Parameter Estimation Of PEIV Model And Its Application In Surveying And Mapping Data Processing

In recent years,the total least squares method has developed into a new data processing method which is widely used in various disciplines.However,there are still some shortcomings if only general total least squares method is adopted in some surveying and mapping data processing items,such as geodesy and engineering surveying.For example,in the space straight-line fitting problem,the common traditional method is to establish an EIV(errors-in-variables)model of a spatial straight line,and a SVD(singular value decomposition)or iterative method is used to solve the fitting parameters,although considering the coefficient matrix.Although there are random errors,the constant elements in the coefficient matrix are also corrected for errors,and the corrections for the same elements are inconsistent.In order to overcome some of the deficiencies in the mapping data processing talked above,the main research is carried out as follows:1)The construction of the partial errors-in-variables(PEIV)model and the calculation of the covariate matrix for the general equations of the circular curve fitting are introduced.The fitting parameters are obtained by combining the total least square method of the PEIV model of the relevant observations.For the parametric equation of circular curve fitting,its error equation form is obtained through linearization and rewritten into a matrix form EIV model.According to the idea of the PEIV model,the PEIV model is constructed by extracting the random elements from the coefficient matrix,and the parameters are solved by the two-step iterative method of the PEIV model.Simulation data and example data verify the feasibility and effectiveness of the proposed method.2)The PEIV model total least squares method is applied in the spatial plane fitting.Comparing with other WTLS(weight total least squares)methods through simulation examples,the feasibility of the method is verified.According to the existing deficiencies inthe general global least-squares fitting of space linear fitting,the overall minimum of the PEIV model is used.The multiplication algorithm solves the fitting parameters.Detailed calculation steps are given.Combining the example data with other existing methods to demonstrate the effectiveness of the proposed method.3)For the GM(1,1)prediction model,the random term of the coefficient matrix is a feature of the original observation sequence function.With reference to the construction of the PEIV model,the GM(1,1)PEIV model is constructed.Taking into account the correlation between the observation vector and the matrix of the original sequence,the parameters of the relevant observation PEIV model are used to solve the parameters.The experimental data show that this method can be used to solve the GM(1,1)model parameters and model prediction,and the accuracy has certain advantages.4)In view of the low computational efficiency of the overall least-squares transformation of the existing three-dimensional coordinate transformation,the total least-squares method of the PEIV model is used to solve the three-dimensional coordinate transformation.This method can reach the convergence threshold faster.By comparing the experimental data,the effectiveness of the proposed method is verified.The data detection method of three-dimensional coordinate transformation is also introduced.By adjusting the test statistics,the degree of recognition of gross errors is indirectly promoted.Experimental results show that adjusted test statistics can more accurately identify gross errors.