Weighted and partial total least squares method for the EIV model with linear equality and inequality constraints

Abstract

A weighted and partial total least squares method for the errors-in-variables (EIV) model with linear equality and inequality constraints is presented. A collected observation vector is formed by the independent variables both in the observation vector and the design matrix. The proposed model is solved based on the Lagrange method and by transforming the problem into a linear complementary problem. The performance of the proposed method is studied by two numerical experiments. The results show that, the proposed method is capable of solving the linearly constrained EIV model efficiently.

Keywords:

• Weighted total least squares
• Partial total least squares
• EIV model
• Equality and inequality constraints
• Linear complementary problem

Disclosure statement

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

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under grant [nos. 42071372, and 41601414].

Notes on contributors

Yanmin Jin

Yanmin Jin received her B.S. degree from Taiyuan University of Technology, China, in 2007 and her Ph.D. degree from Tongji University, China, in 2015. Since 2015, she has been an assistant professor at Tongji University. Her research interests are in GIS spatial data processing and data quality control.

Lizhou Sun

Lizhou Sun received his B.S. degree from Taiyuan University of Technology, China, in 2020. Currently, he is working toward the M.S. degree in College of Surveying and Geo-informatics, Tongji University, China. His research interest includes spatial data error processing.

Xiaohua Tong

Xiaohua Tong received his Ph.D. degree from Tongji University, China, in 1999. He has been a professor at Tongji University since 2005. His current research interests include remote sensing, geographic information systems, uncertainty and spatial data quality, and image processing for high-resolution and hyperspectral images.

Shijie Liu

Shijie Liu received his B.S., M.S., and Ph.D. degrees from Tongji University, China, in 2006, 2008, and 2012, respectively. Since 2016, he has been an associate professor at Tongji University. His research interests are in high-resolution remote sensing and high-precision geometric processing and application.

Yongjiu Feng

Yongjiu Feng received Ph.D. degree from Tongji University in 2009. From 2015 to 2016, he was a Visiting Academic at the University of Queensland. Currently, he is a professor at the College of Surveying and Geo-Informatics, Tongji University, Shanghai, China and Honorary Associate Professor at the University of Queensland, Brisbane, Australia. His research interests include spatial analysis, land use change odellingg, cellular automata, and remote sensing image processing.

Sicong Liu

Sicong Liu received his B.S. and M.S. degrees from China University of Mining and Technology, China, in 2009 and 2011, respectively, and his Ph.D. degree from University of Trento, Italy, in 2015. Since 2020, he has been an associate professor at Tongji University, China. His research interests are in multisource spatial information fusion and multitemporal remote sensing dynamic monitoring technology and applications.