Several Applied Studies Based On Population Least Squares Adjustment

The traditional least squares adjustment method in the adjustment of measured data,the hypothesis function model coefficient matrix without error,only considering the observation vector containing the accidental error,however,the actual function coefficient matrix in the model can also be calculated by the observed data,and observed data itself contains random error,the error propagation rate also contains accidental error coefficient matrix,the theoretical analysis shows the parameters of least squares method to calculate is no longer a statistically optimal solution,in view of the function model coefficient matrix error problem in the field of mathematics using EIV model of total least squares adjustment,the EIV model can take into account both the coefficient matrix and the observation vector with accidental errors.total least squares method in recent years on the mathematical theory research has obtained certain achievements,but in the application of total least squares there are problems when processing measurement data,the actual adjustment calculating is different from the pure theory in mathematics and in connection with the,should be combined with the characteristics application field is analyzed,so this article focuses on the total least squares problem of the coefficient matrix of error,measuring instance will total least squares method in pure mathematics theory in the field of measurement data processing,the main research content is as follows:1.On the basic principle of classic least square method and method of solving parameters is presented,and analyzed the law without considering matrix error in measurement data processing problem,according to this problem based on the total least squares solution of EIV model derivation parameters,the concept of overall,the basic principle of least squares adjustment principles,calculating methods and accuracy evaluation made a detail,expounds the general least squares matrix decomposition and iteration of three different ways to solve the calculation of parameters and accuracy evaluation formula,analyzes the characteristics and the advantages of various methods,finally,the overall development theory of the least-square method,the mixed total least squares method and weighted least squares,expanding theory of overall configuration method,the solution formula of extension theory is summarized.2.The application of the total least square algorithm in deformation monitoring,elevation anomaly,coordinate transformation and rear rendezvous is discussed with examples.By comparing the prediction error values in deformation monitoring,the accuracy of the total least square method is about 18% higher than that of the least square method.in datum transformation example application analysis of the least square method and total least square method and total least squares solution of mixed results,the results also showed that the total least square method calculating precision is better than the least squares method,through comparing two kinds of configuration algorithm simulation example,can be concluded that the overall accuracy of least square collocation method is superior to the least squares method,the same conclusion is obtained in the cases of rear rendezvous,deformation monitoring and target ball positioning,and the accuracy of the total least square method considering the coefficient matrix and observation vector error is better than that of the traditional least square method.