<50 meters) Level lines were used to transfer height information from one location to another 02/11/02 12.540Lec02

02/11/02 12.540 Lec 02 10 Height coordinates • Two major techniques: – Measurement of vertical angles (atmospheric refraction) – “Leveling” measurement of height differences over short distances (<50 meters). – Level lines were used to transfer height information from one location to another