Browsing by Author "Dong, Dalu"

Now showing 1 - 2 of 2

Open Access
Converted Total Least Squares method and Gauss-Helmert model with applications to transformation among ITRF realizations
(2019) Dong, Dalu
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.
Open Access
Study on the Converted Total Least Squares method and its application in coordinate transformation
(2017) Dong, Dalu
This thesis gives a brief introduction to Total Least Squares (TLS) comparing with the classical LS, and its common solutions by singular value decomposition (SVD) approaches and the iteration, also following with the advantages and disadvantages of both methods. One method named Converted Total Least Squares (CTLS) dealing with the errors-in-variables (EIV) model can solve the problems of both. The basic idea of it is to take the stochastic design matrix elements as virtual observations, and the TLS problem can be transformed into a LS problem. The significance of CTLS lies not merely in attaining the optimal estimation of parameters and more importantly in completing the theory of TLS with classical LS. As a comparison, another estimation method based on Partial-EIV model will also be presented, which can deal with the TLS problems with iterative algorithm. The coordinate transformation parameter estimation formula of both algorithms are derived. By specifying the accuracy assessment formulas of CTLS, this thesis identifies rigorously the degree of freedom of the EIV model in theory and solves the bottleneck problem of TLS that restricts the application and development of TLS.