Journal of Geodesy

, Volume 88, Issue 12, pp 1117–1130 | Cite as

Transformation model selection by multiple hypotheses testing

  • Rüdiger LehmannEmail author
Original Article


Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ \({C}_{{p}}\), which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.


Coordinate transformation Hypothesis test Affine transformation Similarity transformation Gauss–Markov model with constraints Normalized Lagrange multiplier Studentized Lagrange multiplier Akaike information criterion  Mallows’ \({C}_{{p}}\) 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Faculty of Spatial InformationUniversity of Applied Sciences Dresden DresdenGermany

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