Total least squares adjustment in inequality constrained partial errors-in-variables models: optimality conditions and algorithms

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.

Keywords:

• Linear inequality constraints
• Partial EIV (Peiv) model
• Weighted total least squares (Wtls)
• Optimality conditions
• Sequential quadratic programming (SQP)
• damped quasi-newton updating

Acknowledgements

The author would like to acknowledge the support of the National Natural Science Foundation of China (No. 41704007; 41877283).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China: [Grant Number 41704007; 41877283].

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.