Total Least Squares Robust Algorithm For High Breakdown Contamination Rate Of Coordinate Transformation

With the progress of science and technology,the techniques and methods of geodesy have been progressed,the measurement data processing theory and technology have been further improved,The scope of application has become wider and wider.Coordinate transformation is a common problems in measurement work,coordinate transformation is used for geodetic surveying,engineering surveying,photogrammetry,and remote sensing.The traditional coordinate transformation model which based on the least squares criterion for adjustment and parameterization,which can not meet the accuracy requirements in many cases.The Gauss-Markov model which based on classical least squares principle is widely used in various geodetic and engineering surveys.The premise of the model establishment is that the assumption coefficient matrix is accurate,and random errors only exist in the observation matrix.However,with the development of the surveying theory and the in-depth study of data processing,when the coefficient matrix error is not taken into account,the adjustment result will be biased,which is not consistent with the actual situation.In order to solve this kind of defect in the theory of least squares,Golub and Van Loan proposed Total Least Squares(TLS),and established a more reasonable and practical Errors-in-Variables(EIV)model.This article describes the common solution to the problem when the coefficient matrix and the observation vector have equal precision and unequal accuracy.Taking the straight line fitting as an example,the parameters were estimated by the TLS method and the weighted TLS method,and compared with the parameter estimates obtained by the least squares estimation.The results show that the parameters obtained by the weighted TLS are obviously better than the LS.In the process of plane coordinate transformation,due to the long establishment time,the reference point may be changed or displaced so that the measurement data contains gross errors.LS,TLS and WTLS all have poor resistance to gross errors,and often due to the presence of gross errors,the resulting parameter estimates have large deviations.In this paper,the weight factor function is constructed by using standardized residuals and the square root of the variance component estimator with robustness is obtained by introducing the median method.A robust WTLS model with high breakdown contamination rate is presented.Through example analysis,it was found that the parameter estimates obtained by the LS method and the TLS method have large variations in the case of gross errors,and the obtained results are no longer applicable,on the other hand,the result of robust solution based on weighted total least squares has little difference with the true value,so it has certain advantages in dealing with gross errors.