Study On The Adjustment Criterion Of The Semi-parametric Adjustment Model

Measurement data processing method and the accuracy requirement gradually improve along with the development of modern surveying technology. Processing systematic error of traditional measurement is simple, easy to operate. However, it already cannot satisfy the requirement of modern surveying and mapping. In this paper, the issue of dealing with systematic errors and the development of relevant theories is mainly discussed. The semi-parametric regression model in dealing with systematic errors is focused on. To make theories of the model more perfect and expression of some issues more clear, we analyze calculating criterion (penalized least square), summarize many methods of getting the regularization parameter and explore its influence factors and regularity. Also, to make the description of smoothness more clear, we deeply analyze smoothness of compensation of the calculating criterion. As a result of above work, a new reference method for the study of Semi-parametric regression models is proposed.The main research works are in the following areas:1. Introducing the processing method and theory of systematic errors in the traditional surveying, background of a semi-parametric regression model, retrospecting the development of semi-parametric regression model in the mathematical statistics and mapping.2. Giving a brief introduction of the two traditional adjustment models dealing with systematic errors, the basic principles and solution with the penalized least squares of semi-parametric regression models, presenting relevant statistics'characteristic of the model.3. The theory of penalized least squares to get a more exact result is not completed, and the influence factors of regularization parameter are analyzed in this paper. As we know, there are many methods for choosing regularization parameter, but results getting from them are different to the same model. After comparing L-Curve, GCV and quasi observation, we can draw a conclusion:Regularization parameter determination is closely related with the signal-to-noise ratio (SNR); With the increase of system error and constant magnitude of random error (that is, the signal-to-noise ratio is gradually increasing), various methods to determine the regularization parameters result in different trends.4. There are some problems about smoothness and regularization matrix. Such as how to connect smoothness and regularization matrix, what the relationship between them is, and how to describe the smoothness more completely. To get a better explanation, we make further analysis of smoothness of compensation, by making systematic analysis of the background of various methods for determine regularization matrix, as well as summarizing the source of the major methods. Finally, we propose a method to determining regularization matrix by periodic spline function and prove this method available to some extent.