Geodetic Surveying B SVY3107

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Geodetic Surveying BSVY3107

• Coordinate Transformations

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Learning Objectives

• After completing this lecture you will be able
  to
• Demonstrate the general process of 7 parameter
  datum transformations
• Explain why residual distortion grids are needed
  for accurate transformations

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Lecture Outline

• Background and Review of Terminology
• Coordinate Conversions
• Coordinate Transformations
• Block Shift
• Molodensky
• 7 Parameter
• Residual Distortions
• Conclusion

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Coordinates Systems
- X Y - Z ECEF Cartesian
Geodetic Coordinates
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Conversions XYZ ? ??h

• YES!!!
• You guessed it!

• We have a spreadsheet that will do these
  calculations for us!

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Ellipsoids and Geoids
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AGD - The Old Datum

• Terrestrial Observations
• Systematic Errors
• Constrained by Doppler (transformed)
• Distribution
• Homogeneity
• Location of Marks

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GDA

• GPS Observations
• Small Random Errors
• Constrained by GPS
• Distribution
• Homogeneity
• Marks are Accessible

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GDA and the ITRF
Link to ITRF by GPS observations at IGS sites and
the Australian National Network (500km). GDAs
link to ITRF makes it compatible with WGS84
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Universal Transverse Mercator Projections
Scale Factor 0.9996
ZONE 55
ZONE 54
ZONE 56
6o wide zones
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UTM Coordinates
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Australian Terminology
GDA Datum
AGD Datum
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Coordinate Transformations

• Block Shift
• Molodenskys formulae
• 7 Parameter transformation
• Distortion Modeling (Surface interpolation)
• Height is not critical!

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Block shift Transformation
GDA94
Accuracy 10 m
AGD66
AGD84
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Molodenskys Formulae
GDA94
Accuracy 5 m
AGD66
AGD84
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Molodenskys Formulae

• National AGD66 AGD84 parameters
• No coordinate conversion required
• Simple formulae
• Accuracy 5 m
• Assumes no rotations (4 parameter)

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General Form ofDatum Transformation

• 3 Directional Translation (dX, dY, and dZ)
• 3 Rotations (about X, Y and Z axes)
• 3 Scale Errors (X, Y and Z directions)
• 3 Shear Distortions
• Total of 12 parameters
• Ignore Shear and use similarity transformation
  7 parameters

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7 Parameter Transformation

• 7 Parameters 3 Origin Shifts, 3 Rotations and 1
  Scale

Z

• 3D Transformation between AGD84 and GDA94
• Use published parameters
• 2-3 metre accuracy

Y
X
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AGD84 to GDA94
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7 Parameter Transformation
GDA94
Accuracy 2-3 m
AGD66
AGD84
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7 Parameter Transformation

• National AGD84 parameters
• Accuracy 2-3 m
• Also some regional AGD66 parameters (NSW, ACT
  Tasmania)

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Spreadsheets for Calculations
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7 Parameter Transformation
Bowrings or Bomfords Formula, or similar
Redfearns Formula
GRS 80
ANS
UTM
UTM
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Calculating the 7 Parameters
Not recommended!
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Distortions between Transformed AGD84 and GDA94
Western Qld
Central Coast
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Summary of Accuracy
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Distortion Grid
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Distortion Modelling (Surface Interpolation)

• Accuracy 5 cm
• Based on State/Territory subsidiary positions
• Can include distortion modeling
• Complex calculations
• For simple interpolation, a standard, national
  grid of accurate shifts is available - GDAy

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NTv2 Grid Format

• In use bymany some software packages
• (e.g. ArcInfo)
• Variable grid density
• Can be extended as required

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GDAy
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Practical Problem
AGD Base
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Conclusion

• You can now
• Demonstrate the general process of 7 parameter
  datum transformations
• Explain why residual distortion grids are needed
  for accurate transformations

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Self Study

• Read relevant module in Study Book

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Review Questions