The Theory And Application In Geodesy Of Semi-parametric Model

Semiparametric model have been important statistics model since 1980s, it imports nonparametric components to describe systematic errors and model errors, so it is a fire-new method to research and resolve model errors. The semiparametric model includes not only parametric components, but also nonparametric components, so it has the advantages of the parametric model and the nonparametric model. By dealing with the theories and methods of semiparametric model, this paper did some work as follows:Firstly, it researches the estimation methods of semiparametric model based on regular matrix; gives some statistical properties for the estimates of the semiparametric model. Then the choices of regular matrix and smoothing factor are systematically discussed. At last, the writer puts forward a new method to choose smoothing factor named pseudo variance components estimation.Secondly, especially researching the ill-conditioned problem of the semiparametric model, using three different kinds of ridge estimation model to deal with the ill-conditioned problem, and giving the formulas of the ridge estimation model. The choices of ridge parameter are discussed particularly, finally giving some statistical properties for the estimates of ridge estimation for semiparametric model.Thirdly, in the chapter 4, it gives some normal methods of GPS elevation, and discusses the precision assessing of normal methods. Then it researches the semiparametric model of Polynomial fitting and Hardy function interpolation, gives the formulas of the model. The nonparametric components are derived by using for reference of collocation, and the precision assessing of semiparametric methods applied in GPS elevation are given. Finally, it gets the method to choose regular matrix for GPS elevation.In the chapter 5, it introduces the Helmert transformation and interpolation method of coordinate transformation in geodetic coordinate system, gives the semiparametric model of seven parameter model and three parameter model, then discusses the method to choose regular matrix which can counteract the model error derived from distortion of the local coordinate.At last, the whole research work was summarized, and the next work was also showed.