2. Geodetic Surveying B SVY3107 Coordinate Transformations

3. Learning Objectives After completing this lecture you will be able to: zDemonstrate the general process of 7 parameter datum transformations zExplain why residual distortion grids are needed for accurate transformations

4. Lecture Outline zBackground and Review of Terminology zCoordinate Conversions zCoordinate Transformations yBlock Shift yMolodensky y7 Parameter yResidual Distortions zConclusion

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

6. Conversions XYZ   h zYES!!! zYou guessed it! zWe have a spreadsheet that will do these calculations for us!

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

8. AGD - The Old Datum zTerrestrial Observations zSystematic Errors zConstrained by Doppler (transformed) zDistribution zHomogeneity zLocation of Marks

9. GDA zGPS Observations zSmall Random Errors zConstrained by GPS zDistribution zHomogeneity zMarks are Accessible

10. 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 GDA and the ITRF

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

12. UTM Coordinates N AMG N MGA E MGA E AMG

13. Australian Terminology Latitudes, Longitudes & heights ANSAGD84 GRS80GDA94 ? GDA Datum AGD Datum

14. zBlock Shift zMolodensky’s formulae z7 Parameter transformation zDistortion Modeling (Surface interpolation) zHeight is not critical! Coordinate Transformations

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

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

18. zNational AGD66 & AGD84 parameters zNo coordinate conversion required zSimple formulae zAccuracy ~ 5 m zAssumes no rotations (4 parameter) Molodensky’s Formulae

19. General Form of Datum Transformation z3 Directional Translation (dX, dY, and dZ) z3 Rotations (about X, Y and Z axes) z3 Scale Errors (X, Y and Z directions) z3 Shear Distortions zTotal of 12 parameters zIgnore Shear and use “similarity” transformation = 7 parameters Y X Z Y X Z Dx Dy Dz Rx Ry Rz

20. 7 Parameter Transformation z7 Parameters : 3 Origin Shifts, 3 Rotations and 1 Scale Y X Z Y X Z XX YY ZZ RX RY RZ 3D Transformation between AGD84 and GDA94 Use published parameters 2-3 metre accuracy

21. AGD84 to GDA94 ANS/AGD Bowring’s or Bomford’s Formula, or similar ECEF - XYZ GRS80/GDA 7 Parameter Transformation Latitudes, Longitudes & heights ANSAGD84GRS80GDA94 ?

22. 7 Parameter Transformation Accuracy ~ 2-3 m GDA94 AGD84 AGD66

23. zNational AGD84 parameters zAccuracy ~ 2-3 m zAlso some regional AGD66 parameters (NSW, ACT & Tasmania) 7 Parameter Transformation

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

25. GDA94AGD84 Latitudes, Longitudes & h AMG84MGA94 Eastings, Northings & Zone (maybe RL) Redfearn’s Formula GRS80ANS XYZ Bowring’s or Bomford’s Formula, or similar UTMUTM ANS GRS 80 7 Parameter Transformation

26. Calculating the 7 Parameters Not recommended!

27. Distortions between Transformed AGD84 and GDA94 Western QldCentral Coast

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

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

30. Distortion Modelling (Surface Interpolation) zAccuracy ~ 5 cm zBased on State/Territory subsidiary positions zCan include distortion modeling zComplex calculations zFor simple interpolation, a standard, national grid of accurate shifts is available - GDAy

31. NTv2 Grid Format zIn use by many some software packages (e.g. ArcInfo) zVariable grid density zCan be extended as required

32. GDAy

33. Practical Problem AGD Base WGS84 Rover GPS Baseline  X  Y  Z WGS84 Base Dodgy AGD Rover Reverse Dodgy Dodgy may not be good enough True WGS84/GDA94 Base True WGS84/GDA94 Rover

34. Conclusion You can now: zDemonstrate the general process of 7 parameter datum transformations zExplain why residual distortion grids are needed for accurate transformations

35. Self Study zRead relevant module in Study Book

36. Review Questions