The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion

A situation in which an image is combined with multiple images to form interferometric pairs is often observed in small baseline subset-interferometric synthetic aperture radar (SBAS-InSAR) deformation inversion, and this situation leads to a near linear correlation between the column vectors of the...

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Autores principales:	Min Zhai, Guolin Liu, Qiuxiangtao, Ke Wang, Yang Chen, Guangyong Pan, Mingzhen Xin
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Liu-type estimator iterative method L-curve ill-posed problem biased estimator least squares estimator Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/278f96854c3943cd9a3b7f14ab31d04e
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spelling	oai:doaj.org-article:278f96854c3943cd9a3b7f14ab31d04e2021-11-19T00:05:07ZThe Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion2169-353610.1109/ACCESS.2020.3046676https://doaj.org/article/278f96854c3943cd9a3b7f14ab31d04e2021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9302571/https://doaj.org/toc/2169-3536A situation in which an image is combined with multiple images to form interferometric pairs is often observed in small baseline subset-interferometric synthetic aperture radar (SBAS-InSAR) deformation inversion, and this situation leads to a near linear correlation between the column vectors of the model design matrix. The Liu-type estimator introduces the parameters <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> into the normal equation to reduce the condition number of the design matrix and to improve the fitting properties. As the parameter <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is mainly used to reduce ill-posed problems of the design matrix, the value of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is not limited. However, the value of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, as determined by existing methods, is usually too large or too small. Since the calculation of the mean square error involves true values, the parameter <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> is often affected by errors in the estimation results, which leads to the decreased accuracy of Liu-type estimation results. To determine the optimal value of <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>, an iterative Liu-type estimator is proposed to eliminate errors. Then, the <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>-curve optimization method and iterative Liu-type estimator are combined to achieve the optimal <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>. The reliability and accuracy of the methods are analyzed through SBAS-InSAR deformation experiments. The experimental results show that after using the <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>-curve method and an iterative operation to optimize <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>, the accuracy of the Liu-type estimator based on parameter optimization is clearly improved compared with that of the ridge estimator and the Liu-type estimator.Min ZhaiGuolin Liu QiuxiangtaoKe WangYang ChenGuangyong PanMingzhen XinIEEEarticleLiu-type estimatoriterative methodL-curveill-posed problembiased estimatorleast squares estimatorElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 9, Pp 1076-1086 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Liu-type estimator iterative method L-curve ill-posed problem biased estimator least squares estimator Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Liu-type estimator iterative method L-curve ill-posed problem biased estimator least squares estimator Electrical engineering. Electronics. Nuclear engineering TK1-9971 Min Zhai Guolin Liu Qiuxiangtao Ke Wang Yang Chen Guangyong Pan Mingzhen Xin The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion
description	A situation in which an image is combined with multiple images to form interferometric pairs is often observed in small baseline subset-interferometric synthetic aperture radar (SBAS-InSAR) deformation inversion, and this situation leads to a near linear correlation between the column vectors of the model design matrix. The Liu-type estimator introduces the parameters <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> into the normal equation to reduce the condition number of the design matrix and to improve the fitting properties. As the parameter <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is mainly used to reduce ill-posed problems of the design matrix, the value of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> is not limited. However, the value of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, as determined by existing methods, is usually too large or too small. Since the calculation of the mean square error involves true values, the parameter <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> is often affected by errors in the estimation results, which leads to the decreased accuracy of Liu-type estimation results. To determine the optimal value of <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>, an iterative Liu-type estimator is proposed to eliminate errors. Then, the <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>-curve optimization method and iterative Liu-type estimator are combined to achieve the optimal <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>. The reliability and accuracy of the methods are analyzed through SBAS-InSAR deformation experiments. The experimental results show that after using the <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>-curve method and an iterative operation to optimize <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>, the accuracy of the Liu-type estimator based on parameter optimization is clearly improved compared with that of the ridge estimator and the Liu-type estimator.
format	article
author	Min Zhai Guolin Liu Qiuxiangtao Ke Wang Yang Chen Guangyong Pan Mingzhen Xin
author_facet	Min Zhai Guolin Liu Qiuxiangtao Ke Wang Yang Chen Guangyong Pan Mingzhen Xin
author_sort	Min Zhai
title	The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion
title_short	The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion
title_full	The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion
title_fullStr	The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion
title_full_unstemmed	The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion
title_sort	liu-type estimator based on parameter optimization and its application in sbas deformation model inversion
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/278f96854c3943cd9a3b7f14ab31d04e
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The Liu-Type Estimator Based on Parameter Optimization and its Application in SBAS Deformation Model Inversion

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