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Closed-form and iterative weighted least squares solutions of Helmert transformation parameters
KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
2013 (English)In: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 3, no 1, 7-11 p.Article in journal (Refereed) Published
Abstract [en]

The Helmert transformation is the most common transformation between different geodetic systems. In 2-D, in contrast to higher dimensions, it is a well-known procedure how to determine the 4 transformation parameters in a closed form. Here we derive the closed-form weighted least squares solution in m-dimensional space for an arbitrary number (≥ m) of coordinate set-ups in two related systems. The solution employs singular value decomposition (SVD) for the rotation matrix, while the translation vector and scale parameters are obtained in simpler ways. To avoid the SVD routine, we also present an iterative approach to solve for the rotation matrix. The paper is completed with a test procedure for detecting outlying coordinate pairs. 

Place, publisher, year, edition, pages
2013. Vol. 3, no 1, 7-11 p.
Keyword [en]
Helmert transformation, Procrustes problem, registration, singular value decomposition
National Category
Other Engineering and Technologies not elsewhere specified
URN: urn:nbn:se:kth:diva-166627DOI: 10.2478/jogs-2013-0002OAI: diva2:811653

QC 20150513

Available from: 2015-05-12 Created: 2015-05-12 Last updated: 2015-05-13Bibliographically approved

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Sjöberg, Lars E.
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