On partial errors-in-variables models with inequality constraints of parameters and variables

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• 作者：Wenxian Zeng (1)
  Jingnan Liu (2)
  Yibin Yao (1)
  
  1. School of Geodesy and Geomatics ; Wuhan University ; 129 Luoyu Road ; Wuhan ; 430079 ; China
  2. Research Center of GNSS ; Wuhan University ; 129 Luoyu Road ; Wuhan ; 430079 ; China
  
• 关键词：Total least squares ; Partial errors ; in ; variables model ; Inequality constraints ; Linear complementarity problem ; Precision description
• 刊名：Journal of Geodesy
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：89
• 期：2
• 页码：111-119
• 全文大小：194 KB
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• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geophysics and Geodesy
  Mathematical Applications in Geosciences
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1394

文摘

Recent studies have extensively discussed total least squares (TLS) algorithms for solving the errors-in-variables (EIV) model with equality constraints but rarely investigated the inequality-constrained EIV model. The most existing inequality-constrained TLS algorithms assume that all the elements in the coefficient matrix are random and independent and that their numerical efficiency is significantly limited due to combinatorial difficulty. To solve the above issues, we formulate a partial EIV model with inequality constraints of both unknown parameters and the random elements of the coefficient matrix. Based on the formulated EIV model, the inequality-constrained TLS problem is transformed into a linear complementarity problem through linearization. In this way, the inequality-constrained TLS method remains applicable even when the elements of the coefficient matrix are subject to inequality constraints. Furthermore, the precision of the constrained estimates is put forward from a frequentist point of view. Three numerical examples are presented to demonstrate the efficiency and superiority of the proposed algorithm. The application is accomplished by preserving the structure of random coefficient matrix and satisfying the constraints simultaneously, without any combinatorial difficulty.