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: | , , , , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
IEEE
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/278f96854c3943cd9a3b7f14ab31d04e |
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| Sumario: | 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. |
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