GNSS World of China

Volume 46 Issue 6
Dec.  2021
Turn off MathJax
Article Contents
Article Navigation >  GNSS World of China  > 2021  >  46(6): 84-89
WENG Ye, SHAO Desheng. Generalized ridge estimation method for morbid weighted total least squares[J]. GNSS World of China, 2021, 46(6): 84-89. doi: 10.12265/j.gnss.2021061601
Citation: WENG Ye, SHAO Desheng. Generalized ridge estimation method for morbid weighted total least squares[J]. GNSS World of China, 2021, 46(6): 84-89. doi: 10.12265/j.gnss.2021061601
shu

Generalized ridge estimation method for morbid weighted total least squares

doi: 10.12265/j.gnss.2021061601
  • 1.

    Seismological Bureau of Yunnan Province, Kunming 650200, China

  • 2.

    Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China

  • Received Date: 2021-06-16
    Available Online: 2021-12-21
    Abstract
  • For the variable error (EIV) model in the weighted case, the generalized ridge estimation method is used to deal with the morbid problem of the total least squares adjustment. Combined with optimization criterion and covariance propagation rate, the correction formula of unknown parameters is derived. Accordsing to the principle of minimizing mean square error of parameter estimation, the iterative solution of ridge parameter in generalized ridge estimation is given by solving partial derivative, and the meaning and function of generalized ridge parameter are discussed. The weighted least squares estimation, total least squares estimation, the weighted least squares ridge estimation, total least squares ridge estimation, generalized ridge estimation of the weighted least squares and generalized ridge estimation of total least squares are compared and analyzed by examples. The advantages and disadvantages of generalized ridge estimation of weighted total least squares are described.

     

    • FullText(HTML)
  • loading
    • References(18)
  • [1]
    武汉大学测绘学院测量平差学科组. 误差理论与测量平差基础[M]. 武汉: 武汉大学出版社, 2003.
    [2]
    曾文宪, 刘泽邦, 方兴, 等. 通用EIV平差模型的线性化估计算法[J]. 武汉大学学报(信息科学版), 2021, 46(9): 1284-1290.
    [3]
    LENTH R V, HUFFEL S V, VANDEWALLE J, et al. The total least squares problem: computational aspects and analysis[J]. Journal of the american statistical association, 1999, 94(447): 983. DOI: 10.2307/2670017
    [4]
    ADCOCK R J. Note on the method of least squares[J]. The analyst, 1877, 4(6): 183-184. DOI: 10.2307/2635777
    [5]
    FIERRO R D, GOLUB G H, HANSEN P C, et al. Rcgularization by truncated total least squares[J]. SLAM journal on scientific and statistical computing, 1997, 18(4): 1223-1241. DOI: 10.1137/S1064827594263837
    [6]
    HOERL A E, KENNARD R W. Ridge regression: biased estimation for non-orthogonal problems[J]. Technometrics, 1970, 12(1): 55-67. DOI: 10.2307/1267351
    [7]
    HOERL A E, KENNARD R W. Ridge regression: applications to nonorthogonal problems[J]. Technometrics, 1970, 12(1): 69-86. DOI: 10.2307/1267352
    [8]
    GOLUB G H, HANSEN P C, O’LEARY D P. Tikhonov regularization and total least squares[J]. SIAM journal on matrix analysis and applications, 1999, 21(1): 185-194. DOI: 10.1137/S0895479897326432
    [9]
    钱峰, 张一枝. 广义c-K估计优良性及其应用[J]. 统计与决策, 2018, 34(21): 86-89.
    [10]
    黄海兰, 牛犇. 岭参数确定的研究[J]. 测绘科学, 2011, 36(4): 31-32.
    [11]
    王振杰, 欧吉坤. 用L-曲线法确定岭估计中的岭参数[J]. 武汉大学学报(信息科学版), 2004, 29(3): 235-238.
    [12]
    鲁洋为, 王振杰. 用U曲线法确定岭估计中的岭参数[J]. 导航定位学报, 2015, 3(3): 132-134,138.
    [13]
    黄维彬. 近代平差理论及其应用[M]. 北京: 解放军出版社, 1992.
    [14]
    王乐洋, 许才军, 鲁铁定. 病态加权总体最小二乘平差的岭估计解法[J]. 武汉大学学报(信息科学版), 2010, 35(11): 1346-1350.
    [15]
    TIKHONOV A N. Solution of incorrectly formulated problems and the regularization method[J]. Soviet mathematics doklady, 1963(4): 1305-1308.
    [16]
    HANSEN P C. Analysis of discrete ILL-posed problems by means of the L-curve[J]. SIAM review, 1992, 34(4): 561-580. DOI: 10.1137/1034115
    [17]
    王乐洋, 于冬冬. 病态总体最小二乘问题的虚拟观测解法[J]. 测绘学报, 2014, 43(6): 575-581.
    [18]
    鲁铁定. 总体最小二乘平差理论及其在测绘数据处理中的应用[D]. 武汉: 武汉大学, 2010.
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(2)  / Tables(2)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (339) PDF downloads(26) Cited by()
    Proportional views
    Related

    Copyright © 2009《 GNSS World of China 》 Editorial Office

    Address：84 Jianshe Dong Lu, Muye District, Xinxiang City, Henan Province, ChinaChina Pos：453000Tel：0373-3712411Fax：0373-3052232Email：qqdwxt@126.com

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return