Abstract
The partial errors-in-variables (PEIV) model is a structured form of errors-in-variables (EIV) model reformulated by collecting all the independent random elements of the coefficient matrix. When some reliable inequality constraints are taken into account, the adjustment results of inequality constrained PEIV (ICPEIV) model are probably improved. In this contribution, we first present the optimality conditions for inequality constrained weighted total least squares (ICWTLS) solution in ICPEIV model. Then we modified the existing linear approximation (LA) approach to make it suitable for cross-correlated data. The sequential quadratic programming (SQP) method is proposed based on the optimality conditions. Since the Hessian matrix is difficult to compute in the SQP algorithm and it converges slowly or even not converges when the Hessian matrix is indefinite positive, the damped quasi-Newton (DQN) SQP method is proposed. Finally, three examples are given to show the feasibility and performance of the proposed algorithms.
Acknowledgements
The author would like to acknowledge the support of the National Natural Science Foundation of China (No. 41704007; 41877283).
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No potential conflict of interest was reported by the author(s).
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Notes on contributors
Jian Xie
Jian Xie is currently a lecturer at Hunan Province Key Laboratory of Coal Resources Clean-utilization and Mine Environment Protection, Hunan University of Science and Technology, China. He received his Ph.D. degree in Geodesy and Surveying adjustment from Central South University in 2014. His current research interest is in surveying data processing.
Dongfang Lin
Dongfang Lin is a lecturer at National-Local Joint Engineering Laboratory of Geo-spatial Information Technology, Hunan University of Science and Technology, China. He received his Ph.D. degree in Geodesy from Central South University in 2017. His current research is in surveying adjustment and its applications on PolInSAR.
Sichun Long
Sichun Long is a professor at Hunan Province Key Laboratory of Coal Resources Clean-utilization and Mine Environment Protection, Hunan University of Science and Technology, China. He received his Ph.D. degree in InSAR from Wuhan University in 2009. His current research interest is differential InSAR and geodetic surveying.