Procedure for GPS Height TransformationProcedure for GPS Height Transformationwithin a Small Local Areawithin a Small Local Area

SatRef - Knowledge Sharing SatRef - Knowledge Sharing PlatformPlatform

JAMES WONG, LS/G(NT)JAMES WONG, LS/G(NT)

SatRef - Knowledge Sharing PlatformSatRef - Knowledge Sharing Platform

Purposes of this briefingPurposes of this briefing

• To share the knowledge of how to create a To share the knowledge of how to create a Localized Height Localized Height Transformation Parameter FileTransformation Parameter File for the transformation of for the transformation of GPS surveyed ellipsoidal height to HKPD Height in a small GPS surveyed ellipsoidal height to HKPD Height in a small area.area.

• To release the To release the height model data setheight model data set for the creation of the for the creation of the Localized Height Transformation Parameter File.Localized Height Transformation Parameter File.

Relationship between Ellipsoidal Height (GPS Relationship between Ellipsoidal Height (GPS Height) and Orthometric Height (Local Height)Height) and Orthometric Height (Local Height)

Current ProblemsCurrent Problems

• The existing 7-Parameter Set published by the Geodetic Survey The existing 7-Parameter Set published by the Geodetic Survey Section of SMO is used for the datum transformation between Section of SMO is used for the datum transformation between ITRF96 and HK1980 Geodetic Datums.ITRF96 and HK1980 Geodetic Datums.

• It is not used for transformation between the GPS surveyed It is not used for transformation between the GPS surveyed ellipsoidal height and orthometric height (local height).ellipsoidal height and orthometric height (local height).

• Hence, the problem is how to transform the GPS surveyed Hence, the problem is how to transform the GPS surveyed ellipsoidal height to orthometric height for the determination of ellipsoidal height to orthometric height for the determination of the local height for various applications.the local height for various applications.

• Actually, there is no high accuracy Geoid Model of Hong Kong for Actually, there is no high accuracy Geoid Model of Hong Kong for the determination of geoid-ellipsoid separation for the GPS height the determination of geoid-ellipsoid separation for the GPS height transformation.transformation.

Height Model Data

Height Model Data SetHeight Model Data Set

Which approach to useWhich approach to use

• This question is almost impossible to answer since the approach used will This question is almost impossible to answer since the approach used will depend totally on local conditions and information.depend totally on local conditions and information.

• If you wish to keep the GPS measurements totally homogenous and the If you wish to keep the GPS measurements totally homogenous and the information about the local map projection is available, the information about the local map projection is available, the Classical 3DClassical 3D approach would be the most suitable. approach would be the most suitable.

• If you are unsure of the local height information but the position If you are unsure of the local height information but the position information is accurate and you wish to keep the GPS measurements information is accurate and you wish to keep the GPS measurements homogenous in position, then the homogenous in position, then the StepwiseStepwise approach may be the most approach may be the most suitable.suitable.

• For cases where there is no information regarding the ellipsoid and/or map For cases where there is no information regarding the ellipsoid and/or map projection and/or you wish to force the GPS measurements to tie in with projection and/or you wish to force the GPS measurements to tie in with local existing control then the local existing control then the One-StepOne-Step approach may be the most approach may be the most suitable. Alternatively if a large number of common points are available suitable. Alternatively if a large number of common points are available and a more accurate approximation is required the and a more accurate approximation is required the InterpolationInterpolation approach approach can be used.can be used.

• The Two-Step approach also treats position and height information The Two-Step approach also treats position and height information separately which allows for position only control points to be used as well. separately which allows for position only control points to be used as well. Compared to the One-Step approach, information regarding the ellipsoid Compared to the One-Step approach, information regarding the ellipsoid and map projection has to be known. The advantage is that this approach and map projection has to be known. The advantage is that this approach can be used for larger areas than the One-Step.can be used for larger areas than the One-Step.

Two StepTwo Step

• This transformation approach works by treating the height and This transformation approach works by treating the height and position transformation separately. For the position transformation position transformation separately. For the position transformation the WGS 84 coordinates are first transformed using a Classical 3D the WGS 84 coordinates are first transformed using a Classical 3D pre-transformation to obtain preliminary local cartesian pre-transformation to obtain preliminary local cartesian coordinates. These are projected onto a preliminary grid using the coordinates. These are projected onto a preliminary grid using the specified ellipsoid and map projection. Then the 2 shifts, the specified ellipsoid and map projection. Then the 2 shifts, the rotation and the scale factor of a Classical 2D transformation are rotation and the scale factor of a Classical 2D transformation are calculated to transform the preliminary to the “real” local calculated to transform the preliminary to the “real” local coordinates.coordinates.

• The position transformation requires knowledge of the local map The position transformation requires knowledge of the local map projection and the local ellipsoid. However, as the distortions of the projection and the local ellipsoid. However, as the distortions of the map projection are taken into account, Two Step transformations map projection are taken into account, Two Step transformations can be used for larger areas than One Step transformations.can be used for larger areas than One Step transformations.

• The height transformation is a The height transformation is a single dimension height single dimension height approximationapproximation..

AdvantagesAdvantages::

• Errors in local heights do not affect the position Errors in local heights do not affect the position transformationtransformation

• The points used for determining the position and height The points used for determining the position and height transformation do not necessarily have to be the same points.transformation do not necessarily have to be the same points.

• The distortions of the map projection are taken into account The distortions of the map projection are taken into account which enables you to use this kind of transformation for larger which enables you to use this kind of transformation for larger areas.areas.

DisadvantageDisadvantage::

• Knowledge of the local projection and local ellipsoid are Knowledge of the local projection and local ellipsoid are required.required.

Two StepTwo Step

Establishing Transformation Establishing Transformation Relationship using Leica LGO V3.0Relationship using Leica LGO V3.0

Data Set (ITRF96 Geodetic Coordinates)Data Set (ITRF96 Geodetic Coordinates)

Data Set (HK80 Grid Coordinates + Height above Data Set (HK80 Grid Coordinates + Height above HKPD)HKPD)

Datum and Map FunctionDatum and Map Function

Datum and Map FunctionDatum and Map Function

Datum and Map FunctionDatum and Map Function

Datum and Map FunctionDatum and Map Function

Datum and Map FunctionDatum and Map Function

Datum and Map FunctionDatum and Map Function

Two Step – Transformation ReportTwo Step – Transformation Report

Two Step – Transformation ReportTwo Step – Transformation Report

Two Step – Transformation ReportTwo Step – Transformation Report

Two Step – Transformation ReportTwo Step – Transformation Report

Final Product :Final Product : A Localized Height Transformation Parameter FileA Localized Height Transformation Parameter File

• A localized height transformation parameter file A localized height transformation parameter file called called “GPSTRF.DAT”“GPSTRF.DAT” or or “TRFSET.DAT”“TRFSET.DAT” is produced is produced by Leica LGO V3.0/ SKI-Pro V3.0.by Leica LGO V3.0/ SKI-Pro V3.0.

• Users can import the finalized transformation Users can import the finalized transformation parameter file into the Leica LGO/ SKIPro software for parameter file into the Leica LGO/ SKIPro software for coordinates transformation in office.coordinates transformation in office.

• Users can also import the finalized transformation Users can also import the finalized transformation parameter file into the Leica GPS receivers for parameter file into the Leica GPS receivers for carrying out RTK/ DGPS surveys in real-time on site.carrying out RTK/ DGPS surveys in real-time on site.

ExampleExample

Establishment of a Height Transformation Establishment of a Height Transformation RelationshipRelationship

for Kowloon Areafor Kowloon Area

Example: Height Model of Kowloon AreaExample: Height Model of Kowloon Area

Two Step – Transformation Report

Data Set (10 control points used)Data Set (10 control points used)

Checking Point Distribution for Testing of the Finalized Height Checking Point Distribution for Testing of the Finalized Height Transformation Relationship (Total no. of points = 22)Transformation Relationship (Total no. of points = 22)

ConclusionsConclusions

• Average difference in Height above HKPD = 1 cmAverage difference in Height above HKPD = 1 cm

• Maximum difference in Height above HKPD = 4 cmMaximum difference in Height above HKPD = 4 cm

• The height differences depends on the GPS measurement The height differences depends on the GPS measurement accuracy and the height transformation accuracy.accuracy and the height transformation accuracy.

• The height transformation accuracy is about 2 cm in this The height transformation accuracy is about 2 cm in this small area.small area.

(i.e. 11 km x 12 km area)(i.e. 11 km x 12 km area)

RemarksRemarks

• This procedure is suitable for establishing GPS height transformation This procedure is suitable for establishing GPS height transformation relationship within the small local area, say 15 km x 15 km area.relationship within the small local area, say 15 km x 15 km area.

• Checking points should be provided to test the transformation Checking points should be provided to test the transformation accuracy.accuracy.

• The number of control points of the height model data set will be The number of control points of the height model data set will be increased if resources are permitted.increased if resources are permitted.

• The accuracy of the control points will be improved as far as possible.The accuracy of the control points will be improved as far as possible.

• A Geoid Model should be eventually produced for providing A Geoid Model should be eventually produced for providing the territory-wide solution of the geoid-ellipsoid separation for the territory-wide solution of the geoid-ellipsoid separation for GPS height transformation.GPS height transformation.

Thank you !!Thank you !!