总体最小二乘平差方法及若干测绘应用研究

发布时间：2018-03-25 15:43

本文选题：EIV模型　切入点：总体最小二乘　出处：《中国矿业大学》2017年硕士论文

【摘要】：本文以丰富总体最小二乘平差方法及拓展其应用为主线,以理论分析、仿真计算和实际应用为研究手段,以最小二乘理论、广义逆理论、稳健估计等理论为研究方法,围绕总体最小二乘方法的函数模型与随机模型中的若干问题,开展了相应的理论与应用研究工作。论文的主要研究内容和研究成果如下:(1)从函数模型与随机模型两方面系统地介绍现有的总体最小二乘平差方法,给出了各种具体的参数估计与精度评定公式,并指出各种方法的特点;介绍了用于处理观测值具有序贯特征的递归总体最小二乘算法,并分析指出其在算法耗时方面相较于总体最小二乘方法具有的优越性。(2)提出了隐式标度因子总体最小二乘平差方法。研究并指出了现有标度总体最小二乘的平差准则存在的问题,在此基础上提出了附隐式标度因子的EIV模型,并导出相应的隐式标度因子总体最小二乘方法及其基本向量的协因数阵公式。仿真计算结果表明本文导出的隐式标度因子总体最小二乘法能够有效解决现有标度总体最小二乘平差准则存在的问题。(3)提出了改进的混合总体最小二乘平差方法。研究复杂EIV模型的总体最小二乘平差问题。提出采用一般线性函数关系式对函数独立、非函数独立(零、重复、互为相反数等各种线性函数关系)的系数阵误差元素进行数学统一描述,并导出了适用于混合EIV模型的改进混合总体最小二乘方法。仿真计算结果表明了该方法的正确有效性。(4)提出了多变量稳健总体最小二乘平差方法。研究稳健总体最小二乘平差问题。指出了现有稳健总体最小二乘平差方法在处理EIV模型多类观测信息时存在的问题,在此基础上提出了多变量稳健估计权函数,并导出了相应稳健总体最小二乘估计的参数估计与精度评定公式。仿真计算结果验证了本文的多变量稳健总体最小二乘平差方法的正确有效性。(5)研究总体最小二乘方法在测绘领域的应用。结果表明总体最小二乘方法的实际应用效果视研究的问题而异。在香港地区的高程异常拟合中,其平差结果与经典最小二乘平差结果无明显差别。在全球范围的坐标基准框架准换、某地区的边长变化反演地壳应变参数、遥感影像的叶面积指数反演模型中,其参数估计结果优于经典最小二乘平差结果。在地球自转参数预报模型中,其预报结果低于最小二乘法的预报结果。
[Abstract]:The main line of this paper is to enrich the total least square adjustment method and to expand its application, taking theoretical analysis, simulation calculation and practical application as the research means, and taking the least square theory, generalized inverse theory and robust estimation theory as the research methods. Some problems in the function model and stochastic model of the total least squares method are discussed. The main contents and results of this paper are as follows: 1) the existing methods of total least square adjustment are systematically introduced from two aspects: function model and stochastic model. The parameters estimation and precision evaluation formulas are given, and the characteristics of various methods are pointed out, and the recursive population least squares algorithm used to deal with the sequential characteristics of observed values is introduced. Compared with the total least squares method, this paper presents an implicit scaling factor total least square adjustment method and studies and points out the adjustment of the existing scale total least squares method, and points out the advantages of the algorithm in comparison with the total least squares method. (2) the implicit scaling factor of the total least squares adjustment method is proposed, and the adjustment of the existing scale population least squares method is studied and pointed out. Problems with the criteria, On this basis, the EIV model with implicit scaling factor is proposed. The corresponding implicit scaling factor total least squares method and the cofactor matrix formula of the basic vector are derived. The simulation results show that the implicit scale factor total least square method derived in this paper can effectively solve the existing scale. In this paper, an improved mixed population least square adjustment method is proposed. The problem of total least square adjustment for complex EIV model is studied. The general linear function relation is proposed to be independent of the function. The error elements of the coefficient matrix of non-functional independence (zero, repetition, reciprocal opposite number and other linear function relations) are described mathematically. An improved hybrid population least squares method suitable for mixed EIV model is derived. The simulation results show that the method is correct and effective. (4) A multivariable robust population least squares adjustment method is proposed, and robust population adjustment is studied. The problem of least square adjustment is pointed out. The problems existing in the existing robust global least squares adjustment methods in dealing with various kinds of observation information of EIV model are pointed out. On this basis, a multivariable robust estimation weight function is proposed. The parameter estimation and precision evaluation formula of the corresponding robust population least squares estimation are derived. The simulation results verify the validity of the multivariable robust population least squares adjustment method. The application of multiplicative method in surveying and mapping. The results show that the practical application effect of the total least squares method is different from that of the research. In the height anomaly fitting of Hong Kong area, There is no obvious difference between the adjustment results and the classical least square adjustment results. In the model of inversion of crustal strain parameters and leaf area index of remote sensing image, the global coordinate datum frame is changed correctly, the variation of side length of a certain area is used to invert crustal strain parameters, and the inversion model of leaf area index of remote sensing image is obtained. The result of parameter estimation is superior to that of classical least square adjustment, and in the prediction model of earth rotation parameter, the prediction result is lower than that of least square method.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P207.2

【参考文献】