Lecture 3

GE 161 – Geome Geometric tric Geodesy Geodesy

Introduction to Geodesy: Concepts in Geodesy

Position, Position, Positioning Positioning Modes, Modes, and and the the Geodetic Geodetic Models Models Lecture No. 3 Department of Geodetic Engineering University of the Philippines

a.s. caparas/06

Positioning Positioning in in Geodesy Geodesy •

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Geodesy is interested in positioning points on the surface of the earth. For a layman “Positio “Position” n” mean means s where were are… In geodesy, it has a more detailed meaning and involves several technical and mathematical considerations… In geodesy, a position is a result of a measurement method on the surface of the earth based on a certain coordinate system and a reference model for the earth’s surface. GE 161 161 – – Geometric Geodesy

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Concepts in Geodesy: Position, Position, Positioning Positioning Modes, Modes, and the Geodetic Models

A A Coordinate Coordinate System System and and A A Reference Reference Model Model • A position cannot be expressed using a single quantity. • It is expressed in two or more quantities or parameters, called the “coordinates coordinates”” of a po poin int. t. • The coordinates of a point is based upon a certain coordinate system. • In geodesy, there are several coordinate systems being used from which the position of a point on the surface of the earth is being referred. Lecture 3

Example of a Coordinate System

GE 161 161 – – Geometric Geodesy


Coordinate Coordinate Systems Systems and and Reference Reference Model Model •

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A coordinate system is then needed neede d to be “put-o “put-on” n” a model that closely fits the surface of the earth. In geometric geodesy, the earth is represented by an ellipsoid of revolution whose dimensions fits closely the surface of the earth. This ellipsoid of revolution is known as the reference ellipsoid (other older literature termed this as “spheroid”). The coordinate system and the reference system are the essential components of a reference framework.

The earth, the reference ellipsoid, and its coordinate systems



Different Different Positioning Positioning in in Geodesy • There are several positioning modes in the realm if geodesy: 1. Point Positioning 2. Relative Positioning 3. Kinem Kinematic atic Posit Positioni ioning/N ng/Navig avigation ation • Each positioning mode can be done using one or more surveying operations/methods operations/me thods by terrestrial, celestial, or orbital flatform. Lecture 3



Point Point Positioning Positioning •

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Point Positioning is the determination of the coordinates of points based on a fixed object not lying on the terrestrial surface. It is not possible to determine either 3D either 3D or 2D (horizontal) positions of isolated points on the earth surface by terrestrial means. For point positioning we must be looking at celestial objects, objects , meaning that we must be using either optical techniques to observe stars (geodetic (geodetic astronomy), astronomy ), or electronic/optical techniques to observe earth’s artificial satellites (satellite positioning). positioning ). GE 161 161 – – Geometric Geodesy


Relative Relative Positioning Positioning • It is the process of positioning of a point with respect to an existing point or points. • This mode of positioning is the preferred mode in geodesy. • The classical terrestrial techniques for 2D relative positioning make use of angular (horizontal) and distance measurements, which always involve two or three points.

Triangulation

Geodetic Traverse Lecture 3



Relative Relative Positioning Positioning • In geodetic astronomy, relative positioning is radioastronomical observations of quasars. • In satellite surveying, relative positioning is done by observing a set of satellites from two locations simultaneously.

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Kinem Kinematic atic Posit Positionin ioning g and Nav on Kinematic Kinematic Positioni Positioning ng and Navigati Navigati Navigation igation on • As we have seen so far, classical geodetic positioning deals with stationary points (objects). • In recent times, however, geodetic positioning has found its role also in positioning moving objects, objects, such as ships, aircraft and cars. • This application became known as kinematic positioning,, and it is positioning understood as being the real-time positioning part of navigation.. navigation Lecture 3



Kinem Kinematic atic Posit Positionin ioning g and Nav on Kinematic Kinematic Positioni Positioning ng and Navigati Navigati Navigation igation on • The velocity vector can vector can be measured on the moving vehicle in relation to the surrounding space,, or in relation to an inertial coordinate space system by an inertial positioning system. system. • Alternatively, optical astronomy or point satellite positioning produces directly the string of positions, that describe the required trajectory of the vehicle, without the necessity of integrating over velocities. • Relative satellite positioning is also being used for kinematic kinematic posi positio tionin ning. g. Lecture 3



Coordinate Coordinate Systems Systems Recall… • Position of a point is described by two or more coordinates based on a certain coordinate system… •

There are general types of coordinates systems: According to the parameters used: 1. Rectilinear Type of Coordinate System 2. Curvilinear type of Coordinate System According to the surface/space dimension used: 1. Linear (One-Dimension) Coordinate System 2. Planar (Two-Dimensional) Coordinate System 3. Space (Three-Dimensional) Coordinate System

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Coordinate Coordinate Systems Systems • In geodesy, we are concern on positioning points on the three-dimensi three-dimensional onal surface of the earth which can be represented in a two-dimensional or or three-dimensional three-dimensional geodetic models. • In the study of geodesy, coordinate system is under both rectilinear and curvilinear type on a planar or threedimensional surface. Lecture 3



Coordinate Coordinate Systems Systems In studying Geometric Geodesy, three coordinate systems are commonly in use: 1. The Cartesian-Space Rectangular Coordinate System 2. The Geodetic Coordinate System 3. The Map-Grid Coordinate System

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Cartesian-Space Cartesian-Space Rectangular Rectangular Coordinate Coordinate System System • a rectilinear type of coordinate coord inate system on a three-dimensional surface where the position of the points is expressed as coordinates of a rightGreenwich handed orthogonal meridian system whose origin coincides with the center of the ellipsoid, ellipsoid, XZ-plane XP defines the zero meridian and XY plane defines the equator X • Uses (X,Y,Z) as its coordinate components Lecture 3


Z ZP

Point P

YP

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Equator

Space-Rectangular Coordinate System Concepts in Geodesy: Position, Position, Positioning Positioning Modes, Modes, and the Geodetic Models

Geodetic Geodetic Coordinate Coordinate System System • a curvilinear type of coordinate system on three-dimensional space which uses a an surface to define the position of point on the earth. • This coordinate system also uses three parameters to define the position of a point: 1. Geodetic latitude (φ): the angle between the ellipsoid normal through the point and the equator. (0≤ φ ≤ 90N or S) 2. Geodetic Longitude (λ): the angle in the equatorial plane between the zero meridian and the meridian of the point. (0 ≤ λ ≤180E or W) 3. Ellipsoidal height (h) height (h):: the distance along the normal from the surface of the ellipsoid to point P. Lecture 3

Geodetic Coordinate System



Geodetic Geodetic vs. vs. Geographic Geographic Coordinates Coordinates •

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In many mapping textbooks, we will often find that (φ, λ) is referred as geographic coordinates of a point. We need to be aware of the difference between geodetic coordinates and geographic coordinates. Geographic coordinates are general position of points on the surface of the earth used basically in mapping. In geodesy, geographic coordinates can be either geodetic coordinates or or natural natural coordinates

Geographic Coordinates (φ, λ )

Geodetic Coordinates

Natural Coordinates

(φ, λ )

(Φ, ∆)



Map-Grid Map-Grid Coordinate Coordinate System System •

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A rectilinear type of coordinate system on a planar surface where the horizontal position of a point is define The idea of which is to make the curved surface of the Earth by some mathematical transformation (map projection) into a plane. It uses basically two parameters to define the position of a point: 1. Northing, N 2. Easting, E The third component of the position of a point which is the t he Elevation becomes an attribute in this coordinate system GE 161 161 – – Geometric Geodesy


The The Geodetic Geodetic Models Models of of the the Earth Earth • Position of points on the surface of the earth can now be represented into what we call a geodetic model. • A geodetic model is a scheme/system into which a position of points are process to come up with a geodetic reference system/network. system/network. • There are two geodetic models of the earth being used in geodesy. 1. The Two-Dimensional Geodetic Model 2. The Three-Dimensional Geodetic Model Lecture 3



The The Two-Dimensional Two-Dimensional Geodetic Geodetic Models Models • In a two-dimensional geodetic model, the stations/points are parametized in terms of geodetic latitude and longitude or mapping coordinates, coordina tes, Northi Northings ngs and Eastings Eastings.. • The third dimension, the height height,, does not appear explicitly as a parameter. • Computations on the ellipsoid and the conformal mapping are inherently two-dimensional. • This type of geodetic models produces two separate geodetic networks: the “horizontal” and the “vertical” network.

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The The Three-Dimensional Three-Dimensional Geodetic Geodetic Model Model • The advent of satellite positioning (GPS), breaks the separation of a geodetic network into horizontal and vertical. • Since GPS can provide accurate three dimensional position, one can create a network based on a three-dimensional model using a space rectangular coordinate system. system. • A three-dimensional geodetic model is one that represents the position of points on the surface of the earth using three parameters that can be separated.. separated Lecture 3



Conclusion Conclusion • Positioning of points is one major interest in geodesy. • There are several modes of positioning in geodesy which each branch deals with. • Coordinate system and reference ellipsoid are essential in a reference framework for positioning points. • Geometric geodesy provides the knowledge in coordinate system, reference ellipsoids and the computation of position on a reference framework. Lecture 3



References: References: • National Imagery and Mapping Agency (NIMA), Geodesy for the Layman (online) • Vanicek, P., An P., An Online Tutorial on Geodesy (online), Geodesy (online), University of Brunswick, Canada • Leick, A., GPS Surveying 3rd Edition

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