The Detection And Location Of Gross Errors In Total Least Squares

When there are errors in coefficient matrix and observation vector at the same time. The least squares is not unbiased.The errors-in-variables model would be erected and the total least squares is applied to solve problems.Then,because both errors in coefficient matrix and observation vector are be considered in total least squares.It is mean that total least squares should consider all the gross errors in coefficient matrix and observation vector when there are gross errors in observation data.A lot of inconvenience is brought to detection and localization of gross errors in total least squares.Before we research method to detect and locate gross errors in total least squares.It is inevitable to analysis reliability of total least squares and separability and discover ability of gross errors.Only could the gross errors be discovered,The gross errors in adjustment system could be located correctly. The method to detect and locate gross errors should be found on the basis of the analyzed result of separability and discover ability of gross errors.(I)On the basis of partial-EIV model,the theory of separability and discover ability on two alternative hypothesis is cited in.The method to analysis separability and discover ability of gross errors in total least squares is provided.And the relative conclusion is obtained through example analysis.(II)Based on the analyzed result of separability and discover ability of gross errors,the method based on Gauss-helmert weighted total least squares to detect gross errors is proposed in the paper.(III)In order to locate the gross errors in coefficient matrix and observation vector,the robust estimation is cited into total least squares.The robust total least squares is researched to achieve the purpose of eliminate gross errors and making unknown valuation to avoid influence of gross errors.(IV)The robust weighted total least squares based on Singular Value Decomposition is proposed.There is the same effect to eliminate the gross errors in coefficient matrix and observation vector.