Use of Total Least Squares Adjustment in Geodetic Applications

This article discusses the method of computing the values of the unknowns under the condition of the minimum sum of the squares of the residuals of the observations, also known as the least squares method, with the additional condition of taking into account the errors in the unknowns. The problem has already been treated by many authors, especially in the field of regression analysis and the computation of transformation parameters. We give an overview of the theoretical foundations of the least squares method and extensions of this method by considering the errors in the unknowns in the model matrix. So, the total least squares method is presented in this paper, fitting the regression line to a set of points and computing transformation parameters for the transition between the old and the new Slovenian national coordinate systems. Furthermore, for the first time, the method is also presented and tested in the S-transformation between different geodetic datum-dependent solutions. Also, for the first time, we systematically compare the results of the approach with conventional approaches in all three considered tasks. With the results based on relevant statistics, we confirm the suitability of the described method for dealing with the considered computational tasks.