The Research On Total Least Squares And Its Application In Deformation Monitoring

The Least-Squares (LS) method is one of the most basic and widely method for data processing. But the application has a premise that the random error exists only in the observation vector, without considering the coefficient matrix interfered by error (the Gauss-Markov model, G-M model). However, most measurement problems are called variable containing the error model (error-in-variables, EIV),because some of the elements of the coefficient matrix interfered by the personnel model, the environment, equipment, and other factors, so that the coefficient matrix is not completely accurate, the coefficient matrix and observation vector also contains the error. From statistical view, it is not reasonable to solve the EIV model with LS, and can not get the optimal solution. Therefore, there is an urgent need for a more reasonable method to solve such problems.Golub and Van Loan advanced the Total Least-Squares (TLS) to solve the EIV model in the eighties of last century. TLS minimizes all variables which need to be fixed, so we can use this method to establish a more reasonable data processing model and get more accurate results. In the past three decades, the TLS as a new data processing method has become a hot topic. At present, this method has been successfully applied to spectral analysis, parameter estimation, automatic control, image processing, system identification, signal processing, and other related fields. At the same time, the TLS has made a big advance. The improved models have been proposed. Based on the advantages of the TLS, it is theoretical and worth to introduce this method into the measurement field.Someone did some exploration research in Utilization of TLS in the problem of measurement data processing, but there were few systematic studies. This paper systematically expounded the basic ideas and principles of TLS, compared to the LS, a dissection of the advantages and disadvantages of the TLS was made in the basic ideas and principles level. Then we deduced in detail the most commonly TLS model and compared each model, and derived a new solution method-improved WTLS in connection with the characteristics of the EIV model of measurement data processing. Finally, different methods were selected to solute the line fitting, the two-dimensional Cartesian coordinate transformation and the three-dimensional small-angle datum transformation problem. CWTLS method and MTLS method were applied to three-dimensional coordinate transformation adapted to arbitrary rotation in the first time. Proposed overall deformation monitoring method based on the TLS. Applied three-dimensional small-angle datum transformation based on the TLS to the deformation monitoring data processing. Used C#and Matlab wrote interrelated procedures and verified the effect of TLS to solving the problem of measurement data processing.