# Procedure for GPS Height Transformation within a Small Local Area

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Procedure for GPS Height Transformation within a Small Local Area
SatRef - Knowledge Sharing Platform Procedure for GPS Height Transformation within a Small Local Area JAMES WONG, LS/G(NT)

SatRef - Knowledge Sharing Platform
Purposes of this briefing To share the knowledge of how to create a Localized Height Transformation Parameter File for the transformation of GPS surveyed ellipsoidal height to HKPD Height in a small area. To release the height model data set for the creation of the Localized Height Transformation Parameter File.

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

Current Problems The existing 7-Parameter Set published by the Geodetic Survey Section of SMO is used for the datum transformation between ITRF96 and HK1980 Geodetic Datums. It is not used for transformation between the GPS surveyed ellipsoidal height and orthometric height (local height). Hence, the problem is how to transform the GPS surveyed ellipsoidal height to orthometric height for the determination of the local height for various applications. Actually, there is no high accuracy Geoid Model of Hong Kong for the determination of geoid-ellipsoid separation for the GPS height transformation.

Height Model Data Set Height Model Data

Which approach to use This question is almost impossible to answer since the approach used will depend totally on local conditions and information. If you wish to keep the GPS measurements totally homogenous and the information about the local map projection is available, the Classical 3D approach would be the most suitable. If you are unsure of the local height information but the position information is accurate and you wish to keep the GPS measurements homogenous in position, then the Stepwise approach may be the most suitable. 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 local existing control then the One-Step approach may be the most suitable. Alternatively if a large number of common points are available and a more accurate approximation is required the Interpolation approach can be used. The Two-Step approach also treats position and height information separately which allows for position only control points to be used as well. Compared to the One-Step approach, information regarding the ellipsoid and map projection has to be known. The advantage is that this approach can be used for larger areas than the One-Step.

Two Step This transformation approach works by treating the height and position transformation separately. For the position transformation the WGS 84 coordinates are first transformed using a Classical 3D pre-transformation to obtain preliminary local cartesian coordinates. These are projected onto a preliminary grid using the specified ellipsoid and map projection. Then the 2 shifts, the rotation and the scale factor of a Classical 2D transformation are calculated to transform the preliminary to the “real” local coordinates. The position transformation requires knowledge of the local map projection and the local ellipsoid. However, as the distortions of the map projection are taken into account, Two Step transformations can be used for larger areas than One Step transformations. The height transformation is a single dimension height approximation.

Two Step Advantages: Errors in local heights do not affect the position transformation The points used for determining the position and height transformation do not necessarily have to be the same points. The distortions of the map projection are taken into account which enables you to use this kind of transformation for larger areas. Disadvantage: Knowledge of the local projection and local ellipsoid are required.

Establishing Transformation Relationship using Leica LGO V3.0

Data Set (ITRF96 Geodetic Coordinates)

Data Set (HK80 Grid Coordinates + Height above HKPD)

Datum and Map Function

Datum and Map Function

Datum and Map Function

Datum and Map Function

Datum and Map Function

Datum and Map Function

Two Step – Transformation Report

Two Step – Transformation Report

Two Step – Transformation Report

Two Step – Transformation Report

Final Product : A Localized Height Transformation Parameter File
A localized height transformation parameter file called “GPSTRF.DAT” or “TRFSET.DAT” is produced by Leica LGO V3.0/ SKI-Pro V3.0. Users can import the finalized transformation parameter file into the Leica LGO/ SKIPro software for coordinates transformation in office. Users can also import the finalized transformation parameter file into the Leica GPS receivers for carrying out RTK/ DGPS surveys in real-time on site.

Example Establishment of a Height Transformation Relationship
for Kowloon Area

Example: Height Model of Kowloon Area

Data Set (10 control points used)
Two Step – Transformation Report

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

Conclusions Average difference in Height above HKPD = 1 cm
Maximum difference in Height above HKPD = 4 cm The height differences depends on the GPS measurement accuracy and the height transformation accuracy. The height transformation accuracy is about 2 cm in this small area. (i.e. 11 km x 12 km area)

Remarks This procedure is suitable for establishing GPS height transformation relationship within the small local area, say 15 km x 15 km area. Checking points should be provided to test the transformation accuracy. The number of control points of the height model data set will be increased if resources are permitted. The accuracy of the control points will be improved as far as possible. A Geoid Model should be eventually produced for providing the territory-wide solution of the geoid-ellipsoid separation for GPS height transformation.

Thank you !!

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