Converted Total Least Squares method and Gauss-Helmert model with applications to transformation among ITRF realizations

Abstract

This thesis is an extension and improvement of the theory and applications of Converted Total Least Squares method (CTLS). Converted Total Least Squares (CTLS) dealing with the errors-in-variables (EIV) model take the stochastic design matrix elements as virtual observations, and the TLS problem can be transformed into a LS problem. In the coordinate transformation, the transformation model is always used after centering like it is published in most papers. This thesis directly uses the transformation model to generate a new design matrix with CTLS method. The result will present the consistency of the transformation model with and without centering in coordinates transformation. Then the 3D Helmert-transformation in Gauss-Helmert and Gauss-Markoff model is introduced (Koch 2002). The study is to find that, the connections between CTLS and the Gauss-Helmert model. To prove their similarity is a strong support for the theory of the CTLS method. After that, this thesis gives a brief introduction to the International Terrestrial Reference System (ITRF). The CTLS has been proved itself with coordinate transformation in Baden-Württemberg with equal weight and large scale. The new application with more parameters and smaller scale together with the weight information in ITRF is presented. The comparison and accuracy assessment of the published parameters and the parameters estimated by CTLS are discussed in detail with the applications.