A Study On The Algorithms Of Semiparametric Regression Model Based On Helmert Variance Component Estimation

In this paper , the issue of dealing with systematic errors is mainly discussed by using the modern surveying and mapping science and technology. Firstly, the essay studies the theory of semiparametric regression model based on Helmert variance component estimation; moreover, taking account of the practical problems of geodesy, we propose several algorithms of semiparametric regression model; finally, we also make the semiparametric regression model more widely used in the field of surveying and mapping engineering through analysing the feasibility and effectiveness of the theory and algorithms.The following aspects are primaryly foused on in this thesis:1. A systematical analysis of research background of systematic errors is presented, especially in retrospect the research status of adjustment model, semiparametric regression model and posterior estimation of adjustment stochastic model.2. Briefly introducing the principle of semiparametric regression model, Helmert variance component estimation and the virtual solution of the semiparametric regression model.3. According to the weakness of penalized least squares method, conceiving the virtual solution of the semiparametric model based on semivariogram by utilization of regionalized variable theory and Helmert variance component estimation, this method is successfully applied in GPS height fitting, and the effect was significant.4. Reference of the latest theories and methods of collocation, two minimization steps estimation of semiparametric regression model is proposed based on Helmert variance component estimation. By using this, the realization of modeling systematic errors by steps is generated that improving the accuracy of the parameter estimation, and the feasibility and rationality of the algorithm is proved by numerical simulation.5. Considering the ill-posedness of semiparametric regression model and the practical situation of geodesy, semiparametric regression model with priori information constrained was established. Meanwhile, the algorithms with equality or inequality constrained were respectively studied by Helmert variance component estimation. And the free network adjustment algorithm was produced. Finally, the necessity and effectiveness of proposed algorithm is confirmed in the simulation analysis.