The Algorithms And Application Research Of Robust Total Least Squares

The Gauss-Markov model, because it can be effective for error, thus becoming the most widely used measure boundary in data processing. The classical Gauss-Markov model assumes that function model is known, non-randomized, and assumes that the coefficient matrix can be given precise, the observed value vector only contains random errors. However, In many practical problems, such as digital terrain model fitting, geodetic inversion, GIS spatial data analysis, landslide monitoring and coordinate transformation and other mathematical models, the observation vector and the coefficient matrix both composed by the observational data, and both contain random errors. Such adjustment model called EIV (error-in-variables) model. The LS asked that the sum of squared residuals in observation vector for minimize, It did not consider the error which the coefficient matrix contains. So, Using the LS for solving the EIV model is unreasonable. So, we urgent need to introduce a more reasonable approach to solve such problems. Until the 1880s, Golub and Van Loan proved Total Least-Squares (TLS) which based on previous research ideas for EIV model. TLS ask the sum of observation vector and the coefficient matrix minimum residual squares for minimum, can estimate EIV model better. TLS extension as a classic least squares estimation methods, the past 30 years has been widely used in signal processing, computer vision, image processing, communications, engineering and geodetic and photogrammetric mapping and other related fields, become the basic method for data processing in various of professional fields.Surveying the earliest field start of studying the TLS and apply it to coordinate conversion, digital terrestrial sphere fitting and regression analysis. Along with research on the continuous development of the total least squares algorithm, It’s various improvement model and calculation methods have been proposed, Its application in the field of surveying and mapping are increasingly widespread. However, the current research on the total least squares are basically only for incidental observations contain errors, when the observation vector and the coefficient matrix still exist gross errors, the resulting model is distorted, and causing serious misrepresentation parameter estimation. As we all know, in the survey observations, due to the impact equipment, environmental, operational staff and other factors, the observed data will inevitably contain a certain amount of accidental error even gross errors. For the presence of gross errors, if you rely solely on the adjustment is carried out vetting by some simple methods, and singled out the gross error use of artificial methods, not only work hard, and the adjustment results often depends on the seriousness and theoretical knowledge of operating personnel, and a simple test method can not be found in a small observation gross error. Therefore, how to effectively against EIV model automatically be gross errors become a hot research topic at home and abroad.This paper aims to study the robust estimation method for EIV model witch called the robust total least-squares method (RTLS). In theory, this paper basically followed the general idea of robust estimation of least squares, starting with robust principles, by selecting the appropriate weighting function, combined with the overall iterative method of least squares, in an iterative process to correct the value of the right, observations which contains gross errors in the iterative process will get a smaller weight and gradually approaches zero, this will achieve a gross error automatically locate and correct. In the experiment, the paper using the surface fitting for example, validate the robust total least squares for two steps. Firstly, use LS, TLS, WTLS and RTLS to estimate the unknown parameters when only occasionally contain errors and observations in both cases, and do comparative analysis. Secondly, using the classic article LS, minimum norm rights method, Huber rights method, Hampel weight function method, Krarup rights method and posterior variance method to getting the right of RTLS to estimate the unknown parameters, and analyze the difference between the observed value containing crude right value iteration changes. In the application, this paper using coordinate transformations, GPS height fitting and image matching three aspects for example, by LS, TLS and RTLS comparison analysis to verify the feasibility and applicability of RTLS.