Study on the Converted Total Least Squares method and its application in coordinate transformation

Abstract

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.