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Geodetic Surveying B SVY3107 Coordinate Transformations

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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

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

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

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

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

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

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

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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

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

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UTM Coordinates N AMG N MGA E MGA E AMG

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

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

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Block shift Transformation GDA94 AGD84 AGD66 Accuracy ~ 10 m

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Molodensky’s Formulae Accuracy ~ 5 m GDA94 AGD84 AGD66

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

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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

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

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

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

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

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

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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

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Calculating the 7 Parameters Not recommended!

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Distortions between Transformed AGD84 and GDA94 Western QldCentral Coast

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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

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

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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

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

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GDAy

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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

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

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Self Study zRead relevant module in Study Book

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Review Questions

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