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

• Published in: Journal of geodesy Vol. 89; no. 2; pp. 111 - 119
• Main Authors: Zeng, Wenxian, Liu, Jingnan, Yao, Yibin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2015; Springer Nature B.V
• Subjects: Algorithms; Earth and Environmental Science; Earth Sciences; Geodetics; Geophysics/Geodesy; Mathematical models; Original Article; Total least squares; Precision description; Linear complementarity problem; Inequality constraints; Partial errors-in-variables model
• ISSN: 0949-7714; 1432-1394
• DOI: 10.1007/s00190-014-0775-z

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.