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首页> 外文期刊>Surveys in Geophysics: An International Review Journal of Geophysics and Planetary Sciences >Fast Estimation of Covariance Parameters in Least-Squares Collocation by Fisher Scoring with Levenberg-Marquardt Optimization
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Fast Estimation of Covariance Parameters in Least-Squares Collocation by Fisher Scoring with Levenberg-Marquardt Optimization

机译：利用Levenberg-Marquardt优化的Fisher评分，快速估计相协方差参数

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摘要

Maximum likelihood (ML) and restricted maximum likelihood (REML) are nowadays very popular in geophysics, geodesy and many other fields. There is also a growing number of investigations into how to calculate covariance parameters by ML/REML accurately and fast, and assure the convergence of the iteration steps in derivative-based approaches. The latter condition is not satisfied in many solutions, as it requires composed procedures or takes an unacceptable amount of time. The article implements efficient Fisher scoring (FS) to covariance parameter estimation in least-squares collocation (LSC). FS is optimized through Levenberg-Marquardt (LM) optimization, which provides stability in convergence when estimating two covariance parameters necessary for LSC. The motivation for this work was a very large number of non-optimized FS in the literature, as well as a deficiency of its scientific and engineering applications. The example work adds some usefulness to maximum likelihood estimation (ML) and FS and shows a new application-an alternative approach to LSC-a parametrization with no empirical covariance estimation. The results of LM damping applied to FS (FSLM) require some additional research related with optimal LM parameter. However, the method appears to be a milestone in relation to non-optimized FS, in terms of convergence. The FS with LM provides a reliable convergence, whose speed can be adjusted by manipulating the LM parameter.
机译：现在，最大可能性（ML）和受限制的最大可能性（REML）在地球物理学，大地测量和许多其他领域非常流行。如何准确且快速地计算ML / REML的协方差参数越来越多的调查，并确保基于衍生物的方法的迭代步骤的收敛性。在许多解决方案中，后一种条件不满足，因为它需要编组程序或采取不可接受的时间。该物品实现了有效的Fisher评分（FS）到最小二乘搭配（LSC）的协方差参数估计。通过Levenberg-Marquardt（LM）优化优化FS，该优化在估算LSC所需的两个协方差参数时提供稳定性。这项工作的动机是文献中的一大批非优化的FS，以及其科学和工程应用的缺点。示例性工作为最大似然估计（ML）和FS增加了一些有用性，并显示了一种新的应用程序 - 一种替代方法，即LSC-A的参数化，没有经验协方差估计。应用于FS（FSLM）的LM阻尼的结果需要一些与最佳LM参数有关的额外研究。然而，在收敛方面，该方法似乎是与非优化FS相关的里程碑。具有LM的FS提供可靠的收敛性，其通过操纵LM参数可以调整其速度。

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