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Geodetic Surveying B SVY3107

Geodetic Surveying B SVY3107. Coordinate Transformations. 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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Geodetic Surveying B SVY3107

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  1. Geodetic Surveying BSVY3107 Coordinate Transformations

  2. 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

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

  4. Z Semi-minor axis (b) Semi-major axis (a) X Y f l Geodetic Coordinates h Coordinates Systems - X + Y - Z ECEF Cartesian Geodetic Coordinates

  5. ConversionsXYZ h • YES!!! • You guessed it! • We have a spreadsheet that will do these calculations for us!

  6. Geocentric Datum (best fit globally) Local Datum AGD84 (best fits Australia) The Geoid (Mean Sea Level) Ellipsoids and Geoids

  7. AGD - The Old Datum • Terrestrial Observations • Systematic Errors • Constrained by Doppler (transformed) • Distribution • Homogeneity • Location of Marks

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

  9. GDA and the ITRF Link to ITRF by GPS observations at IGS sites and the Australian National Network (500km). GDA’s link to ITRF makes it compatible with WGS84

  10. 144o 147o 150o Universal Transverse Mercator Projections Scale Factor 0.9996 ZONE 54 ZONE 55 ZONE 56 6o wide zones

  11. NMGA NAMG EAMG EMGA UTM Coordinates

  12. GDA94 AGD84 Latitudes, Longitudes & heights ? ANS GRS80 Australian Terminology GDA Datum AGD Datum

  13. Coordinate Transformations • Block Shift • Molodensky’s formulae • 7 Parameter transformation • Distortion Modeling (Surface interpolation) • Height is not critical!

  14. Block shift Transformation GDA94 Accuracy ~ 10 m AGD66 AGD84

  15. Molodensky’s Formulae GDA94 Accuracy ~ 5 m AGD66 AGD84

  16. Molodensky’s Formulae • National AGD66 & AGD84 parameters • No coordinate conversion required • Simple formulae • Accuracy ~ 5 m • Assumes no rotations (4 parameter)

  17. Z Z Y Rz Y Ry Dz Dx Dy X Rx X 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

  18. Z Y RZ RY DZ DX DY X RX 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

  19. 7 Parameter Transformation GRS80/GDA ECEF - XYZ ANS/AGD Bowring’s or Bomford’s Formula, or similar GDA94 AGD84 Latitudes, Longitudes & heights ? ANS GRS80 AGD84 to GDA94

  20. 7 Parameter Transformation GDA94 Accuracy ~ 2-3 m AGD66 AGD84

  21. 7 Parameter Transformation • National AGD84 parameters • Accuracy ~ 2-3 m • Also some regional AGD66 parameters (NSW, ACT & Tasmania)

  22. 2. Change Datums 1. Reverse sign for reverse calculations Spreadsheets for Calculations

  23. Latitudes, Longitudes & h XYZ AGD84 ANS GDA94 GRS80 Eastings, Northings & Zone (maybe RL) AMG84 MGA94 7 Parameter Transformation Bowring’s or Bomford’s Formula, or similar Redfearn’s Formula GRS 80 ANS UTM UTM

  24. Calculating the 7 Parameters Not recommended!

  25. Distortions between Transformed AGD84 and GDA94 Western Qld Central Coast

  26. abt. 5cm True GDA 2-3 metres Shift determined from Distortion Modelling (Most of what’s left) Shift determined from 7 Parameter Transformation (most of 200m shift) abt.190 metres True AGD abt. 110 m Summary of Accuracy

  27. Component in E-W Direction Differences between GDA94 derived from AGD84 and TRUE GDA94 Component in N-S Direction Distortion Grid

  28. 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

  29. NTv2 Grid Format • In use bymany some software packages (e.g. ArcInfo) • Variable grid density • Can be extended as required

  30. GDAy

  31. AGD Rover ReverseDodgy Dodgy Dodgy may not be good enough GPS Baseline DX DY DZ WGS84 Base WGS84 Rover True WGS84/GDA94 Rover True WGS84/GDA94 Base Practical Problem AGD Base

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

  33. Self Study • Read relevant module in Study Book

  34. Review Questions

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