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

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## Abstract

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.

### Keywords

Total least squares Partial errors-in-variables model Inequality constraints Linear complementarity problem Precision description## Notes

### Acknowledgments

The first author thanks her supervisor, Dr. Peiliang Xu, for suggesting this topic to investigate and for his suggestion to use LCP methods to solve problems of this kind. This research was supported by the National Natural Science Foundation of China (41474006; 41404005; 41231174; 41274022).

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