Comparative Review of Molodensky–Badekas and Burša–Wolf Methods for Coordinate Transformation

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.