XIE Jian, ZHOU Cui, LIN Dongfang, LONG Sichun, LAI Xiangen. Optimal Selection of the Adjustment Principles for Structured Weighted Total Least Squares Model[J]. Geomatics and Information Science of Wuhan University, 2024, 49(12): 2223-2231. DOI: 10.13203/j.whugis20220745
Citation: XIE Jian, ZHOU Cui, LIN Dongfang, LONG Sichun, LAI Xiangen. Optimal Selection of the Adjustment Principles for Structured Weighted Total Least Squares Model[J]. Geomatics and Information Science of Wuhan University, 2024, 49(12): 2223-2231. DOI: 10.13203/j.whugis20220745

Optimal Selection of the Adjustment Principles for Structured Weighted Total Least Squares Model

More Information
  • Received Date: March 22, 2023
  • Available Online: March 22, 2023
  • Objectives 

    In the structured errors-in-variables (EIV) model encountered in spatial coordinate transformation, part of the random observations (or their negative values) in the coefficient matrix appear repeatedly in different positions. Whether the repetitions of the random errors should be taken into account and how to deal with the repetitions in the adjustment principle, no consensus has been reached up to now.

    Methods 

    A generalized structured EIV model is proposed and a synthetic weight is introduced to describe different adjustment principles. The generalized EIV model is transformed to the Gauss-Helmert model through linear approximation. The solution and its approximate variance are derived.

    Results 

    It is verified that the repetitions should not be taken into consideration in the adjustment principle from the aspects of model analysis and numerical simulation.

    Conclusions 

    The optimal adjustment principle is confirmed and the approximate formula to calculate the accuracy is proved to be feasible and effective.

  • [1]
    Fang X. Weighted Total Least Squares: Necessary and Sufficient Conditions, Fixed and Random Parameters[J]. Journal of Geodesy, 2013, 87(8): 733-749.
    [2]
    姚宜斌, 黄书华, 张良, 等. 求解三维坐标转换参数的整体最小二乘新方法[J]. 武汉大学学报(信息科学版), 2015, 40(7): 853-857.

    Yao Yibin, Huang Shuhua, Zhang Liang, et al. A New Method of TLS for Solving the Parameters of Three-Dimensional Coordinate Transformation[J]. Geomatics and Information Science of Wuhan University, 2015, 40(7): 853-857.
    [3]
    姚宜斌, 熊朝晖, 张豹, 等. 顾及设计矩阵误差的AR模型新解法[J]. 测绘学报, 2017, 46(11): 1795-1801.

    Yao Yibin, Xiong Zhaohui, Zhang Bao, et al. A New Method to Solving AR Model Parameters Considering Random Errors of Design Matrix[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(11): 1795-1801.
    [4]
    姚宜斌, 黄书华, 张良, 等. 求解三维坐标转换参数的整体最小二乘新方法[J]. 武汉大学学报(信息科学版), 2015, 40(7): 853-857.

    Yao Yibin, Huang Shuhua, Zhang Liang, et al. A New Method of TLS for Solving the Parameters of Three-Dimensional Coordinate Transformation[J]. Geomatics and Information Science of Wuhan University, 2015, 40(7): 853-857.
    [5]
    Aoki M, Yue P. On a Priori Error Estimates of some Identification Methods[J]. IEEE Transactions on Automatic Control, 1970, 15(5): 541-548.
    [6]
    de Moor B. Structured Total Least Squares and L2 Approximation Problems[J]. Linear Algebra and Its Applications, 1993, 188:163-205.
    [7]
    Abatzoglou T J, Mendel J M, Harada G A. The Constrained Total Least Squares Technique and Its Applications to Harmonic Superresolution [J]. IEEE Transactions on Signal Processing, 1991, 39(5): 1070-1087.
    [8]
    Akyilmaz O. Total Least Squares Solution of Coordinate Transformation[J]. Survey Review, 2007, 39(303): 68-80.
    [9]
    Zhou Y, Fang X. A Mixed Weighted Least Squares and Weighted Total Least Squares Adjustment Method and Its Geodetic Applications[J]. Survey Review, 2016, 48(351): 421-429.
    [10]
    Xu P L, Liu J N, Shi C. Total Least Squares Adjustment in Partial Errors-in-Variables Models: Algorithm and Statistical Analysis[J]. Journal of Geodesy, 2012, 86(8): 661-675.
    [11]
    Shi Y, Xu P L, Liu J N, et al. Alternative Formulae for Parameter Estimation in Partial Errors-in-Variables Models[J]. Journal of Geodesy, 2015, 89(1): 13-16.
    [12]
    Han J, Zhang S L, Li Y L, et al. A General Partial Errors-in-Variables Model and a Corresponding Weighted Total Least-Squares Algorithm[J]. Survey Review, 2020, 52(371): 126-133.
    [13]
    Fang X. A Structured and Constrained Total Least-Squares Solution with Cross-Covariances[J]. Studia Geophysica et Geodaetica, 2014, 58(1): 1-16.
    [14]
    Markovsky I, Van Huffel S, Pintelon R. Block-Toeplitz/Hankel Structured Total Least Squares[J]. SIAM Journal on Matrix Analysis and Applications, 2005, 26(4): 1083-1099.
    [15]
    吕志鹏, 隋立芬. 基于变量投影的结构总体最小二乘算法[J]. 武汉大学学报(信息科学版), 2021, 46(3): 388-394.

    Zhipeng Lü, Sui Lifen. Structured Total Least Squares Method Based on Variable Projection[J]. Geomatics and Information Science of Wuhan University, 2021, 46(3): 388-394.
    [16]
    Markovsky I, Huffel S V, Kukush A. On the Computation of the Multivariate Structured Total Least Squares Estimator[J]. Numerical Linear Algebra with Applications, 2004, 11(5/6): 591-608.
    [17]
    Ben Rosen J, Park H, Glick J. Total Least Norm Formulation and Solution for Structured Problems[J]. SIAM Journal on Matrix Analysis and Applications, 1996, 17(1): 110-126.
    [18]
    Van Huffel S, Park H, Rosen J B. Formulation and Solution of Structured Total Least Norm Problems for Parameter Estimation[J]. IEEE Transactions on Signal Processing, 1996, 44(10): 2464-2474.
    [19]
    Mastronardi N, Lemmerling P, Van Huffel S. Fast Structured Total Least Squares Algorithm for Solving the Basic Deconvolution Problem[J]. SIAM Journal on Matrix Analysis and Applications, 2000, 22(2): 533-553.
    [20]
    Lemmerling P, Mastronardi N, Van Huffel S. Fast Algorithm for Solving the Hankel/Toeplitz Structured Total Least Squares Problem[J]. Numerical Algorithms, 2000, 23(4): 371-392.
    [21]
    Zhang S L, Zhang K, Han J, et al. Total Least Norm Solution for Linear Structured EIV Model[J]. Applied Mathematics and Computation, 2017, 304: 58-64.
    [22]
    Schaffrin B, Lee I, Choi Y, et al. Total Least-Squares (TLS) for Geodetic Straight-Line and Plane Adjustment[J]. Bollettino Di Geodesia e Scienze Affini, 2006, 65(3): 141-168.
    [23]
    Neitzel F. Generalization of Total Least-Squares on Example of Unweighted and Weighted 2D Similarity Transformation[J]. Journal of Geodesy, 2010, 84(12): 751-762.
    [24]
    Shen Y Z, Li B F, Chen Y. An Iterative Solution of Weighted Total Least-Squares Adjustment[J]. Journal of Geodesy, 2011, 85(4): 229-238.
  • Related Articles

    [1]PANG Qipei, WU Yunlong, XU Jingtian, SHI Xuguo, ZHANG Yi. Deep Structural Characteristics and Dynamic Processes of the Ms 6.2 Jishishan Earthquake and Its Adjacent Areas[J]. Geomatics and Information Science of Wuhan University, 2025, 50(2): 356-367. DOI: 10.13203/j.whugis20240085
    [2]YANG Jiuyuan, WEN Yangmao, XU Caijun. Seismogenic Fault Structure of the 2023 Ms 6.2 Jishishan (Gansu,China) Earthquake Revealed by InSAR Observations[J]. Geomatics and Information Science of Wuhan University, 2025, 50(2): 313-321. DOI: 10.13203/j.whugis20230501
    [3]WU Yunlong, LI Hao, ZHANG Fan, PANG Qipei, ZHANG Yi, YAN Jianguo, CHU Risheng. Analysis of Deep Tectonic Characteristics and Seismogenic Environment of the Ms 6.8 Earthquake in Dingri,Xizang,China[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20250052
    [4]YANG Jiuyuan, XU Caijun. Ramp-flat Seismogenic Structure of the 2020 Yutian (Xinjiang, China) MW 6.3 Earthquake Revealed by InSAR Observations[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20240482
    [5]LI Zhenhong, HAN Bingquan, LIU Zhenjiang, ZHANG Miaomiao, YU Chen, CHEN Bo, LIU Haihui, DU Jing, ZHANG Shuangcheng, ZHU Wu, ZHANG Qin, PENG Jianbing. Source Parameters and Slip Distributions of the 2016 and 2022 Menyuan, Qinghai Earthquakes Constrained by InSAR Observations[J]. Geomatics and Information Science of Wuhan University, 2022, 47(6): 887-897. DOI: 10.13203/j.whugis20220037
    [6]LIU Yang, XU Caijun, WEN Yangmao, LI Zhicai. InSAR Inversion and Boundary Element Analysis of the Zadoi Mw 5.9 Earthquake Fault Slip[J]. Geomatics and Information Science of Wuhan University, 2020, 45(11): 1678-1686. DOI: 10.13203/j.whugis20190368
    [7]WANG Leyang, LI Haiyan, CHEN Hanqing. Source Parameters and Slip Distribution Inversion of 2013 Lushan Ms 7.0 Earthquake[J]. Geomatics and Information Science of Wuhan University, 2019, 44(3): 347-354. DOI: 10.13203/j.whugis20160485
    [8]XU Caijun, HE Ping, WEN Yangmao, ZHANG Lei. Coseismic Deformation and Slip Distribution for 2011 Tohoku-Oki Mw 9.0 Earthquake:Constrained by GPS and InSAR[J]. Geomatics and Information Science of Wuhan University, 2012, 37(12): 1387-1391.
    [9]Lin Aiwen. The Research on Fault Structure in the Wuhan Area[J]. Geomatics and Information Science of Wuhan University, 1992, 17(3): 69-76.
    [10]Guo Qingsheng. Structural Principle and Realization by Computer for Areal Regular Pattern[J]. Geomatics and Information Science of Wuhan University, 1992, 17(1): 28-33.
  • Cited by

    Periodical cited type(19)

    1. 李雨森,李为乐,许强,许善淼,王运生. 2023年积石山Ms6.2级地震InSAR同震形变探测与断层滑动分布反演. 成都理工大学学报(自然科学版). 2024(01): 22-32+75 .
    2. 王乐洋,孙龙翔,许光煜. 利用GPS数据反演震源参数的单纯形组合加权距离灰狼优化算法. 武汉大学学报(信息科学版). 2024(07): 1140-1154 .
    3. 王乐洋,席灿. 贝叶斯框架下利用GPS数据反演震源参数的一种改进MCMC算法. 地球物理学报. 2024(09): 3367-3385 .
    4. 程燕,蒋亚楠,侯中健,曾锐,罗袆沅. 2016年和2022年青海门源强震活动的InSAR形变观测与区域强震危险性分析. 地质力学学报. 2024(06): 965-977 .
    5. 于仪,李雪,孙振,刘珠妹,张朝阳. 2022年青海门源地震震源机制与同震滑动分布研究. 大地测量与地球动力学. 2023(01): 46-51 .
    6. 刘洋,李航昊,熊露雲,温扬茂,杨九元. 联合地震位错模型和ESISTEM方法提取地震同震三维形变场. 武汉大学学报(信息科学版). 2023(03): 349-358+395 .
    7. 钟储汉. 基于InSAR技术的输气管道工程穿越煤矿采空区形变特征分析研究. 石油工程建设. 2023(03): 10-16 .
    8. 李媛,杨周胜,庞亚瑾,梁洪宝,刘峡. 2022年门源M_S6.9地震前断层活动及应力状态的数值模拟. 地震地质. 2023(06): 1286-1308 .
    9. 颜丙囤,季灵运,蒋锋云,殷海涛,陈其峰,连凯旋. InSAR数据约束的2022年1月8日青海门源M_S6.9地震发震构造研究. 地震工程学报. 2022(02): 450-457 .
    10. 郭东美,何慧优. 应用全张量重力梯度组合识别并提取中国南海断裂. 武汉大学学报(信息科学版). 2022(05): 738-746 .
    11. 李振洪,韩炳权,刘振江,张苗苗,余琛,陈博,刘海辉,杜静,张双成,朱武,张勤,彭建兵. InSAR数据约束下2016年和2022年青海门源地震震源参数及其滑动分布. 武汉大学学报(信息科学版). 2022(06): 887-897 .
    12. 何秀凤,高壮,肖儒雅,罗海滨,贾东振,章浙涛. InSAR与北斗/GNSS综合方法监测地表形变研究现状与展望. 测绘学报. 2022(07): 1338-1355 .
    13. 梁斌,魏冠军. 利用InSAR技术观测台湾花莲地震断层滑动与运动机理分析. 测绘通报. 2022(09): 68-73 .
    14. 金鑫田,王世杰,姜鑫,张兰军. 2022年青海门源M_W6.9地震同震形变及断层滑动分布反演. 地球物理学进展. 2022(06): 2267-2274 .
    15. 付阿龙,安张辉,范莹莹,侯泽宇. 2022年1月8日青海门源县M_S 6.9地震地电场响应特征. 地震地磁观测与研究. 2022(06): 30-40 .
    16. 钟储汉,王强,王霞迎,张双成,牛玉芬. 基于InSAR技术的东营市地面沉降监测及多诱发因素分析. 大地测量与地球动力学. 2021(07): 727-731 .
    17. 温少妍,李成龙,李金. 2020年1月19日新疆伽师M_S6.4地震InSAR同震形变场特征及发震构造初步探讨. 内陆地震. 2020(01): 1-9 .
    18. 徐小波,连达军,白俊武. 基于CRInSAR与PSInSAR技术监测断裂带震间形变研究. 苏州科技大学学报(自然科学版). 2020(04): 51-58 .
    19. 万秀红,屠泓为,姚生海,殷翔,蔡丽雯. InSAR技术在青海地区地震中的应用研究. 高原地震. 2019(04): 14-20 .

    Other cited types(14)

Catalog

    Article views (540) PDF downloads (61) Cited by(33)
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return