等价条件平差模型的方差-协方差分量最小二乘估计方法

doi:10.11947/j.AGCS.2019.20180227

测绘学报 ›› 2019, Vol. 48 ›› Issue (9): 1088-1095.doi: 10.11947/j.AGCS.2019.20180227

等价条件平差模型的方差-协方差分量最小二乘估计方法

刘志平¹, 朱丹彤¹, 余航¹, 张克非^1,2

1. 中国矿业大学环境与测绘学院, 江苏徐州 221116;
2. 皇家墨尔本理工大学空间科学研究中心, 澳大利亚维多利亚州墨尔本 3001

收稿日期:2018-01-22 修回日期:2018-11-28 出版日期:2019-09-20 发布日期:2019-09-25
作者简介:刘志平(1982-),男,博士,副教授,研究方向为混合误差理论与反演、全源定位导航与应用。
基金资助:
国家自然科学基金重点项目（41730109）；国家自然科学基金（41771416；41204011）；江苏省"双创团队"项目（CUMT07180005）；江苏省"双创个人"项目（CUMT07180003）；自然资源部精密工程与工业测量重点实验室开放基金（PF2017-12）

Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model

LIU Zhiping¹, ZHU Dantong¹, YU Hang¹, ZHANG Kefei^1,2

1. School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China;
2. Space Research Centre, RMIT University, Australia VIC 3001

Received:2018-01-22 Revised:2018-11-28 Online:2019-09-20 Published:2019-09-25
Supported by:
The State Key Program of National Natural Science Foundation of China (No. 41730109);The National Natural Science Foundation of China (Nos. 41771416;41204011);The Jiangsu Dual Creative Teams Programme Projects Awarded In 2017 (No. CUMT07180005);The Jiangsu Dual Creative Tanlents Programme Projects Awarded In 2017 (No. CUMT07180003);The Open Foundation of Precise Engineering & Industry Surveying Key Laboratory of Natural Resources Ministry (No. PF2017-12)

摘要/Abstract

摘要： 提出等价条件闭合差的方差-协方差分量最小二乘估计方法，简称LSV-ECM法。首先，利用等价条件平差模型建立了基于等价条件闭合差二次型的方差-协方差分量估计方程，由矩阵半拉直算子将其变换为线性Gauss-Markov形式，进而通过最小二乘准则导出了具有模型通用性、形式简洁性且满足无偏性和最优性的方差-协方差分量估计公式。其次，证明了LSV-ECM方法与残差型VCE方法的等价性，并在此基础上通过计算复杂度定量分析了所提方法的计算高效性。最后，通过边角网平差和中国区域GNSS站坐标时序建模及其结果分析，验证了所提新方法的正确性和计算高效性。

关键词: 等价条件平差模型, 方差-协方差分量估计, LSV-ECM法, 边角网, GNSS站坐标时间序列

Abstract: A VCE method termed the least-square variance-covariance component estimation method based on the equivalent conditional misclosure (LSV-ECM) is developed. Three steps are involved. First, the equivalent conditional misclosure is extracted using the projection matrix in the equivalent conditional adjustment model, of which the quadratic equations are established for variance-covariance component estimation. The quadratic equations in the form of matrix are then transformed to the linearized Gauss-Markov form using the half-vectorization operator. A simplified and generalized LSV-ECM method is derived using the least-square principle with an unbiased and optimal estimation.Furthermore, the equivalence between the LSV-ECM and the existing VCE methods is proven mathematically, and computational complexities of the LSV-ECM and the existing VCE methods are quantitatively analyzed and investigated in the indirect adjustment model. It is shown that the new method gives the highest computational efficiency. Finally, the performance and superiority of the new method is evaluated through an adjustment of a triangulateration network and an analysis of a coordinate time series of GNSS stations.

Key words: equivalent conditional adjustment model, variance-covariance component estimation, LSV-ECM method, triangulateration network, GNSS station coordinate time series

中图分类号:

P207

刘志平, 朱丹彤, 余航, 张克非. 等价条件平差模型的方差-协方差分量最小二乘估计方法[J]. 测绘学报, 2019, 48(9): 1088-1095.

LIU Zhiping, ZHU Dantong, YU Hang, ZHANG Kefei. Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(9): 1088-1095.

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等价条件平差模型的方差-协方差分量最小二乘估计方法

Least-square variance-covariance component estimation method based on the equivalent conditional adjustment model

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