Lecture 18

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a.s. caparas/06a.s. caparas/06

GE 161 – Geometric Geodesy

Lecture 18

Department of Geodetic EngineeringUniversity of the Philippines

Datum TransformationDatum TransformationDatum Transformation

Geodetic Datum and Geodetic Reference SystemsGeodetic Datum and Geodetic Reference Systems

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Datum Transformation Datum Transformation

changing the coordinates of a point from one datum to another while in the same coordinate system is called datum transformation.

Example:(X, Y, Z) WGS84 (X, Y, Z)PRS92

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Coordinate ConversionCoordinate Conversion

changing the coordinates of a point from one coordinate system to another while in the same datum is called coordinate conversion.

Example:(φ, λ, h)PRS92 (X, Y, Z)PRS92

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Different Transformation Different Transformation MethodsMethods• Transformation of coordinate frames may be

classified as:1. First Order Transformation (Linear)2. Second Order Transformation (Quadratic)3. Third Order Transformation (Cubic)4. Nth Order Transformation involves warping or

rubber-sheeting of the input coordinate frame

Parallel lines remain parallel after the transformation

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Different Transformation Different Transformation MethodsMethods• In datum transformation, the first order

transformation method is usually being employed.

• Among the first order transformation methods (which includes Affine, Hermert, etc.), it is the Affine transformation which is usually being used to perform datum transformation.

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Affine Transformation MethodAffine Transformation Method

• In the Affine transformation, a coordinate frame id being transform using different transformation parameters which includes:

1. Translation Parameters2. Rotation Parameters3. Scale Parameters

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Translations ParametersTranslations ParametersMovement of points along an Axis

∆X ∆Y

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Rotations ParametersRotations ParametersMovement of points around an Axis

ε ψ

ω

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Scale ParameterScale ParameterChanging the distance between points

S

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Methods of Datum Methods of Datum TransformationTransformation1. Three-Parameter Transformation• Simplest among the transformation

methods• Uses three parameters only for

translating the origin of one datum to another.

• Assumes conformity in the orientation and size of the reference ellipsoid.

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Methods of Datum Methods of Datum TransformationTransformation2. Molodensky’s Formulae• often used in handheld GPS receivers and GIS

softwares• uses 5 parameters: 3 for the shift between the

centers of the 2 ellipsoids (∆X, ∆Y, ∆Z) and 2 for the differences in semi-major axes and flattening (simple subtraction)

• simple derivation and application• assumes internally consistent networks• limited accuracy: 5 meters• requires ellipsoidal heights

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Methods of Datum Methods of Datum TransformationTransformation

3. Bursa-Wolfe Seven Parameter Transformation• uses 7 parameters: 3 translation(∆X, ∆Y, ∆Z), 3 rotation

(RX, RY and RZ) and 1 scale (Sc)• parameters are derived by observing at least 3 points or

more in two datums and doing a least-squares fit• accuracy: 1 to 2 meters• requires ellipsoidal heights• accuracy limited by network consistency• used in the Philippines and in many GIS packages.

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Methods of Datum Methods of Datum TransformationTransformation

translation

rotationDatum A

Datum B

scale

3. Bursa-Wolfe Seven Parameter Transformation

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

3. Bursa-Wolfe Seven Parameter Transformation

Methods of Datum Methods of Datum TransformationTransformation

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Methods of Datum Methods of Datum TransformationTransformation4. Surface Fitting/Grid Distortion Modeling (Higher Order

Transformation)• many points are observed (preferably in grid formation) in

both datum to generate a surface of distortion (like a contour map), one for latitude and another for longitude

• distortion between the two systems for points in between grid lines are interpolated

• accuracy: 0.1 m or 10 cm (can be better if more points are observed)

• very complex to derive and many points are needed to be observed to accurately model network inconsistencies

• also known as Minimum Curvature Method (USA), Multiple Regression Method (Canada) & Collocation Method

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Differences Between Horizontal Differences Between Horizontal DatumsDatums

• The two ellipsoid centers called ∆ X, ∆ Y, ∆ Z • The rotation about the X,Y, and Z axes in seconds of arc• The difference in size between the two ellipsoids• Scale Change of the Survey Control Network ∆S

Z

Y

X

System 1WGS-84

System 2NAD-27

∆X

∆ Z∆ Y

ω

ψε

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

77--Parameters TransformationParameters Transformation

∆X∆Y∆Z

S Rxyz +X’Y’Z’

=XYZ

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

33--ParametersParameters

∆X∆Y∆Z

+XYZ

X’Y’Z’

=

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Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

Transformation ProcessTransformation Process

Reporting System(GEOREF)

ConversionGrid Coordinates

(UTM-coordinates)

Reporting System(Military Grid Reference System)

Conversion

Conversion

Geographic Coordinates (Latitude, Longitude, Height)

Grid Coordinates(TM-coordinates)

Reporting System(Irish National Grid)

Conversion

Conversion

DATUM (World Geodetic System 1984) DATUM (Ireland Datum 1965)

Reporting System(GEOREF)

Conversion

Conversion

Geographic Coordinates (Latitude, Longitude, Height)

Cartesian Coordinates (X, Y, Z)

Conversion

Cartesian Coordinates (X, Y, Z)7, 5, 3Parameter

Molodenskyand MRE

Transformations

Lecture 18Lecture 18 GE 161 GE 161 –– Geometric GeodesyGeometric GeodesyGeodetic Datum and Geodetic Reference Geodetic Datum and Geodetic Reference

Systems: Datum TransformationSystems: Datum Transformation

More Precise DeterminationMore Precise DeterminationLocal Control Points

in Local Datum

Local Control Pointsin WGS-84

Survey UsingWGS-84

Control Pointsin WGS-84

TransferControl

Derive TransformationParameters

Transform LocalPoints

Local Pointsin WGS-84

Standard Molodensky FormulaMultiple Regression Equations

7, 5, or 3 Parameter Transformation