加权混合估计中权值的确定方法

doi:10.11947/j.AGCS.2020.20180359

测绘学报 ›› 2020, Vol. 49 ›› Issue (1): 34-41.doi: 10.11947/j.AGCS.2020.20180359

加权混合估计中权值的确定方法

宋迎春^1,2, 宋采薇^1,2, 左廷英^1,2

1. 中南大学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;
2. 中南大学地球科学与信息物理学院, 湖南长沙 410083

收稿日期:2018-07-30 修回日期:2019-08-25 发布日期:2020-01-16
通讯作者: 左廷英 E-mail:zty2003@163.com
作者简介:宋迎春(1963-),男,博士,教授,研究方向为测量数据处理理论与方法。E-mail:csusyc@csu.edu.cn,csusyc@qq.com
基金资助:
国家自然科学基金（41574006；41674009；41674012）

A method for determining the weight in weighted mixed estimation

SONG Yingchun^1,2, SONG Caiwei^1,2, ZUO Tingying^1,2

1. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha 410083, China;
2. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China

Received:2018-07-30 Revised:2019-08-25 Published:2020-01-16
Supported by:
The National Natural Science Foundation of China (Nos. 41574006;41674009;41674012)

摘要/Abstract

摘要： 综合了大地测量中各种异方差多源观测模型和联合平差方法，说明了混合估计方法可以用于测量数据融合，平衡附加信息和样本信息对参数估计的影响。通过求取权值使参数估计的协方差阵的迹最小的方法，给出了一个权的最优选择方法。本文扩展了已有的加权混合估计方法，使得新方法中的权不受验前单位权方差的限制，能有效应用于大地测量数据处理。

关键词: 随机约束, 平差模型, 加权混合估计, 最优线性无偏估计

Abstract: In this paper, multi-source observation models with various heteroscedastic and combined adjustment methods in geodesy are summarized. It shows that the mixed estimation method can be used for measurement data fusion, and can balance the influence of additional information and sample information on parameter estimation. By calculating the weights to minimize the trace of the covariance matrix of parameter estimation, an optimal selection method of weights is given. This paper extends the existing weighted mixing method so that the given method are not limited by the prior unit weight variance, and can be effectively applied to large measurement data processing.

Key words: stochastic constraint, adjustment model, weighted mixed estimation, optimal linear unbiased estimation

中图分类号:

P207

宋迎春, 宋采薇, 左廷英. 加权混合估计中权值的确定方法[J]. 测绘学报, 2020, 49(1): 34-41.

SONG Yingchun, SONG Caiwei, ZUO Tingying. A method for determining the weight in weighted mixed estimation[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(1): 34-41.

参考文献

[1] 杨元喜. 综合PNT体系及其关键技术[J]. 测绘学报, 2016, 45(5):505-510. DOI:10.11947/j.AGCS.2016.20160127. YANG Yuanxi. Concepts of comprehensive PNT and related key technologies[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5):505-510. DOI:10.11947/j.AGCS.2016.20160127.
[2] 杨元喜, 曾安敏. 大地测量数据融合模式及其分析[J]. 武汉大学学报(信息科学版), 2008, 33(8):771-774. YANG Yuanxi, ZENG Anmin. Fusion modes of various geodetic observations and their analysis[J]. Geomatics and Information Science of Wuhan University, 2008, 33(8):771-774.
[3] 杨元喜. 多源传感器动、静态滤波融合导航[J]. 武汉大学学报(信息科学版), 2003, 28(4):386-388, 396. YANU Yuanxi. Kinematic and static filtering for multi-sensor navigation systems[J]. Geomatics and Information Science of Wuhan University, 2003, 28(4):386-388, 396.
[4] 张正禄. 监测大区域地壳垂直形变的重复精密重力和水准测量联合平差模型[J]. 测绘学报, 1986, 15(3):208-216. ZHANG Zhenglu. Repeated precise gravity and leveling combined adjustment model for monitoring vertical crustal deformation in large regions[J]. Acta Geodaetica et Cartographica Sinica, 1986, 15(3):208-216.
[5] 周忠谟, 晁定波. GPS空间基线向量网与地面控制网的联合平差模型[J]. 武汉测绘科技大学学报, 1987, 12(2):20-28. ZHOU Zhongmo, CHAO Dingbo. The combined adjustment model for GPS space baseline vector network and terrestrial control network[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1987, 12(2):20-28.
[6] 杨沾吉, 於宗俦, 于正林, 等. GPS水准、天文重力水准与重力大地水准面多种数据联合处理的研究[J]. 武汉测绘科技大学学报, 1996, 21(4):330-337. YANG Zhanji, YU Zongchou, YU Zhenglin, et al. A study of combined data processing with GPS leveling, astrogravimetric leveling and gravimetric geoid[J]. Journal of Wuhan Technical University of Surveying and Mapping, 1996, 21(4):330-337.
[7] 杨元喜, 曾安敏, 景一帆. 函数模型和随机模型双约束的GNSS数据融合及其性质[J]. 武汉大学学报(信息科学版), 2014, 39(2):127-131. YANG Yuanxi, ZENG Anmin, JING Yifan. GNSS data fusion with functional and stochastic model constraints as well as property analysis[J]. Geomatics and Information Science of Wuhan University, 2014, 39(2):127-131.
[8] 张朝玉, 陶本藻, 时晋. 多类观测量联合平差中方差分量估计的序贯算法[J]. 大地测量与地球动力学, 2005, 25(3):34-38. ZHANG Chaoyu, TAO Benzao, Shi Jin. Sequential algorithm on variance component estimation in joint adjustment of various observations[J]. Journal of Geodesy and Geodynamics, 2005, 25(3):34-38.
[9] 成英燕, 程鹏飞, 顾旦生, 等. 联合平差中的方差分量估计问题的探讨[J]. 测绘科学, 2005, 30(2):51-54. CHENG Yingyan, CHENG Pengfei, GU Dansheng, et al. Variance component's estimation in the combined adjustment[J]. Science of Surveying and Mapping, 2005, 30(2):51-54.
[10] 独知行, 欧吉坤, 靳奉祥, 等. 联合反演模型中相对权比的优化反演[J]. 测绘学报, 2003, 32(1):15-19. DOI:10.3321/j.issn:1001-1595.2003.01.004. DU Zhixing, OU Jikun, JIN Fengxiang, et al. Optimization inversion of the relative weight ratio λ in the joint inversion models[J]. Acta Geodaetica et Cartographica Sinica, 2003, 32(1):15-19. DOI:10.3321/j.issn:1001-1595.2003.01.004.
[11] 王乐洋, 许才军, 张朝玉. 一种确定联合反演中相对权比的两步法[J]. 测绘学报, 2012, 41(1):19-24. WANG Leyang, XU Caijun, ZHANG Chaoyu. A two-step method to determine relative weight ratio factors in joint inversion[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(1):19-24.
[12] 刘长建, 吴洪举, 黄勇. 一种调整两类观测值权比的新方案[J]. 测绘通报, 2006(9):47-48, 68. DOI:10.3969/j.issn.0494-0911.2006.09.013. LIU Changjian, WU Hongju, HUANG Yong. A new scheme for adjusting weight ratio of two kinds of observations[J]. Bulletin of Surveying and Mapping, 2006(9):47-48, 68. DOI:10.3969/j.issn.0494-0911.2006.09.013.
[13] 王松桂. 线性模型的理论及其应用[M]. 合肥:安徽教育出版社, 1987. WANG Songgui. The theory and application of linear model[M]. Hefei:Anhui Education Press, 1987.
[14] 王松桂, 范永辉. Panel模型中两步估计的优良性[J]. 应用概率统计, 1998, 14(2):177-184. WANG Songgui, FAN Yonghui. Optimality of two-stage estimator in Panel models[J]. Chinese Journal of Applied Probability and Statistics, 1998, 14(2):177-184.
[15] 邬吉波, 杨虎. 回归系数的加权混合估计与最小二乘估计的相对效率[J]. 应用概率统计, 2015, 31(1):11-19. WU Jibo, YANG Hu. The relative efficiency of weighted mixed estimator with respect to least squares estimator in linear regression model[J]. Chinese Journal of Applied Probability and Statistics, 2015, 31(1):11-19.
[16] 陈玉蓉. 回归系数的混合估计与最小二乘估计的两种相对效率[J]. 数学杂志, 2007, 27(1):83-87. CHEN Yurong. Two kinds of relative efficiencies of mixed estimator with respect to LS estimator in linear regression model[J]. Journal of Mathematics, 2007, 27(1):83-87.
[17] DURBIN J. A note on regression when there is extraneous information about one of the coefficients[J]. Journal of the American Statistical Association, 1953, 48(264):799-808.
[18] THEIL H, GOLDBERGER A S. On pure and mixed statistical Estimation in economics[J]. International Economic Review 1961, 2:65-78.
[19] THEIL H. On the use of incomplete prior information in regression analysis[J]. Journal of the American Statistical Association, 1963, 58(302):401-414.
[20] SCHAFFRIN B, TOUTENBURG H. Weighted mixed regression[J]. Zeitschrift fur Angewandte Mathematik und Mechanik, 1990, 70(6):T735-T738.
[21] 李广云. 混合估计及其应用[J]. 勘察科学技术, 1993(1):44-46. LI Guangyun. Mixed estimation and its application[J]. Site Investigation Science and Technology, 1993(1):44-46.
[22] KAKWANI N C. Note on the unbiasedness of a mixed regression estimator[J]. Econometrica, 1968, 36(3-4):610-611.

加权混合估计中权值的确定方法

A method for determining the weight in weighted mixed estimation

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