Coordinate transformation with variable number of parameters

Similarity transformation model does not provide a satisfactory solution for non-uniformly deformed systems because it allows only for a uniform scale and right angles. Instead, an affine model can be used, since it characterizes non-uniform dilatations and obliquity of the three axes. The general affine transformation contains 12 parameters. Nonetheless, it is not always necessary to use them all. The question of how many parameters should take part in the transformation and in what combinations is examined in the paper. In order to choose the proper transformation, a refined AIC is proposed. The paper also presents how to conduct the conversion of parameters between different coordinate systems with reference to the invariance property of coordinate transformation. To demonstrate the impact of using variable number of parameters and to observe the influence of coordinate systems on the transformation outcome, we use a network of 18 permanent GNSS stations in Israel as a case study.