Application Of Robust WTLS In GPS Elevation Fitting

In the field of mapping and geographic information,least squares(LS)is the most basic and widely used data processing method.However,there is a precondition for the application of this method,that is,the method considers that there is no accidental error in the coefficient matrix when performing parameter estimation calculation,and the accidental error only exists in the observation vector.However,in the specific data acquisition process,due to various practical conditions,the coefficient matrix is not completely accurate.In order to consider the possible accidental errors in the coefficient matrix,the total least squares(TLS)has been developed in recent decades.The overall least squares method has been widely applied since its introduction,covering a wide range of areas.Considering the problem of unequal precision in data collection,weighted total least squares(WTLS)has also been gradually proposed by scholars.In the data acquisition,it is easy to be affected by various factors,so that the data contains not only accidental errors,but also coarse errors.At this time,the weighted total least squares method for data processing will not obtain reliable results.In view of this situation,based on the robust estimation IGG-III scheme and weighted total least squares method proposed by professor Yang Yuanxi,the two methods are combined to form robust weighted total least squares(RWTLS).In order to evaluate the reliability and effectiveness of the method,the error in the unit weight and the parameter estimation result of the model are used as evaluation indicators.The method was compared with the least squares method and the weighted total least squares method through simulated experimental data and actual case data.The experimental results of the simulation data show that when the number of gross errors and the gross error in the observed data are increasing,the parameter estimation results obtained by the least squares method and the weighted total least square method are linearly changed in the unit weight.The parameter estimation results obtained by the robust weighted total least squares method are more stable than the errors in the unit weight.This indicates that the robust weighted total least squares method can resist the gross errors existing in the data,and further proves that the method can locate and identify the gross errors in the data,and the results are also better than the least squares method and the weighted total least squares method.The results obtained should be reliable.Surface fitting is a common fitting method for GPS elevation fitting.In the traditional elevation fitting,the estimation of the model parameters is usually carried out by using the least squares method of considering the error in the observation vector.In order to consider the error in the coefficient matrix and the possible gross error in the observation vector,the robust weighted total least squares method is used to fit the GPS measurement data of the high-speed railway CPI point to the plane fitting and quadratic surface fitting.By comparing the data,the method is compared and analyzed with the plane fitting and quadratic fitting based on least squares method,total least squares method and weighted total least squares method.The experimental results show that the error and standard deviation in the unit weight of the results obtained by the total least squares method,the weighted total least squares method and the robust weighted total least squares method are smaller than the least squares method when the modeling data does not contain gross errors.The error and standard deviation of the unit weight of the result,In the case where the data contains gross errors,the error and standard deviation of the unit weights obtained by the robust weighted total least squares method are smaller than the unit weights of the results obtained by least squares method,total least squares method,and weighted total least squares method.Medium error and standard deviation,This indicates that the robust weighted total least squares method used in this paper to perform GPS elevation fitting can effectively locate and eliminate the gross error in the data.The results obtained are more robust and reliable than the least squares method,the overall least squares method,and the weighted total least squares method.