变异函数模型参数的加权总体最小二乘回归法
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摘要
顾及距离值的随机误差,提出用加权总体最小二乘回归法估计变异函数模型参数。通过协方差传播律发现,分组后的变异函数值和距离值是不等精度的。给出距离值的定权方法,结合熵权法和点对数法迭代解算模型参数。以幂函数模型为例,模拟数据和实测数据的结果表明,加权总体最小二乘回归法更加合理,参数的估计精度也更高。
Considering errors of distances,weighted total least squares regression is applied to estimate parameters of variogram model.According to variance-covariance propagation law,variogram values and distances after classification are found unequally accurate.Combined with two weighting methods of variogram values,the entropy weight method and number of points method,the weight method of distances derived by the variance-covariance propagation law is used to estimate parameters.Taking the power function model as an example,weighted total least squares regression is proven to be more reasonable and accurate by results of simulated and actual data.
Considering errors of distances,weighted total least squares regression is applied to estimate parameters of variogram model.According to variance-covariance propagation law,variogram values and distances after classification are found unequally accurate.Combined with two weighting methods of variogram values,the entropy weight method and number of points method,the weight method of distances derived by the variance-covariance propagation law is used to estimate parameters.Taking the power function model as an example,weighted total least squares regression is proven to be more reasonable and accurate by results of simulated and actual data.
引文
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[2]王仁铎,胡光道.线性地质统计学[M].北京:地质出版社,1988(Wang Renduo,Hu Guangdao.Linear Geostatistics[M].Beijing:Geological Press,1988)
[3]矫希国,刘超.变差函数的参数模拟[J].物化探测技术,1996,18(2):157-161(Jiao Xiguo,Liu Chao.Estimation of Variation Parameter[J].Computing Techniques for Geophysical and Geochemical Exploration,1996,18(2):157-161)
[4]李玲,何涛,张武,等.变异函数线性化的统一参数估计方法研究[J].长江大学学报:自然科学版(理工卷),2010,7(2):127-129(Li Ling,He Tao,Zhang Wu,et al.Study on the Unity Parameter Estimation Method of Linear Variogram[J].Journal of Yangtze University:Nat Sci Edit,2010,7(2):127-129)
[5]李明,高星伟,文汉江,等.Kriging方法在GPS水准拟合中的应用[J].测绘科学,2009,34(1):106-107(Li Ming,Gao Xingwei,Wen Hanjiang,et al.The Application of Kriging Method in GPS Leveling Fitting[J].Science of Surveying and Mapping,2009,34(1):106-107)
[6]郭泉河,李秀海.不同变异函数的泛Kriging法的GPS高程拟合结果[J].黑龙江工程学院学报:自然科学版,2011,25(4):26-28(Guo Quanhe,Li Xiuhai.Application of Universal Kriging Technology with Different Semivariation Function Models to GPS Height Anomaly Fitting[J].Journal of Heilongjiang Institute of Technology,2011,25(4):26-28)
[7]潘家宝,戴吾蛟,章浙涛,等.变异函数模型参数估计的信息熵加权回归法[J].大地测量与地球动力学,2014,34(3):125-128(Pan Jiabao,Dai Wujiao,Zhang Zhetao,et al.Parameter Estimation of Variogram Model by Using Information Entropy Weighted Regression[J].Journal of Geodesy and Geodynamics,2014,34(3):125-128)
[8]严华雯,吴健平.加权最小二乘法改进遗传克里金插值方法研究[J].计算机技术与发展,2012,22(3):92-95(Yan Huawen,Wu Jianping.Reasearch on Genetic Algorithm Kriging Optimized by Weight Least Square[J].Computer Technology and Development,2012,22(3):92-95)
[9]曾怀恩,黄声享.基于Kriging方法的空间数据插值研究[J].测绘工程,2007,16(5):5-13(Zeng Huaien,Huang Shengxiang.Research on Spatial Data Interpolation Based on Kriging Interpolation[J].Engineering of Surveying and Mapping,2007,16(5):5-13)
[10]Golub G H,Loan C V.An Analysis of the Total LeastSquares Problem[J].SIAM Journal on Numerical Analysis,1980,17(6):883-893
[11]王乐洋.总体最小二乘解性质研究[J].大地测量与地球动力学,2012,32(5):48-52(Wang Leyang.Research on Properties of Total Least Squares Estimation[J].Journal of Geodesy and Geodynamics,2012,32(5):48-52)
[12]王乐洋,许才军.总体最小二乘研究进展[J].武汉大学学报:信息科学版,2013,38(7):850-856(Wang Leyang,Xu Caijun.Progress in Total Least Squares[J].Geomatics and Information Science of Wuhan University,2013,38(7):850-856)
[13]Felus Y A,Schaffrin B.A Total Least-Squares Approach in Two Stages for Semivariogram Modeling of Aeromagnetic Data[C].IAMG2005,Toronto,2005
[14]王乐洋,鲁铁定.总体最小二乘平差法的误差传播定律[J].大地测量与地球动力学,2014,34(2):55-59(Wang Leyang,Lu Tieding.Propagation Law of Errors in Total Least Squares Adjustment[J].Journal of Geodesy and Geodynamics,2014,34(2):55-59)
[15]Fang X.Weighted Total Least Squares Solutions for Applications in Geodesy[D].Hanover:Leibniz University of Hanover,2011
[16]Jazaeri S,Amiri-Simkooei A R,Sharifi M A.Iterative Algorithm for Weighted Total Least Squares Adjustment[J].Survey Review,2014,46(334):19-27
[17]朱卫东,李全海.基于标准化动量BP神经网络的GPS高程转换[J].大地测量与地球动力学,2010,30(1):123-125(Zhu Weidong,Li Quanhai.Conversion of GPS Height Based on Standardization Momentum BP Neural Network[J].Journal of Geodesy and Geodynamics,2010,30(1):123-125)
[18]黎剑.区域GPS高程异常拟合及建模方法研究[D].昆明:昆明理工大学,2013(Li Jian.Research on Regional GPS Height Anomaly Fitting and Modeling[D].Kunming:Kunming University of Science and Technology,2013)