Weak Nonlinearity in a Model Which Arises from the Helmert Transformation

Abstract

Nowadays, the algorithm most frequently used for determination of the estimators of parameters which define a transformation between two coordinate systems (in this case the Helmert transformation) is derived under one unreal assumption of errorless measurement in the first system. As it is practically impossible to ensure errorless measurements, we can hardly believe that the results of this algorithm are “optimal”.In 1998, Kubáček and Kubáčková proposed an algorithm which takes errors in both systems into consideration. It seems to be closer to reality and at least in this sense better. However, a partial disadvantage of this algorithm is the necessity of linearization of the model which describes the problem of the given transformation. The defence of this simplification especially with respect to the bias of linear functions of the final estimators, or better to say the specification of conditions under which such a modification is statistically insignificant is the aim of this paper.