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  本文選題：EIV模型　切入點：總體最小二乘　出處：《中國礦業(yè)大學》2017年碩士論文

【摘要】：本文以豐富總體最小二乘平差方法及拓展其應(yīng)用為主線,以理論分析、仿真計算和實際應(yīng)用為研究手段,以最小二乘理論、廣義逆理論、穩(wěn)健估計等理論為研究方法,圍繞總體最小二乘方法的函數(shù)模型與隨機模型中的若干問題,開展了相應(yīng)的理論與應(yīng)用研究工作。論文的主要研究內(nèi)容和研究成果如下:(1)從函數(shù)模型與隨機模型兩方面系統(tǒng)地介紹現(xiàn)有的總體最小二乘平差方法,給出了各種具體的參數(shù)估計與精度評定公式,并指出各種方法的特點;介紹了用于處理觀測值具有序貫特征的遞歸總體最小二乘算法,并分析指出其在算法耗時方面相較于總體最小二乘方法具有的優(yōu)越性。(2)提出了隱式標度因子總體最小二乘平差方法。研究并指出了現(xiàn)有標度總體最小二乘的平差準則存在的問題,在此基礎(chǔ)上提出了附隱式標度因子的EIV模型,并導出相應(yīng)的隱式標度因子總體最小二乘方法及其基本向量的協(xié)因數(shù)陣公式。仿真計算結(jié)果表明本文導出的隱式標度因子總體最小二乘法能夠有效解決現(xiàn)有標度總體最小二乘平差準則存在的問題。(3)提出了改進的混合總體最小二乘平差方法。研究復雜EIV模型的總體最小二乘平差問題。提出采用一般線性函數(shù)關(guān)系式對函數(shù)獨立、非函數(shù)獨立(零、重復、互為相反數(shù)等各種線性函數(shù)關(guān)系)的系數(shù)陣誤差元素進行數(shù)學統(tǒng)一描述,并導出了適用于混合EIV模型的改進混合總體最小二乘方法。仿真計算結(jié)果表明了該方法的正確有效性。(4)提出了多變量穩(wěn)健總體最小二乘平差方法。研究穩(wěn)健總體最小二乘平差問題。指出了現(xiàn)有穩(wěn)健總體最小二乘平差方法在處理EIV模型多類觀測信息時存在的問題,在此基礎(chǔ)上提出了多變量穩(wěn)健估計權(quán)函數(shù),并導出了相應(yīng)穩(wěn)健總體最小二乘估計的參數(shù)估計與精度評定公式。仿真計算結(jié)果驗證了本文的多變量穩(wěn)健總體最小二乘平差方法的正確有效性。(5)研究總體最小二乘方法在測繪領(lǐng)域的應(yīng)用。結(jié)果表明總體最小二乘方法的實際應(yīng)用效果視研究的問題而異。在香港地區(qū)的高程異常擬合中,其平差結(jié)果與經(jīng)典最小二乘平差結(jié)果無明顯差別。在全球范圍的坐標基準框架準換、某地區(qū)的邊長變化反演地殼應(yīng)變參數(shù)、遙感影像的葉面積指數(shù)反演模型中,其參數(shù)估計結(jié)果優(yōu)于經(jīng)典最小二乘平差結(jié)果。在地球自轉(zhuǎn)參數(shù)預報模型中,其預報結(jié)果低于最小二乘法的預報結(jié)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.
【學位授予單位】：中國礦業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：P207.2

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本文編號：1663779