Robust estimation of model parameters of the probability integral method based on CA-rPSO

Abstract

This paper introduces a framework for robustly estimating the parameters of the probability integral method (PIM). According to the framework, the initial robust estimates of the PIM parameters are firstly obtained by combining the cultural algorithm and rand particle swarm optimisation (CA-rPSO) with the LTS method. As a byproduct, an initial standard deviation can be calculated and used to determine the initial weights of the measurements according to the Institute of Geodesy and Geophysics (IGGIII) down-weighting scheme. Meanwhile, a modified CA-rPSO (referred to as CA-rPSO-IGGIII) is constructed, where the IGGIII scheme is introduced to alleviate the adverse influence of outliers. Then, the initial robust estimates and the standard deviation can act as a priori information for the CA-rPSO-IGGGIII to search for the optimal estimates. Experiments with simulated and real data demonstrate that the proposed method can robustly estimate the PIM parameters.

Keywords:

• Robust estimation
• Probability integral method
• Particle swarm optimisation
• Outliers
• Cultural algorithm
• Down-weighting

Acknowledgements

The authors would also like to thank the anonymous reviewers for the constructive comments. Z. W. and C. Z. initiated the study, Z. W. provided the software for analysis and analysed the data, C. Z. analysed the data and wrote the manuscript. H. Z., J. K. and J. H. provided advice and reviewed the manuscript.

Data availability statement

The datasets analysed in this study are managed by the Jiangsu Normal University, Xuzhou 221116, China and Hunan University of Science & Technology, Xiangtan 411201, China. All the datasets can be made available by the corresponding author on request.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [grant numbers 41901373 and 41671395], the Natural Science Foundation of Hunan Province [grant number: 2019JJ50190].

Notes on contributors

Zhengshuai Wang

Zhengshuai Wang is currently a Lecturer with the School of Geography, Geomatics and Planning, Jiangsu Normal University, Xuzhou, Jiangsu Province. His current research interests include data mining and mining subsidence.

Chuanguang Zhu

Chuanguang Zhu is currently a Lecturer with the Hunan University of Science and Technology, Xiangtan, China. His current research interests include InSAR data processing and monitoring and mapping of mining-induced subsidence.

Hongzhen Zhang

Hongzhen Zhang is currently a Lecturer with the University of Mining and Technology, Xuzhou, Jiangsu. His current research interests include mining subsidence and surveying and mapping engineering.

Jianrong Kang

Jianrong Kang is currently a professor with the School of Geography, Geomatics and Planning, Jiangsu Normal University, Xuzhou, Jiangsu Province. Dr. Kang is a member of the Mine Survey Committee and the Mining Damage Technical Appraisal Committee of China Coal Society. His research interests include the areas of surveying and mapping engineering, mining subsidence, environmental treatment and data processing.

Jinshan Hu

Jinshan Hu is currently an associate professor with the School of Geography, Geomatics and Planning, Jiangsu Normal University, Xuzhou, Jiangsu Province. His research interests include the areas of surveying and mapping engineering and ecological environment control in mining area.