Abstract
J. Badekas reinterpreted M. S. Molodensky’s three-dimensional similarity transformation as a vector solution using a centroid. The solution has since been (mis)interpreted by some others with inconsistent reference to the methods of both Molodensky and Badekas, principally relating to the translation vector and the stochastic model. This appears to have led to incorrect claims that the Molodensky–Badekas method is superior to the Helmert similarity and Burša–Wolf methods. This paper reviews the development and description of the original Badekas method, reconfirming its equivalence to the Burša–Wolf method in the forward direction, and provides an alternative solution that suits the same-formula reversal common in commercial surveying software. It is also demonstrated that the Molodensky–Badekas method has no inherent superiority over the Burša–Wolf method, has an ambiguous functional model, and nominally underestimates its parameter statistics when these are compared directly with those from the Burša–Wolf method.
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Data Availability Statement
All data generated or used during the study are available from the corresponding author by request.
Acknowledgments
The authors wish to thank the reviewers for their insight and detailed critiques that improved this paper. The first author would also like to acknowledge the contribution of an Australian Government Research Training Program Scholarship in supporting this research.
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Published In
Journal of Surveying Engineering
Volume 146 • Issue 3 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jun 25, 2019
Accepted: Jan 3, 2020
Published online: Apr 18, 2020
Published in print: Aug 1, 2020
Discussion open until: Sep 18, 2020
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