Robust Total Least Squares Method for Multivariable EIV Model

LI Sida; LIU Lintao; LIU Zhiping; AI Qingsong

doi:10.13203/j.whugis20170232

Volume 44 Issue 8

Aug. 2019

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Geomatics and Information Science of Wuhan University > 2019 > 44(8): 1241-1248. > DOI: 10.13203/j.whugis20170232

LI Sida, LIU Lintao, LIU Zhiping, AI Qingsong. Robust Total Least Squares Method for Multivariable EIV Model[J]. Geomatics and Information Science of Wuhan University, 2019, 44(8): 1241-1248. DOI: 10.13203/j.whugis20170232

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Robust Total Least Squares Method for Multivariable EIV Model

LI Sida^{1, 2,},
LIU Lintao¹,
LIU Zhiping^3, ,,
AI Qingsong^{1, 2}

1.
State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China
3.
School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China

Funds:

The National Key Scientific Instrument and Equipment Development Project, Ministry of Science and Technology of the People's Republic of China 2011YQ120045

the National Natural Science Foundation of China 41074050

the National Natural Science Foundation of China 41204011

the National Natural Science Foundation of China 41504032

the National Key Research and Development Program of China 2016YFC0803103

the National Key Research and Development Program of China 2016YFB0502102

the Open Foundation of Key Laboratory of Precise Engineering and Industry Surveying of NSMG PF2017-12

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Author Bio:
LI Sida, PhD candidate, specializes in surveying data processing. E-mail:sdlicumt@163.com
Corresponding author:
LIU Zhiping, PhD, associate professor. E-mail:zhpliu@cumt.edu.cn
Received Date: December 05, 2018
Published Date: August 04, 2019

Graphical Abstract

Abstract

Abstract

The reliability of the solution to the errors-in-variables (EIV) model can be improved through robust total least square method. The false robust estimation problem that the existed robust total least squares method gives priority to reduce the weights of some columns which have large product of estimated parameters and prior cofactors in the multivariable EIV model is pointed out in detail. To tackle this problem, a new robust estimation strategy is presented based on Huber weight function. This new robust estimation strategy copes with each column variable respectively to avoid the false robust estimation problem. Based on this new robust estimation strategy, a multivariate robust total least squares method is proposed and the corresponding estimation results of parameters and variance-covariance matrix are deduced. Experiment results verify the analysis about false robust estimation problem and show the validity of proposed method in coping with false robust estimation problem and detecting the gross error in multivariable EIV model. And compared with the total least squares method and traditional robust least squares method, the proposed method in this paper gets the nearest parameter estimation results to the real value.

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Robust Total Least Squares Method for Multivariable EIV Model

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