Research On The Total Solution For Parameters Estimation And Prediction Based On Total Least Squares

Since observation values may be derived form actual observations,they may contain observation errors.The least squares method is the most commonly used in geodetic data processing.The total least squares method(TLS,total least squares),which considers the observation errors of the coefficient matrix and the observation vector,is a hot research topic in recent decades.Its main function model is based on EIV(EIV,error-in-variables)and Partial EIV(Partial EIV,partial error-in-variables).Although a reasonable regression model can be established by using regression analysis method which takes into account both the observation errors of coefficient matrix and observation vector and their correlation,the traditional methods still neglect the observation errors of independent variables to be predicted when using this model to predict dependent variables,which leads to the decreased prediction accuracy.Therefore,the concept of total solution is proposed,which takes into account the random errors of all variables in regression analysis model and model prediction equation.Then,the prediction effect of the dependent variables in the model is influenced by the accuracy of parameter estimation and prediction independent variables.Based on the existing total least squares algorithm and variance component estimation method,starting from improving the prediction effect of the model,this paper studied the more universal algorithm of the total solution and applies it to the actual situation in order to improve the existing model prediction processing methods.The specific research of this paper is as follows:The total solution for parameter estimation and prediction based on Partial EIV model is studied.It takes into account the observation errors of all variables and noticed that the elements of the coefficient matrix are an expression or a function.The Partial EIV model is transformed into the linear model and constructed in the form of indirect adjustment for iterative solution.With consideration of the errors in independent variables when predicting the corresponding dependent variables with Partial EIV model,the method can achieve a higher degree of predicted accuracy.The variance components estimation algorithm of the total solution based on the least squares method is studied.For the case of an inaccurate random model and the problem that the errors of independent variables were ignored when predicting the corresponding dependent variables,a new complete solution that considered the observation errors of all variables was proposed based on errors-in-variables(EIV for short)model.The formulas of estimation of variance and covariance components are derived and the iterative algorithm was presented in this paper.At last,two examples were given to testify.Experimental results show that the method of this paper can achieve better prediction accuracy within these methods and is feasible.The variance components estimation algorithm of GM(1,1)model based on the total least squares is studied.We considered that the existing grey prediction GM(1,1)model is basically based on the assumption that the observation sequence has the same accuracy or the variance matrix is given according to the prior information.In fact,the observation data are collected in different time periods,which is unequal precision observation.Based on the total least squares method of GM(1,1)model,considering the homologous random errors in the model,this paper gives the solution from the quadratic form of observation value and the minimum norm quadratic unbiased estimation theory.It overcomes the defect that the prior stochastic model of observation data is unreasonable.Two examples of actual data and simulation data show that this method can effectively improve the prediction accuracy compared with other methods.Based on the research of this paper,it is applied to GPS elevation conversion and universal 3D(three-dimensional)similarity transformation model.The GPS elevation conversion accuracy is main influenced by the accuracy of conversion parameter and the coordinate errors of the elevation anomaly point.Variance components estimation for a united model of GPS height conversion is used to deal with it in order to improve model conversion accuracy;3D similarity transformation model is transformed.Nonlinear adjustment is used to deal with it and take into account the observation errors of common points and non-common points in original and target coordinate system respectively.A total solution of universal 3D similarity transformation is proposed in this paper.The experimental results show that the application of variance component estimation to a united model of GPS height conversion can modify the random model to improve model conversion accuracy;In solving universal 3D(three-dimensional)similarity transformation model,the proposed method can obtain reasonable transformation parameters and better coordinate transformation accuracy.