Research On Variance Component Estimation Of Partial EIV Model And Its Application

The prior weights of observations always exist unreliably in adjustment data processing.How to improve the stochastic model and obtain the parameter estimation more reasonably based on the function model and stochastic model which is worthy of study.The error-in-variables(EIV)model has considered the error of coefficient matrix,and the partial error-in-variables(Partial EIV)model has considered the random elements and non-random elements simultaneously in coefficient matrix.The total least squares(TLS)method is the rigorous method of EIV model or Partial EIV model,compared with the various parameter estimation algorithms for Partial EIV model,there is not enough study on stochastic model for Partial EIV model and waits for further research.Based on the exist study of variance components estimation(VCE)methods,the form of stochastic model of Partial EIV model has been extended,the bias of parameter estimation of TLS and the negative variance components have been considered in this paper.Considering the more general method of VCE for Partial EIV model and applying the method to practical are the theme of this paper,this thesis studies obtained the parameter estimation and the weights of observation reasonably.The detailed researches are as follows:The non-negative least square variance components estimation(NNLS-VCE)method of Partial EIV model is researched.The forms of least square variance components estimation(LS-VCE)method for Partial EIV model are derived firstly and the equivalency with exist method is analyzed.Considering the non-negative variance components,combining the non-negative least squares method to improve the variance components estimation and the iterative algorithms are given respectively.The method of this paper inherited the advantages of Partial EIV model and it can obtain the variance components estimation reasonably with the non-negative constrains.The VCE methods of Partial EIV model which consider the correlated observations and the bias of parameter estimation are researched.The iterative algorithms of parameter estimation and VCE with correlated observations are given.The Partial EIV model is considered as a non-linear function,the VCE formulas are derived with the linearization process and the equivalency between various methods are verified through formula derived.Considering the bias of parameter estimation of Partial EIV model,the bias-correction,parameter estimation and VCE are taken as a whole iterative algorithm.The precision estimation of parameter after bias-correct is carried out based on second order approximation function method.The experiments show the VCE method can obtain the reasonable parameter with the corrected stochastic model,the estimation of variance component is approach to the true value and it is better when adding the bias-correct in the simulate experiment,particularly the value of bias is bigger.The application of VCE method in Ill-posed Partial EIV model is researched.Virtual observation method is a united solution of adjustment criteria with parameters,the virtual observation equation is regard as a kind of observation and the VCE formulas of virtual observation method to Ill-posed Partial EIV model are derived.The ridge parameter is determined by the VCE method and the practical mean of ridge parameter is the weight scaling factor of different kind of data.Based on the second order approximation function method,the second order approximate covariance and the mean square error(MSE)are calculated to precision estimation when the virtual observation equation and the practical observation equation are considered as a whole non-linear function.The experiments show it is efficient to use virtual observation method to improve the Ill-posed problem and the VCE converges faster in determining the ridge parameter.The MSE of parameter is small which can be indicated the availability of parameter estimation.The difference between the first order approximation and second order approximation covariance is influenced by the non-linear strength of the non-linear function,and the bigger the non-linear strength,the more obvious the effect is.Based on the research of this paper,the proposed method of this paper is applied to the GPS height fitting and the inversion of the Mogi model of Changbai Tianchi volcano.Considering the different precision between the plane and vertical of GPS coordinates,the VCE method is used to estimate the various variance components and obtain the reasonable parameter estimation.Considering the nonlinear characteristic of the Mogi model,the linearized form and cofactor matrix are introduced.Combining the virtual observation method to solve the Ill-posed problem of the inversion and determining the ridge parameter by the VCE method.Research shows that the VCE method can modified the stochastic model of the observed data efficiently,in the inversion of Mogi model,the proposed method can obtain the reasonable pressure source parameters from three kind of data joint adjustment and has a certain practical application value.