Application Study On The Robust Total Least Squares Method In Linear Regression Under Different Error Influence Models

In the production practice and scientific experiments,due to imperfect observation procedures and check the conditions,measurement data collection process will inevitably appear gross error.Therefore,how to eliminate or weaken the influence of gross error on the parameter estimation becomes another research topic in surveying discipline.With the advent of the robust estimation concept,the domestic and foreign scholars have proposed the robust least squares(RLS)method,but the RLS method can only take into account the influence of the observed vector on the gross margin and neglect the coefficient matrix.The robust overall least squares(RTLS)method,which takes the gross error condition and the coefficient matrix,can take into account both the observation vector and the coefficient matrix.Linear regression is the most commonly used function model in the measurement data processing.In view of the situation that the independent variables and the dependent variables contain gross errors in the linear regression model,some scholars use the idea of the selection iteration to derive the robust overall least squares iteration based on the linear regression modelFormula and solution steps.At the same time,some scholars through the individual examples in the RTLS method to obtain a smaller unit weight than the RLS error,it is concluded that the RTLS method is better than the RLS method.However,for the time being,there is no clear theoretical study to illustrate the advantages and disadvantages of the RLS method and the RTLS method in linear regression.It is proved that the validity of the two parameter estimation methods is too single-sided based on individual examples,It is difficult to explain which parameter estimation method is more reliable in the change of the error in the right,so it is necessary to study the relative effectiveness of the robust total least squares method in the linear regression.In this paper,the application of robust total least squares method in linear regression under different error influence models is studied.According to the different distribution of the error can be divided into three kinds of error influence model:(1)only the observed value contains random error and gross error;(2)coefficient matrix with random error and gross error,the observed value contains only random error;(3)observations containing random error and rough Poor,the coefficient matrix contains only random errors.The relative effectiveness of the robust least squares method and the robust total least squares method in the multiple linear regression are compared by one-way to five-element linear regression example.On the basis of the simulation experiment,The linear regression model was used to discuss the relative effectiveness of RLS and RTLS in multiple linear regression,respectively,underdifferent error effects models,different robust estimation methods,different number of observations,and different slope or different gross errors.It is difficult to explain which RLS method and RTLS method are more effective when the slope of the univariate linear regression model is less(about tan15°).When the slope of the linear regression model is large(about tan45°)Or tan75°),the RLS method is superior to the RTLS method in the first and third error-influenced models.The second error influenced model,the RTLS method is superior to the RLS method.For the binary error analysis model,the RLS method is better than the RTLS method.The second error influenced model,the RTLS method is better than the RLS method.In the third error model,it is difficult to say that RLS Method and RTLS method which is more effective.