一种基于多面函数的改进最小二乘配置方法  

A Refined Least Squares Collocation Method Based on Multiquadric Function

作　　者：谢曦霖 许才军[1,2,3] 温扬茂 周力璇[1] XIE Xilin1, XU Caijun1,2,3, WEN Yangmao1,2,3, ZHOU Lixuan1(1 School of Geodesy and Geomaties, Wuhan University, Wuhan 430079, China ;2 Key Laboratory of Geospace Environment and Geodesy, Ministry o{ Education, Wuhan 430079, China; 3 Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, Chin)

机构地区：[1]武汉大学测绘学院,湖北武汉430079 [2]地球空间环境与大地测量教育部重点实验室,湖北武汉430079 [3]地球空间信息技术协同创新中心,湖北武汉430079

出　　处：《武汉大学学报（信息科学版）》2018年第4期592-598,共7页Geomatics and Information Science of Wuhan University

基　　金：国家高技术研究发展计划(2013AA122501-3);地震行业科研专项基金(201308009);国家自然科学基金(41431069,41574002,41721003,41774011)~~

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。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.

关 键 词：多面函数法 最小二乘配置法 空间插值 病态性 

分 类 号：P223[天文地球—大地测量学与测量工程] P231[天文地球—测绘科学与技术]