451617 Fundamentals of Positioning Technologies

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451-617 Fundamentals of Positioning
Technologies Lecture 2 Geodetic Datums and Map
Projections http//www.colorado.edu/geography/gcr
aft/notes/coordsys/coordsys_f.html http//www.colo
rado.edu/geography/gcraft/notes/mapproj/mapproj.ht
ml
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At the end of this lecture students should know

• How to interpret coordinates described in
  different coordinate systems.
• What is a projection.
• What is a datum.
• Different ways of representing the shape of the
  Earth.
• The relationship between datums, projections and
  coordinate systems
• What are conversions and transformations and why
  are they necessary.
• The coordinate systems, datums and projections
  used in Australia.

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Why?

• Until recently in-depth knowledge of datums were
  confined to geodesists.
• Developments in GIS, GPS and remote sensing
  techniques have changed the way in which we
  acquire data.
• More data available, more people have the means
  and the need to use it.
• Combining data sets now a big problem.

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Typical problems

• Geo-referencing a satellite image with ground
  control points that have been established using
  GPS, and with others that have been obtained from
  a published map.
• Combining digital map data from two different
  survey organisations, for example as part of a
  cross-border collaboration between neighboring
  states.
• Carrying out a survey with high precision GPS and
  bringing it into sympathy with existing mapping
  in a local coordinate system.
• Using handheld GPS receivers on charts prepared
  in a local datum

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Datums
The height of the point is 3.122m The height
above mean sea level is 10.983m The latitude is
32o 10 12.23 The northings of a point are 152
345.834
A datum is a framework that enables us to define
coordinate systems. The framework includes a
definition of the shape of the Earth
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Handling spatial data
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What is a coordinate system?

• In this map, the Blue Lake is located by the
  reference Page 10, D8. This kind of system is
  used in street directories and defines only the
  grid square in which the feature exists. Though
  the coordinate system is repeated on each page,
  by specifying the page number each grid is
  uniquely identified.

• For map reading purposes, an infinite combination
  of lines can be used to divide Australia up into
  equal portions. A common example of a division of
  this kind is the local street directory. Street
  directories use sets of evenly spaced lines,
  known as a coordinate system, to break large
  areas of land into parcels. By giving each
  portion a reference marker in the north-south and
  east-west direction as well as a unique page
  number, features in the directory can be
  identified more efficiently as the area in which
  the feature exists is much smaller.

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What is a coordinate system?

• In this map, the Blue Lake is located by the
  reference 472 500E, 5 802 500N. Though the system
  is more complex it allows features to be located
  more exactly by interpolating coordinate values
  in both directions. Like a street directory, the
  coordinate system is repeated but instead of on
  each page, it is only between zones.

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The coordinate system in Australia

• In Australia, maps are divided into zones. Zones
  cover a much larger area than a single page in a
  Street Directory and are numbered according to a
  world wide convention. Australia is covered by
  zones 49 to 56, each zone covers 6 degrees of
  longitude. Zones are related to the Universal
  Transverse Mercator projection and used by many
  countries to map the Earth.
• The coordinate system used in Australia enables
  features to be pinpointed to a greater degree of
  accuracy than a Street Directory where a grid
  area, in which the feature exists, is defined
  rather than the feature itself. Street
  directories generally use a letter and a number,
  topographic maps use a consecutive range of
  numbers in both directions. The range of numbers,
  allows the position of features to be
  interpolated to much greater degree of accuracy.

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The coordinate system in Australia
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The coordinate system in Australia

• The type of coordinates found in a street
  directory and on Australia's topographic maps are
  known as Cartesian Coordinates. Cartesian
  Coordinates are related to a line in the
  east-west direction, known as the X axis, and a
  line in the north-south direction, known as the Y
  axis.
• Movements by a point away from the axes are
  recorded as a set of two values, known as
  coordinates. Coordinates tell you how far away
  from the origin of the axes, that you are. By
  convention, the point's position is identified by
  quoting the distance along the X axis first, and
  distance along the Y axis second, thus each point
  has a unique name.
• These are the mathematical coordinates you find
  on a map. In cartography and surveying, the X
  axis coordinates are known as Eastings, and the Y
  axis coordinates as Northings.

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Cartesian Coordinates Grid Values X, Y, Z

• Cartesian Coordinates can define a point in
  space, that is, in three dimensions. To do this,
  another axis must be introduced. This axis will
  represent a height above the surface defined by
  the x and y axes. This new axis is known as the Z
  axis. For local 3D cartesian coordinate systems,
  the Z axis represents "up".

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Cartesian Coordinates Grid Values X, Y, Z

• This diagram shows the earth with two local
  coordinate systems defined on either side of the
  earth. The Z axis points directly up into the
  sky.
• These coordinates are read like the 2D Cartesian
  System only there is now an extra coordinate in
  the direction of Z instead of (X,Y) it is
  (X,Y,Z).

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The coordinate system in Australia

• The new cartesian coordinate system that is used
  in Australia is known as the Map Grid of
  Australia 1994 (MGA94).The cartesian system that
  is being phased out is called the Australian Map
  Grid, there are two versions of the coordinates
  from this system, the originals from 1966 and
  their subsequent update in 1984 AMG66/84.

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Geographic Coordinates - Longitude and Latitude

• Lines of longitude intersect both the North and
  South poles. They are numbered using degrees
  beginning at the Royal Greenwich Observatory in
  England, which is designated as 0, and continue
  both East and West until they meet at 180.Lines
  of latitude are measured as an angle from the
  equator (0) to either Pole, 90 South and 90
  North. The equator is a line of
  latitude.Latitude and longitude are collectively
  known as geographic coordinates.
• So any point on the earth's surface can have a
  set of geographic coordinates and a corresponding
  set of cartesian coordinates.

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Geodetic Coordinates - Longitude and Latitude
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As with Cartesian coordinates, one point on the
earth can have many different geographic/geodetic
coordinates assigned to it, depending on how the
shape of the Earth (reference system) was
defined. The Geocentric Datum of Australia
(GDA94) will have longitude and latitude values
that relate to a reference surface called the
Geodetic Reference System 1980 GRS80.
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Figures of the Earth
The terrestrial surface refers to the earth's
topography. It is very complex with mountain
ranges and oceans and it is the surface upon
which we live and measure. Because the earth is
not even, it is not suitable for exact
mathematical computations.
The first simplification estimates the earth's
surface using mean sea level of the ocean with
all continents are removed - this surface is
called the Geoid. Due to variations in the
earth's mass distribution (oceans and land), the
Geoid has an irregular shape that is described as
"undulating". It is an equipotential surface.
This means that potential gravity is the same at
every point on its surface.
The ellipsoid can be further simplified into a
sphere. To define a sphere, only the radius is
required. The radius often used when modeling the
earth as a sphere is 6371 000 meters. This shape
is a close approximation of the earth's shape and
is a suitable approximation for most
applications.
Measurements have shown that the earth is in fact
slightly "squashed" at the poles and bulges at
the equator due to forces acting upon whilst it
spins. Mathematically this shape is described as
an ellipsoid of revolution, an oval that revolves
about its shortest dimension. It is a
mathematical approximation of the Geoid. This
shape is used for exact measurements over long
distances, across continents or oceans.
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Geodetic Datums

• Geodetic datums define the reference systems that
  describe the size and shape of the earth, and the
  origin and orientation of the coordinate systems
  used to map the earth.

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Why did we change Datums in Australia?
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Why did we change Datums in Australia?

• compatibility with satellite navigation systems,
  such as the Global Positioning System (GPS)
• compatibility with national mapping programmes
  already carried out on a geocentric datum,
• single standard for the collection, storage and
  dissemination of spatial information at global,
  national and local levels.

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The geoid
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Map projections

• World globes are a good estimation of the earth's
  surface but their scale is too small to allow you
  to plan trips across town. A flat map of the
  region that we can fold up and put in our pocket
  is more functional.
• To convert the round earth to flat map is
  complicated. The best way to illustrate the
  difficulty in doing this is by thinking of the
  earth as a rubber ball with the land and water
  painted on it. To flatten the rubber ball into a
  flat square we need to cut it up and stretch it.
  Because the rubber ball is being stretched, the
  land shown on it will be distorted from its
  original shape.This same, cutting and
  stretching process is used to make maps through
  mathematical formulae called 'Projections'.
  Projection formulae take the geographic
  coordinates from the spherical earth (longitude
  and latitude) and convert them to cartesian
  coordinates (X Y). There are many projection
  formulae that can be used and consequently maps
  can look very different.

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The ideal map

• Areas on the map would maintain correct
  proportion to areas on the Earth
• Distances on the map would remain true to scale
• Directions and angles on the map would remain
  true
• Shapes on the map would be the same as on the
  Earth

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Map Projections
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Type of geographical representation

• Equidistant - correct representation of distances
  (generally in one direction only)
• Equivalent - correct representation of area
• Conformal - correct representation of shapes

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Developable surfaces
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Most projections are classified firstly according
to the shape of the developable surface, which is
dictated by the geographical area to be mapped,
but also in part by the function of the map, and
secondly by the features on the sphere which are
to be preserved on the projection
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So how does this all fit together?
E, N, h coordinates
f, l, h coordinates
X, Y, Z coordinates
projection
conversion
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Example
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• Name Australian Geodetic Datum (AGD66/84)
• Ellipsoid Australian National Spheroid (ANS)
• Map Grid UTM projection, Australian Map Grid
  (AMG)

• Name Geocentric Datum of Australia(GDA94)
• Ellipsoid Geodetic Reference System (GRS80)
• Map Grid UTM projection, Map Grid of Australia
  (MGA)

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At the end of this lecture students should know

• How to interpret coordinates described in
  different coordinate systems.
• What is a projection.
• What is a datum.
• Different ways of representing the shape of the
  Earth.
• The relationship between datums, projections and
  coordinate systems
• What are conversions and transformations and why
  are they necessary.
• The coordinate systems, datums and projections
  used in Australia.