Variance Components Estimation for Total Least-Squares Regression Prediction Model

WANG Leyang; SUN Jianqiang

doi:10.13203/j.whugis20180450

Volume 46 Issue 2

Jan. 2021

Turn off MathJax

Article Contents

Abstract

References

Geomatics and Information Science of Wuhan University > 2021 > 46(2): 280-288. > DOI: 10.13203/j.whugis20180450

WANG Leyang, SUN Jianqiang. Variance Components Estimation for Total Least-Squares Regression Prediction Model[J]. Geomatics and Information Science of Wuhan University, 2021, 46(2): 280-288. DOI: 10.13203/j.whugis20180450

Citation:

PDF (1454 KB)

Variance Components Estimation for Total Least-Squares Regression Prediction Model

WANG Leyang^1,,
SUN Jianqiang¹

1.
Faculty of Geomatics, East China University of Technology, Nanchang 330013, China

Funds:

The National Natural Science Foundation of China 41874001

The National Natural Science Foundation of China 41664001

the Support Program for Outstanding Youth Talents in Jiangxi Province 20162BCB23050

the National Key Research and Development Program of China 2016YFB0501405

More Information

Author Bio:
WANG Leyang, PhD, professor, specializes in the geodetic inversion and geodetic data processing. E-mail: wleyang@163.com
Received Date: November 09, 2019
Published Date: February 04, 2021

Graphical Abstract

Abstract

Abstract

As a further extension of traditional regression model, the regression prediction model not only involves the fixed parameter estimation of regression model, but also incorporates the model prediction into part of adjustment, which is more in line with the solutions of actual requirements. Focusing on the issues of predicted non-common points (independent variables) polluted with errors and inaccurate stochastic model, this paper proposes a new complete solution with a sufficient consideration to all errors of each variables based on errors-in-variables (EIV) model. Meanwhile, performed with the methodology of variance-covariance component estimation, stochastic model and prior cofactor matrix of the predicted non-common points have been corrected. The corresponding formulas are derived and the iterative algorithm is also presented. Experimental design shows that the presented approach can effectively achieve the estimation of variance components for various types of observations. It provides a feasible means for retrieving more reasonable parameter results and achieving higher prediction accuracy. In addition, the prediction effect of our presented approach is better over other control schemes, especially for the situation where there is a certain correlation between the observed data and the random elements in coefficient matrix.

FullText(HTML)

References (34)

References

[1]	Adcok R. A Problem in Least Squares[J]. Analyst, 1878, 5: 53-54 doi: 10.2307/2635758
[2]	Pearson K. On Lines and Planes of Closest Fit to Systems of Points in Space[J]. Philosophical Magazine and Journal of Science, 2010, 2(11): 559-572
[3]	York D. Least-Squares Fitting of a Straight Line[J]. Canadian Journal of Physics, 1996, 44(5): 1 079-1 086
[4]	Golub G H, van Loan C F. An Analysis of the Total Least Squares Problem[J]. SIAM Journal on Numerical Analysis, 1980, 17(6): 883-893 doi: 10.1137/0717073
[5]	Fang Xing, Wang Jin, Li Bofeng, et al. On Total Least Squares for Quadratic Form Estimation[J]. Studia Geophysica et Geodaetica, 2015, 59(3): 366-379 doi: 10.1007/s11200-014-0267-x
[6]	Shen Yunzhong, Li Bofeng, Chen Yi. An Iterative Solution of Weight Total Least-Squares Adjustment[J]. Journal of Geodesy, 2011, 85(4): 229-238 doi: 10.1007/s00190-010-0431-1
[7]	Fang Xing. Weighted Total Least Squares Solutions for Applications in Geodesy[D]. Germany: Leibniz Universität Hannover, 2011
[8]	Fang Xing. Weight Total Least-Squares with Constraints: A Universal Formula for Geodetic Symmetrical Transformations[J]. Journal of Geodesy, 2015, 89(5): 459-469 doi: 10.1007/s00190-015-0790-8
[9]	Jazaeri S, Amiri-Simkooei A R, Sharfi M A. Iterative Algorithm for Weight Total Least Squares Adjustment[J]. Survey Review, 2014, 46(334): 19-27 doi: 10.1179/1752270613Y.0000000052
[10]	Amiri-Simkooei A R, Jazaeri S. Weighted Total Least Squares Formulated by Standard Least Squares Theory[J]. Jouranal of Geodetic Science, 2012, 2(2): 113-124 doi: 10.2478/v10156-011-0036-5
[11]	汪奇生, 杨德宏, 杨建文.基于总体最小二乘的线性回归迭代算法[J].大地测量与地球动力学, 2013, 33(6): 112-114, 120 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB201306026.htm Wang Qisheng, Yang Dehong, Yang Jianwen. An Iterative Algorithm of Linear Regression Based on Total Least Squares[J]. Journal of Geodesy and Geodynamics, 2013, 33(6): 112-114, 120 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB201306026.htm
[12]	孔建, 姚宜斌, 吴寒.整体最小二乘的迭代解法[J].武汉大学学报∙信息科学版, 2010, 35(6): 711-714 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201006024.htm Kong Jian, Yao Yibin, Wu Han. Iterative Method for Total Least-Squares[J]. Geomatics and Information Science of Wuhan University, 2010, 35(6):711-714 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201006024.htm
[13]	Schaffrin B, Wieser A. On Weighted Total Least-Squares Adjustment for Linear Regression[J]. Journal of Geodesy, 2008, 82(7):415-421 doi: 10.1007/s00190-007-0190-9
[14]	王乐洋, 赵英文, 陈晓勇, 等.多元总体最小二乘问题的牛顿解法[J].测绘学报, 2016, 45(4): 411-417 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201604006.htm Wang Leyang, Zhao Yingwen, Chen Xiaoyong, et al. A Newton Algorithm for Multivariate Total Least Squares Problems[J].Acta Geodaetica et Cartographica Sinica, 2016, 45(4): 411-417 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201604006.htm
[15]	许光煜. Partial EIV模型的总体最小二乘方法及应用研究[D].南昌: 东华理工大学, 2016 Xu Guangyu. The Total Least Squares Method and Its Application of Partial Errors-in-Variables Model[D]. Nanchang: East China University of Technology, 2016
[16]	陶武勇, 鲁铁定, 许光煜, 等.稳健总体最小二乘Helmert方差分量估计[J].大地测量与地球动力学, 2017, 37(11): 1 193-1 197 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB201711019.htm Tao Wuyong, Lu Tieding, Xu Guangyu, et al. Helmert Variance Component Estimation for Robust Total Least Squares[J]. Journal of Geodesy and Geodynamics, 2017, 37(11): 1 193-1 197 https://www.cnki.com.cn/Article/CJFDTOTAL-DKXB201711019.htm
[17]	王乐洋, 许光煜.加权总体最小二乘平差随机模型的验后估计[J].武汉大学学报∙信息科学版, 2016, 41(2): 255-261 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201602018.htm Wang Leyang, Xu Guangyu. Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem[J]. Geomatics and Information Science of Wuhan University, 2016, 41(2): 255-261 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201602018.htm
[18]	杨元喜, 张晓东.基于严密Helmert方差分量估计的动态Kalman滤波[J].同济大学学报(自然科学版), 2009, 37(9): 1 241-1 245 https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ200909021.htm Yang Yuanxi, Zhang Xiaodong. Variance Component Estimation of Helmert Type-Based Dynamic Kalman Filtering[J]. Journal of Tongji University (Natural Science), 2009, 37(9): 1 241-1 245 https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ200909021.htm
[19]	Wang Leyang, Xu Guangyu. Variance Component Estimation for Partial Errors-in-Variables Models[J]. Studia Geophysica et Geodaetica, 2016, 60(1): 35-55 doi: 10.1007/s11200-014-0975-2
[20]	乐科军.基于Helmert方差分量估计的半参数回归模型若干算法研究[D].长沙: 中南大学, 2009 Le Kejun. A Study on the Algorithms of Semiparametric Regression Model Based on Helmert Variance Component Estimation[D]. Changsha: Central South University, 2009
[21]	赵俊, 郭建锋.方差分量估计的通用公式[J].武汉大学学报·信息科学版, 2013, 38(5): 580-583 http://ch.whu.edu.cn/article/id/2639 Zhao Jun, Guo Jianfeng. Auniversal Formula of Variance Component Estimation[J]. Geomatics and Information Science of Wuhan University, 2013, 38(5): 580-583 http://ch.whu.edu.cn/article/id/2639
[22]	Xu Peiliang, Liu Jingnan. Variance Components in Errors-in-Variables Models: Estimability, Stability and Bias Analysis[J]. Journal of Geodesy, 2014, 88(8): 719-734 doi: 10.1007/s00190-014-0717-9
[23]	Amiri-Simkooei A R. Least-Squares Variance Component Estimation: Theory and GPS Applications[D]. Delft: Delft University of Technology, 2007
[24]	Teunissen P J G, Amiri-Simkooei A R. Least-Squares Variance Component Estimation[J]. Journal of Geodesy, 2008, 82(2): 65-82 doi: 10.1007/s00190-007-0157-x
[25]	Amiri-Simkooei A R. Non-negative Least-Squares Variance Component Estimation with Application to GPS Time Series[J]. Journal of Geodesy, 2016, 90(5): 451-466 doi: 10.1007/s00190-016-0886-9
[26]	王乐洋, 温贵森.相关观测PEIV模型的最小二乘方差分量估计[J].测绘地理信息, 2018, 43(1): 8-14 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXG201801002.htm Wang Leyang, Wen Guisen. Least Squares Variance Components Estimation of PEIV Model with Correlated Observations[J]. Journal of Geomatics, 2018, 43(1): 8-14 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXG201801002.htm
[27]	王乐洋, 温贵森. Partial EIV模型的非负最小二乘方差分量估计[J].测绘学报, 2017, 46(7): 857-865 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201707009.htm Wang Leyang, Wen Guisen. Non-negative Least Squares Variance Component Estimation of Partial EIV Model[J]. Acta Geodetica et Cartographica Sinica, 2017, 46(7): 857-865 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201707009.htm
[28]	陶叶青, 蔡安宁, 杨娟.方差分量估计的抗差总体最小二乘算法[J].测绘工程, 2018, 27(3): 1-5 https://www.cnki.com.cn/Article/CJFDTOTAL-CHGC201803001.htm Tao Yeqing, Cai Anning, Yang Juan. Solution for Robust Total Least Squares Based on Variance Component Estimation[J]. Engineering of Surveying and Mapping, 2018, 27(3): 1-5 https://www.cnki.com.cn/Article/CJFDTOTAL-CHGC201803001.htm
[29]	刘志平, 张书毕.方差-协方差分量估计的概括平差因子法[J].武汉大学学报∙信息科学版, 2013, 38(8): 925-929 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201308011.htm Liu Zhiping, Zhang Shubi. Variance-Covariance Component Estimation Method Based on Generalization Adjustment Factor[J]. Geomatics and Information Science of Wuhan University, 2013, 38(8): 925-929 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201308011.htm
[30]	王乐洋, 余航.附有相对权比的加权总体最小二乘联合平差方法[J].武汉大学学报∙信息科学版, 2019, 44(8): 1 233-1 240 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201908018.htm Wang Leyang, Yu Hang. Weighted Total Least Squares Method for Joint Adjustment Model with Weight Scaling Factor[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1 233-1 240 https://www.cnki.com.cn/Article/CJFDTOTAL-WHCH201908018.htm
[31]	王苗苗, 李博峰.无缝线性回归与预测模型[J].测绘学报, 2016, 45(12): 1 396-1 405 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201612003.htm Wang Miaomiao, Li Bofeng. Seamless Linear Regression and Prediction Model[J]. Acta Geodetica et Cartographica Sinica, 2016, 45(12): 1 396-1 405 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201612003.htm
[32]	李博峰, 沈云中, 李微晓.无缝三维基准转换模型[J].中国科学:地球科学, 2012, 42(7): 1 047-1 054 https://www.cnki.com.cn/Article/CJFDTOTAL-JDXK201207012.htm Li Bofeng, Shen Yunzhong, Li Weixiao. The Seamless Model for Three-Dimensional Datum Transformation[J]. Science China: Earth Sciences, 2012, 42(7): 1 047-1 054 https://www.cnki.com.cn/Article/CJFDTOTAL-JDXK201207012.htm
[33]	李博峰.无缝仿射基准转换模型的方差分量估计[J].测绘学报, 2016, 45(1): 30-35 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201601006.htm Li Bofeng. Variance Component Estimation in the Seamless Affine Transformation Model[J]. Acta Geodetica et Cartographica Sinica, 2016, 45(1): 30-35 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201601006.htm
[34]	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 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201004006.htm Li Bofeng, Shen Yunzhong, Lou Lizhi. Variance-Covariance Component Estimation Based on the Equivalent Residuals[J]. Acta Geodetica et Cartographica Sinica, 2010, 39(4): 349-354, 363 https://www.cnki.com.cn/Article/CJFDTOTAL-CHXB201004006.htm

[1]	ZHOU Fangbin, ZOU Lianhua, LIU Xuejun, MENG Fanyi. Micro Landform Classification Method of Grid DEM Based on Convolutional Neural Network[J]. Geomatics and Information Science of Wuhan University, 2021, 46(8): 1186-1193. DOI: 10.13203/j.whugis20190311
[2]	ZOU Kun, WO Yan, XU Xiang. A Feature Significance-Based Method to Extract Terrain Feature Lines[J]. Geomatics and Information Science of Wuhan University, 2018, 43(3): 342-348. DOI: 10.13203/j.whugis20150373
[3]	CAO Zhenzhou, LI Manchun, CHENG Liang, CHEN Zhenjie. Progressive Transmission of Vector Curve Data over InternetCAO ZhenzhouLI Manchun[J]. Geomatics and Information Science of Wuhan University, 2013, 38(4): 475-479.
[4]	ZHENG Shunyi, HU Hualiang, HUANG Rongyong, JI Zheng. Realtime Ranging of Power Transmission Line[J]. Geomatics and Information Science of Wuhan University, 2011, 36(6): 704-707.
[5]	AI Bo, AI Tinghua, TANG Xinming. Progressive Transmission of River Network[J]. Geomatics and Information Science of Wuhan University, 2010, 35(1): 51-54.
[6]	LIU Yan, LIU Jingnan, LI Tao, XIA Ye. Monitoring Damage of State Grid Transmission Tower in Bad Weather by High-Resolution SAR Satellites[J]. Geomatics and Information Science of Wuhan University, 2009, 34(11): 1354-1358.
[7]	YIN Hui, ZHANG Xiaohong, ZHANG Xiaowu, LIU Xingfa. Interference Analysis to Aerial Flight Caused by UHV Lines Using Airborne GPS[J]. Geomatics and Information Science of Wuhan University, 2009, 34(7): 774-777.
[8]	WANG Cheng, HU Peng, LIU Xiaohang, LI Yunxiang. Automated Classification of Martian Landforms Based on Digital Terrain Analysis(DTA) Technology[J]. Geomatics and Information Science of Wuhan University, 2009, 34(4): 483-487.
[9]	ZHENG Jingjing, FANG Jinyun, HAN Chengde. Progressive Transmission Method of DEM Data Based on JPEG2000 Lossless-Compression[J]. Geomatics and Information Science of Wuhan University, 2009, 34(4): 395-399.
[10]	WANG Wei, DU Daosheng, XIONG Hanjiang, ZHONG Jing. 3D Modeling and Data Organization of Power Transmission[J]. Geomatics and Information Science of Wuhan University, 2005, 30(11): 986-990.

Cited By

Cited by

Periodical cited type(7)

1.	邱龙. 基于无人机测绘图像的大面积地形变化特征提取方法. 北京测绘. 2024(06): 930-935 .
2.	邓颖，蒋兴良，张志劲，曾蕴睿，马龙飞. 基于DEM分析的输电线路覆冰微地形分类识别及验证方法. 高电压技术. 2024(11): 4971-4980 .
3.	巩鑫龙，田瑞，王孟. 220?kV正兰甲线所在微地形区域风场特性研究. 电力安全技术. 2024(11): 47-51 .
4.	董慎学，石峰，刘刚，王有威，徐兆国. 垭口地形对输电线路风场分布特性影响分析. 重庆理工大学学报(自然科学). 2023(06): 340-346 .
5.	吴建蓉，文屹，张啟黎，何锦强，张厚荣，龚博. 基于GIS的易覆冰微地形分类提取算法与三维应用. 高电压技术. 2023(S1): 1-5 .
6.	周访滨，钟绍平，朱衍哲，杨自强，马国伟. 顾及爆燃地形特征的峡谷分级提取方法. 测绘科学. 2023(09): 89-98 .
7.	胡京，邓颖，蒋兴良，曾蕴睿. 输电线路覆冰垭口微地形的特征提取与识别方法. 中国电力. 2022(08): 135-142 .

Other cited types(0)

Get Citation

PDF

XML

Article views (1683) PDF downloads (104) Cited by(7)

Variance Components Estimation for Total Least-Squares Regression Prediction Model

Abstract

References

Related Articles

Cited by

Periodical cited type(7)

Other cited types(0)

Catalog

Related

Variance Components Estimation for Total Least-Squares Regression Prediction Model

Abstract

References

Related Articles

Cited by

Periodical cited type(7)

Other cited types(0)

Catalog

Related

Export File

Citation

Format

Content