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XIE Jian, LONG Si-chun, ZHOU Cui. Classical Least Squares Method for Inequality Constrained PEIV Model[J]. Geomatics and Information Science of Wuhan University, 2021, 46(9): 1291-1297. DOI: 10.13203/j.whugis20190196
Citation: XIE Jian, LONG Si-chun, ZHOU Cui. Classical Least Squares Method for Inequality Constrained PEIV Model[J]. Geomatics and Information Science of Wuhan University, 2021, 46(9): 1291-1297. DOI: 10.13203/j.whugis20190196
shu

Classical Least Squares Method for Inequality Constrained PEIV Model

  • 1.

    Hunan Province Key Laboratory of Coal Resources Clean⁃Utilization and Mine Environment Protection, Hunan University of Science and Technology, Xiangtan 411201, China

  • 2.

    College of Science, Central South University of Forestry and Technology, Changsha 410018, China

Funds: 

The National Natural Science Foundation of China 41704007

The National Natural Science Foundation of China 41877283

The National Natural Science Foundation of China 42074016

More Information
  • Author Bio:

    XIE Jian, PhD, specializes in surveying adjustment and data processing. E-mail: hsiejian841006@163.com

  • Received Date: December 01, 2020
  • Published Date: September 17, 2021
    Graphical Abstract
    • Abstract
  •   Objectives  The inequality constrained partial errors-in-variables(ICPEIV) model is mainly solved by linear approximation method and nonlinear programming algorithms. The linear approximation method is computationally inefficient and the nonlinear programming algorithms are complicated because they are based on optimization theory. The nonlinear programming algorithms are impracticable to apply in surveying fields because the connections between nonlinear programming methods and classical adjustment have not been established.
      Methods  Under the total least squares(TLS) criterion, the inequality constrained TLS problem is transformed into the quadratic programming according to the Kuhn-Tucker condition. Then an improved Jacobian iteration approach is proposed to solve the quadratic programming.
      Results  The proposed method does not require the linearization process and has the same form with the classical least squares which is easy to code.
      Conclusions  The numerical examples show that the proposed method is efficient in computation and concise in form and it is a beneficial extension of classical least squares theory.
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    • References (18)
  • [1]
    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 doi: 10.1007/s00190-010-0408-0
    [2]
    Akyilmaz O. Total Least Squares Solution of Coordinate Transformation[J]. Survey Review, 2007, 39 (303): 68-80 doi: 10.1179/003962607X165005
    [3]
    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 doi: 10.1179/1752270615Y.0000000040
    [4]
    Tong X H, Jin Y M, Zhang S L, et al. Bias-Corrected Weighted Total Least-Squares Adjustment of Condition Equations[J]. Journal of American Surveying Engineering, 2014, 141 (2): 04014013 http://d.wanfangdata.com.cn/periodical/26f7db7fb994669a82ad317964b29beb
    [5]
    陈义, 陆珏, 郑波. 总体最小二乘方法在空间后方交会中的应用[J]. 武汉大学学报·信息科学版, 2008, 33 (12): 1 271-1 274 http://ch.whu.edu.cn/article/id/1776

    Chen Yi, Lu Jue, Zheng Bo. Application of Total Least Squares to Space Resection[J]. Geomatics and Information Science of Wuhan University, 2008, 33(12): 1 271-1 274 http://ch.whu.edu.cn/article/id/1776
    [6]
    Xu C J, Wang L Y, Wen Y M, et al. Strain Rates in the Sichuan-Yunnan Region Based upon the Total Least Squares Heterogeneous Strain Model from GPS Data[J]. Terrestrial Atmospheric and Oceanic Sciences, 2011, 22 (2): 133-147 doi: 10.3319/TAO.2010.07.26.02(TibXS)
    [7]
    Fang X. Weighted Total Least Squares: Necessary and Sufficient Conditions, Fixed and Random Parameters[J]. Journal of Geodesy, 2013, 87(8): 733-749 doi: 10.1007/s00190-013-0643-2
    [8]
    Mahboub V. On Weighted Total Least-Squares for Geodetic Transformations[J]. Journal of Geodesy, 2012, 86 (5): 359-367 doi: 10.1007/s00190-011-0524-5
    [9]
    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 doi: 10.1007/s00190-010-0431-1
    [10]
    Amiri-Simkooei A, Jazaeri S. Weighted Total Least Squares Formulated by Standard Least Squares Theory[J]. Journal of Geodetic Sciences, 2012, 2 (2): 113-124 doi: 10.2478/v10156-011-0036-5
    [11]
    Schaffrin B, Felus Y A. An Algorithmic Approach to the Total Least-Squares Problem with Linear and Quadratic Constraints[J]. Studia Geophysica et Geodaetica, 2009, 53 (1): 1-16 doi: 10.1007/s11200-009-0001-2
    [12]
    Zhang S L, Tong X H, Zhang K. A Solution to EIV Model with Inequality Constraints and Its Geodetic Applications[J]. Journal of Geodesy, 2013, 87 (1): 23-28 doi: 10.1007/s00190-012-0575-2
    [13]
    Fang X. On Non-combinatorial Weighted Total Least Squares with Inequality Constraints[J]. Journal of Geodesy, 2014, 88 (8): 805-816 doi: 10.1007/s00190-014-0723-y
    [14]
    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 doi: 10.1007/s00190-012-0552-9
    [15]
    Shi Y, Xu P L, Liu J N, et al. Alternative Formulae for Parameter Estimation in Partial Errors-inVariables Models[J]. Journal of Geodesy, 2015, 89 (1): 13-16 doi: 10.1007/s00190-014-0756-2
    [16]
    Zeng W X, Liu J N, Yao Y B. On Partial Errors-inVariables Models with Inequality Constraints of Parameters and Variables[J]. Journal of Geodesy, 2015, 89 (2): 111-119 doi: 10.1007/s00190-014-0775-z
    [17]
    陈宝林. 最优化理论与算法[M]. 北京: 清华大学出版社, 2005

    Chen Baolin. Theory and Algorithm in Optimization[M]. Beijing: Tsinghua University Press, 2005
    [18]
    谢建, 龙四春, 周璀. 不等式约束PEIV模型的最优性条件及SQP算法[J]. 武汉大学学报·信息科学版, 2020, 45 (7): 1 002-1 007 doi: 10.13203/j.whugis20180297

    Xie Jian, Long Sichun, Zhou Cui. Optimality Conditions of Inequality Constrained Partial EIV Model and the SQP Algorithm[J]. Geomatics and Information Science of Wuhan University, 2020, 45(7): 1 002-1 007 doi: 10.13203/j.whugis20180297
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