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dc.contributor.authorPalancz, B.
dc.contributor.authorZaletnyik, P.
dc.contributor.authorAwange, Joseph
dc.contributor.authorHeck, B.
dc.identifier.citationPalancz, B. and Zaletnyik, P. and Awange, J.L. and Heck, B. 2010. Extension of the ABC-Procrustes algorithm for 3D affine coordinate transformation. Earth Planets and Space. 62 (11): pp. 857-862.

The Procrustes method is a very effective method for determining the Helmert's datum transformation parameters since it requires neither initial starting values nor iteration. Due to these attractive attributes, the ABC-Procrustes algorithm is extended to solve the 3D affine transformation problem where scale factors are different in the 3 principal directions X,Y,Z. In this study, it is shown that such a direct extension is restricted to cases of mild anisotropy in scaling. For strong anisotropy, however, the procedure fails. The PZ-method is proposed as an extension of the ABC algorithm for this special case. The procedures are applied to determine transformation parameters for; (i) transforming the Australian Geodetic Datum (AGD 84) to the Geocentric Datum Australia (GDA 94), i.e., mild anisotropy and (ii) synthetic data for strong anisotropy. The results indicate that the PZ-algorithm leads to a local multivariate minimization as opposed to the ABC-algorithm, thus requiring slightly longer computational time. However, the ABC-method is found to be useful for computing proper initial values for the PZ-method, thereby increasing its efficiency.

dc.publisherThe Society of Geomagnetism and Earth, Planetary and Space Sciences (published by Terra Scientific Publishing Company)
dc.subjectsingular value decomposition
dc.subjectanisotropy scaling
dc.subjectcoordinate transformation
dc.subjectglobal minimization
dc.subjectHelmert transformation
dc.titleExtension of the ABC-Procrustes algorithm for 3D affine coordinate transformation
dc.typeJournal Article
dcterms.source.titleEarth Planets Space
curtin.departmentDepartment of Spatial Sciences
curtin.accessStatusOpen access via publisher

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