Global Coordinate System

4 Key excerpts on "Global Coordinate System"

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  eBook - ePub

  Precision Surveying

  The Principles and Geomatics Practice

  • John Olusegun Ogundare(Author)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Three types of coordinating systems are discussed in this chapter: Coordinating with Global Navigation Satellite System (GNSS), the electronic coordinating system, and the terrestrial laser scanning system. Each method offers complementary advantages to surveyors and engineers; however, since the solution for real-time three-dimensional coordinates of remote points is central to most coordinating system applications, more emphasis will be placed on the electronic coordinating system and the terrestrial laser scanning system.

  An integral part of any coordinating system is a reference coordinate system, which must be well understood in order to properly use survey measurements for calculating positions (coordinates of points) and for solving difficult problems in geomatics. Coordinates can be simply defined as separations from a given origin, in certain directions or ordered values (x, y, z) in a given coordinate system. A coordinate system is a methodology or an idealized abstraction for defining the coordinates (or location) of a feature in space. In order for a coordinate system to be usable in locating a point in space, it must have an origin as well as properly defined reference directions for its axes. The coordinate system, therefore, specifies how coordinates are assigned to points (or locations) on the earth and its environment. When the origin and orientation of axes of the coordinate system are specified with regard to the earth, the coordinate system is known as a datum or a coordinate reference system. A datum, however, may be associated with a reference ellipsoid (on which measurements can be reduced for further computations) in addition to a coordinate system or the geoid (in the case of height system). There are three types of coordinate reference systems: one-dimensional coordinate reference systems, two-dimensional coordinate reference systems, and three-dimensional coordinate reference systems.

  The one-dimensional coordinate system is basically about height determination for points on the earth surface or near the earth surface. The determined heights, however, are only useful as one-dimensional coordinates if they are referenced to a well-defined origin or datum (e.g., the geoid) and if they have well-defined unit of measurement in a geometrical sense. In surveying, precise heights are determined from measured elevation differences.

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  eBook - PDF

  Computing in Geographic Information Systems

  • Narayan Panigrahi(Author)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  3 Reference Systems and Coordinate Transformations If geodesy is about modelling the Earth’s surface and shape, the coordinate system connects the model produced by geodesic modelling to a frame of ref-erence for measurement. The coordinate system or reference frame or frame of reference is a mathematical concept for imparting order to a distributed set of objects in sea, space or terrain. The frame of reference helps in conceptual-izing the location of the objects with respect to the common frame and with respect to its surroundings objects. A reference system is a mathematical con-cept for modelling the real world. This chapter starts with the mathematical definition of a coordinate reference system. Then we discuss different types of coordinate systems and their characterization, since the mathematical and computing aspects of GIS used to represent a point in the coordinate system are quite intriguing. Map projection and coordinate system are interrelated mathematically. A discussion on coordinate systems and map projections can be found in Maling [35]. 3.1 Definition of Reference System A reference system is defined by the following: 1. Origin of the reference system 2. The orthogonal or non-orthogonal directrix as reference frames with orientations with respect to each other. The dimension of the reference system is the number of directrix used to describe the objects. Therefore depending on the number of directrix in the reference frame the coordinate system can be classified as 1D,2D,3D,..,nD, where ‘D’ stands for dimension. Depending on the orientation of the coor-dinates with respect to each other they can be classified as orthogonal or non-orthogonal. The origin of the frame of reference can be fitted to a real world object such as planet Earth, the moon, a constellation of stars, space, the center of a city or a building etc. Also it can be attached to some known geometrical 35

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  eBook - ePub

  Geographical Information Systems and Computer Cartography

  • Chris B. Jones(Author)
  • 2014(Publication Date)
  • Routledge

    (Publisher)

  PART 2 Acquisition and Preprocessing of Geo-referenced Data Passage contains an image

  CHAPTER 4 Coordinate systems, transformations and map projections

  DOI: 10.4324/9781315846231-6

  Introduction

  The concept of position as defined by coordinate systems is essential both to the process of map-making and to the performance of spatial search and analysis of geographical information. To plot geographical features on a map, it is necessary to define the position of points on the features with respect to a common frame of reference or coordinate system. Having created such a frame of reference, it also provides a means of partitioning data for purposes of spatial indexing in a database. Thus the coordinate system can be used to guide a search through the database in order to determine which features occur in the vicinity of a point or a region expressed in terms of the coordinates. The coordinate systems that constitute the frames of reference necessary for mapping and searching geographical information allow us to specify position in terms of the distances or directions from fixed points, lines or surfaces (Figure 4.1 ). In Cartesian coordinate systems, positions are defined by their perpendicular distances from a set of fixed axes. The simplest and most familiar example is the case of two straight-line axes intersecting at right angles (Figure 4.1a ). In polar coordinate systems, positions are defined by their distance from a point of origin and an angle, or angles, which give direction relative to an axis or a plane passing through the origin (Fig 4.1c,d ).

  Figure 4.1 Cartesian and polar coordinate systems. Cartesian coordinates consist of distances measured relative to fixed axes. Polar coordinates consist of a distance from a fixed origin and an angle or angles representing direction relative to a fixed axis or to a fixed place.

  Positions on the earth's surface are normally defined by a geographical coordinate system consisting of degrees of latitude and longitude. This is a form of spherical polar coordinate system in which two angles are measured with respect to planes passing through the centre of a sphere or approximate sphere (spheroid) representing the shape of the earth (Figure 4.1d ). Distance is not specified in the coordinate system but it is implicit, being the radius of the earth at any given location on the surface. Because latitude and longitude refer to positions in 3D space, it is necessary for the purposes of cartography to transform them to a 2D planar coordinate system, or map grid. This type of transformation, which is called a projection, can be done in many different ways. The principal types of map projection transform from the earth's surface either directly to a plane, or to a cylindrical or a conical surface which, having been conceptually wrapped around the earth, can be unrolled to form a flat surface. When lines of latitude and longitude are plotted on the map they are referred to as a graticule (Figure 4.2

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  eBook - ePub

  Mobile Robots

  Navigation, Control and Sensing, Surface Robots and AUVs

  • Gerald Cook, Feitian Zhang(Authors)
  • 2020(Publication Date)
  • Wiley-IEEE Press

    (Publisher)

  4 Robot Navigation

  4.1 Introduction

  This chapter introduces the topic of navigation and the various means of accomplishing this. The focus is on Inertial Navigation Systems (INS) (gimbaled and strap‐down) and the Global Positioning System (GPS). Also, briefly discussed is deduced reckoning utilizing less sophisticated methodology.

  4.2 Coordinate Systems

  One definition of navigation is the process of accurately determining position and velocity relative to a known reference or the process of planning and executing the maneuvers necessary to move between desired locations. One important factor in navigation is an understanding of the different coordinate systems. Figure 4.1 shows a sphere representing the earth along with several coordinate frames. To minimize confusion, only the x and z axes are shown. The y axes in each case are such as to form right‐handed coordinate systems.

  4.3 Earth‐Centered Earth‐Fixed Coordinate System

  In Coordinate System I, the z axis points out the North pole, the x axis points through the equator at the prime meridian, and the y axis (not shown) completes the right‐handed coordinate frame. This set of axes is called the earth‐centered earth‐fixed axes (ECEF). As the name implies, this set of axes has its origin at the center of the earth and rotates with the earth. There is a unique relation between the ECEF coordinates of a point on the surface of the earth and its longitude, which is measured positively Eastward from the prime meridian running through Greenwich, England, and its latitude, which is measured positively Northward from the equator. Starting with latitude and longitude the X, Y, and Z in ECEF coordinates can be determined approximately assuming a spherical model of the earth of radius R and using the equations

  (4.1a)

  (4.1b)

  (4.1c)

  Figure 4.1

  Earth and several different coordinate frames.

  It should be pointed out that the earth is not a perfect sphere and that more precise models of its shape do exist. These more precise models account for the flatness of the earth, i.e., the fact that the radius at the poles, 6,356.7 km, is slightly less than the radius at the equator, 6,378.1 km. The spherical model is used in examples here for its simplicity in application.

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