| 基于等效残差的方差-协方差分量估计 |
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| 引用本文： | 李博峰,沈云中,楼立志.基于等效残差的方差-协方差分量估计[J].测绘学报,2010,39(4):349-354,363. |
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| 作者姓名： | 李博峰 沈云中 楼立志 |
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| 作者单位： | 同济大学,测量与国土信息工程系,上海,200092;同济大学,测量与国土信息工程系,上海,200092;现代工程测量国家测绘局重点实验室,上海200092 |
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| 基金项目： | 国家自然科学基金，现代工程测量国家测绘局重点实验室开放课题 |
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| 摘 要： | 首先概括性地阐述方差-协方差分量估计(VCE)理论的发展历史与研究现状;利用正交分解提取出等效残差,建立VCE的基本方程,在此基础上阐述VCE算法的局部最优特性和可能出现负定协方差阵估计结果等两大问题,并分析可能的解决方案及其复杂性;导出初值给定的Helmert,最小二乘和MINQUE VCE的线性逼近估计公式,证明基于等效残差的估计公式与已有VCE公式等价,各种估计方法在本质上是一致的;最后,用两个算例验证本文的观点.
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| 关 键 词： | 方差-协方差分量估计 正交分解 Helmert 方差分量估计 最小范数二次无偏估计 全局最优化 |
Variance-covariance Component Estimation Based on the Equivalent Residuals |
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| LI Bofeng,SHEN Yunzhong,LOU Lizhi.Variance-covariance Component Estimation Based on the Equivalent Residuals[J].Acta Geodaetica et Cartographica Sinica,2010,39(4):349-354,363. |
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| Authors: | LI Bofeng SHEN Yunzhong LOU Lizhi |
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| Institution: | LI Bofeng1,SHEN Yunzhong1,2,LOU Lizhi1,2 1.Department of Surveying and Geo-informatics Engineering,Tongji University,Shanghai 200092,China,2.Key Laboratory of Advanced Surveying Engineering of SBSM |
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| Abstract: | The development of the variance-covariance component estimation(VCE)theory is firstly synoptically reviewed in this paper.Then the equivalent residuals are extracted by using orthogonal decomposition and the fundamental equations for VCE are established.Based on that the two profound and unresolvable problems for VCE theory,namely regional optimality and negative definition for estimated covariance matrix,are explored and the corresponding possible resolvable schemes and their complexity are analysed.Thirdl... |
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| Keywords: | variance-covariance component estimation orthogonal decomposition Helmert VCE MINQUE global optimality |
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