协方差阵非负约束的赫尔默特方差分量估计

doi:10.11947/j.AGCS.2022.20200333

测绘学报 ›› 2022, Vol. 51 ›› Issue (3): 351-360.doi: 10.11947/j.AGCS.2022.20200333

协方差阵非负约束的赫尔默特方差分量估计

王乐洋^1,7, 赵雄^1,2, 许文斌^3,4, 汪驰升⁵, 方楠^3,4, 谢磊⁶

1. 东华理工大学测绘工程学院, 江西南昌 330013;
2. 武汉大学测绘学院, 湖北武汉 430079;
3. 中南大学地球科学与信息物理学院, 湖南长沙 410083;
4. 有色金属成矿预测与地质环境监测教育部重点实验室, 湖南长沙 410083;
5. 深圳大学自然资源部大湾区地理环境监测重点实验室, 广东深圳 518060;
6. 香港理工大学土地测量及地理资讯学系, 香港 999077;
7. 自然资源部环鄱阳湖区域矿山环境监测与治理重点实验室, 江西南昌 330013

收稿日期:2020-07-24 修回日期:2021-08-18 发布日期:2022-03-30
通讯作者: 许文斌 E-mail:wenbin.xu@csu.edu.cn
作者简介:王乐洋(1983-),男,博士,教授,研究方向为大地测量反演及大地测量数据处理。E-mail:wleyang@163.com
基金资助:
国家自然科学基金（41874001；42174011；41664001；41804015）；国家重点研发计划（2019YFC1509205）

Helmert variance component estimation with non-negative constraint of covariance matrix

WANG Leyang^1,7, ZHAO Xiong^1,2, XU Wenbin^3,4, WANG Chisheng⁵, FANG Nan^3,4, XIE Lei⁶

1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
2. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
3. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
4. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Changsha 410083, China;
5. Key Laboratory of Geo-Environmental Monitoring of Great Bay Area, MNR, Shenzhen University, Shenzhen 518060, China;
6. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong 999077, China;
7. Key Laboratory of Mine Environmental Monitoring and Improving around Poyang Lake, Ministry of Natural Resources, Nanchang 330013, China

Received:2020-07-24 Revised:2021-08-18 Published:2022-03-30
Supported by:
The National Natural Science Foundation of China (Nos. 41874001; 42174011; 41664001; 41804015); The National Key Research and Development Program (No. 2019YFC1509205)

摘要/Abstract

摘要： 在多源数据联合反演同震滑动分布过程中，各类观测数据之间相对权比的确定是当今大地测量与地球物理联合反演领域的研究热点和难点。近年来，赫尔默特方差分量估计法因其可以同时估计虚拟观测数据及实际观测数据之间的比例因子的优势，在联合反演滑动分布领域中得到了广泛应用。然而，利用HVCE法确定多源数据联合反演相对权比过程中易出现负方差现象。针对以上问题，本文提出在HVCE法确定联合反演相对权比过程中添加线性不等式约束，利用带有线性不等式约束的平差模型进行求解（LC-HVCE），解决计算过程中出现负方差问题。为了验证LC-HVCE法的有效性，开展模拟地震试验，结果表明LC-HVCE法可以有效地解决HVCE法在确定联合反演相对权比过程中存在的不足，保证了同震滑动分布反演精度。蒙特卡洛模拟试验及拉奎拉实际地震反演结果进一步表明了LC-HVCE法在确定正则化参数与相对权比过程中较HVCE法的适用性与稳定性。

关键词: 赫尔默特方差分量估计, 相对权比, 正则化参数, 线性不等式约束

Abstract: How to determine the relative weight ratio in geodetic data inversion among various datasets is one of the challenging topics. In recent years, Helmert variance component estimation method (HVCE) has been widely used in the field of relative weights of joint inversion slip distributions due to its advantage of simultaneously estimating the scale factors between virtual and actual observations. However, the HVCE method sometimes suffers from the occurrence of negative variance. To overcome these problems, we propose linear inequality constraints based helmert variance component estimation method (LC-HVCE). We carry out synthetic experiment to verify the effectiveness and robustness of the LC-HVCE method and estimate the uncertainty of LC-HVCE method by Monte carlo method. We apply the proposed method to invert for the source parameters of the 2009 Mw6.3 L'Aquila earthquake (Italy). We find that LC-HVCE method is more applicable and stability than HVCE method in determining relative weight ratio and regularization parameter.

Key words: Helmert variance component estimation, relative weight ratio, regularization parameter, linear inequality constraints

中图分类号:

P228

王乐洋, 赵雄, 许文斌, 汪驰升, 方楠, 谢磊. 协方差阵非负约束的赫尔默特方差分量估计[J]. 测绘学报, 2022, 51(3): 351-360.

WANG Leyang, ZHAO Xiong, XU Wenbin, WANG Chisheng, FANG Nan, XIE Lei. Helmert variance component estimation with non-negative constraint of covariance matrix[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(3): 351-360.

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协方差阵非负约束的赫尔默特方差分量估计

Helmert variance component estimation with non-negative constraint of covariance matrix

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