COORDINATE TRANSFORMATIONS

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CO-ORDINATE TRANSFORMATIONS CONVERSIONS TO
ITRF/WGS84
CHARLES L MERRY SCHOOL OF ARCHITECTURE,
PLANNING GEOMATICS UNIVERSITY OF CAPE TOWN
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• INTRODUCTION

• Existing control points, cadastral and
  engineering data, GIS data and maps will
  all need to be converted to the new datum
  from the local datum
• Datum transformation parameters can be
  deduced by tying AFREF points to the local
  network
• Co-ordinate and map conversion will need
  additional common points to obtain better
  precision

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• THREE DIMENSIONAL TRANSFORMATION

• Cartesian Co-ordinate System three
  translations, three rotations, scale

Known as 3D Similarity 3D Helmert Bursa
Bursa-WolfSeven-parameter
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• 3D TRANSFORMATION - 2

• STEPS

• Convert local datum f, l, h to X, Y, Z
• Apply rotations, scale, translations Local
  ?WGS84
• Convert WGS84 X, Y, Z to f, l, h

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• 3D TRANSFORMATION PROBLEMS

• Problem 1 If common points in a small area
  are used to determine the parameters,
  they become highly correlated
• Problem 2 For a country, one set of
  transformation parameters is inadequate to
  model all the distortions in the old
  networks

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• MOLODENSKY 3D TRANSFORMATION

• Remove and restore centre of gravity
• Decorrelates translations from rotations
  and scale
• (also Veis model)

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• TRANSLATIONS ONLY

• No correlation problem
• Low accuracy if single set used for
  entire country, or even a portion of a
  country

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• HEIGHT ISSUE

• X, Y, Z derived from f, l, h (h
  ellipsoidal height)
• How is h obtained on local datum? h
  H N
• Geoidal height N must refer to local datum,
  not WGS84
• To transform NWGS84 to Nlocal requires datum
  transformation parameters, which are not
  yet known!

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• HEIGHT ISSUE - 2

• Solution 1 Ignore geoid, set h H. Derived
  parameters will be valid for f, l , not
  for heights.
• Solution 2 Take GPS measurements at datum
  initial point (where N 0) then
  calculate provisional transformation
  parameters apply these to transform
  WGS84 geoid to local datum calculate parameters
  at all points.

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• DIFFERENTIAL FORMULA

• Vening-Meinesz / Abridged Molodensky

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• 2D CO-ORDINATE CONVERSION

• Only f, l (or E, N) converted
• High accuracy
• Two forms

• Mathematical formulae
• Interpolation on a grid

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• MATHEMATICAL FORMULAE

• 2D Similarity (Helmert) transformation
• Affine transformation
• Algebraic polynomial / Multiple Regression
  Equations
• Minimum curvature / Bicubic splines
• Collocation

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• INTERPOLATION ON A GRID

• For each common point determine df, dl (dE,
  dN)
• Interpolate corrections onto a regular grid
• For any new point, interpolate corrections
  from this grid
• Needs many common points

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• RESOURCES / EXAMPLES 1

• NIMA TR8350.2, Third Edition (3D
  translations, multiple regression equations)
• EPSG Database - use with caution! (3 -
  7 parameter transformations)
• Hartebeesthoek 94 pamphlet (3D
  translations, 2D Helmert transformation)

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• GRID INTERPOLATION

• NADCON (USA ) (grid formed using
  minimum curvature)
• NTv2 (Canada Australia) (grid formed
  using collocation interpolation on a variable
  grid)
• OSTN02 (United Kingdom) (grid nodes
  computed using affine transformation)
• Orion (South Africa) (grid nodes
  computed using similarity transformation)

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• SUMMARY

• For low accuracy applications, use averaged
  translation components
• For small areas, where sufficient data exist,
  use local translation components or 2D
  similarity transformation
• For high accuracy, where sufficient data
  exist, use grid interpolation