引用本文: 谢曦霖, 许才军, 温扬茂, 周力璇. 一种基于多面函数的改进最小二乘配置方法[J]. 武汉大学学报 ( 信息科学版), 2018, 43(4): 592-598.
XIE Xilin, XU Caijun, WEN Yangmao, ZHOU Lixuan. A Refined Least Squares Collocation Method Based on Multiquadric Function[J]. Geomatics and Information Science of Wuhan University, 2018, 43(4): 592-598.
 Citation: XIE Xilin, XU Caijun, WEN Yangmao, ZHOU Lixuan. A Refined Least Squares Collocation Method Based on Multiquadric Function[J]. Geomatics and Information Science of Wuhan University, 2018, 43(4): 592-598.

## A Refined Least Squares Collocation Method Based on Multiquadric Function

• 摘要: 利用最小二乘配置对非平稳空间随机场进行推估时，趋势项数学模型的选择通常无法完整体现非平稳空间随机场的系统性，这将导致经验协方差函数估计出现偏差，最终推估结果可能错误。提出了一种基于多面函数的改进最小二乘配置方法来解决上述问题。该方法引入多面函数拟合区域内的趋势项，通过多次迭代计算得到稳定的待定系数值与协方差函数的参数值，最后综合趋势项与信号项得到最终估值。分别采用了模拟地震垂直形变数据和2009年意大利L’Aquila地震的合成孔径雷达干涉测量（Interferometric SAR，InSAR）与GPS同震位移数据来对该方法进行验证，并将其结果与常规方法进行比较。结果表明，改进方法在外部检核点估值的均方残差要小于多面函数法与常规的最小二乘配置法，且受采样点位的影响最小。

Abstract: Trend removal is the most common approach in conventional least squares collocation (LSC) to deal with nonstationarity. Due to the inaccuracy of the trend model, conventional LSC can barely eliminate the drift component of the data that results in estimation bias of the local covariance function and error of the interpolation values. Here we present a refined LSC method to estimate the drift component of the field and compensate the residualfrom LSC. The refined method employs the mulitiquadric function to approach the drift and the collocation to estimate signals. We apply the refined method to a synthetic data set and coseismic displacement data from the 2009 L'Aquila, Italy earthquake, and compare the results of refined method with conventional methods. The statistical results of residuals indicate that the refined method can achieve a more accurate result than conventional methods and is affected less by the observation distribution.

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