Total Least Squares Adjustment Method And Its Applications In Surveying And Mapping

The thesis aims at enriching total least squares theory based on simulated case study and practical application.Then we use least squares theory,robust estimation theory and generalized inversion theory to analysis functional model and stochastic model of total least squares.The main research contents and results is drawn as(1)Seven kinds of total least squares methods cater for different EIV models are introduced from functional and stochastic model.Then,this thesis introduce the recursive total least squares based on singular value decomposition method that can be regarded as an alternative method for sequentical adjustment.This algorithm has an advantange over classical total least squaes in calculation efficiency,(2)We proposed an scaled total least squares method with implicit scaled factor.This thesis reserched and pointed out the shortcoming of scaled total least squares adjustment criterion,based on which we proposed a new EIV model which was featured with implicit scaled factor in function model instead of in stochastic model.Then we deduced the corresponding parameter estimation formulas of scaled total least squares method with implicit scaled factor and the variance-covariance matrix formula of basic vectors.The simulation case result showed that the proposed mthod can deal with the adjustment problem effectively(3)We proposed an improved mixed total least squares method.This thesis researched on total least squares solution for complicated EIV model.We devided the design matrix by independent and dependent elements in it.Then we constructed a characteristic matrix to show the connections between functional independent elements and functional dependent elements.Based on these,an improved mixed total least squares method is derivated.The simulation case result showed that the proposed method could cope with complicated EIV model effectively and correctly.(4)We proposed an robust total least squares method for multiple variables.This thesis reaseached and pointed out on the shortcoming of robust total least squares which fails to give reasonable estimated result because it calculates robust matrix of elements in EIV model totally.To solve this problem,we proposed weight fuction for multiple variables in EIV model and deduced the corresponding robust total least squares method.The simulation case result showed that the proposed method can deal with EIV model whose multiple variables has gross errors effectively and give reasonable parameter estimation results(5)This thesis research on applications of total least squares in the field of surveying and mapping.The results showed that the effect diverses from one application to another application.The improved mixed total least squares and least squares method show no difference in adjustment results in the GPS elevation anomaly fitting.In the global coordinate frame transformation case,the adjustment result of improved mixed total least squares is slightly better than least square method.In the appliaction of train Inversion from Distance Changes,the adjustment result of improved mixed total least squares is apparently better than least square method.In the application of leaf area index inversion,the adjustment result robust total least squares for multiple variables is better than traditional robust total least squares.However,in the application of polar motion prediction,the least squares method is better than total least square method.