基于整体最小二乘法的GPS地质高程拟合研究
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摘要
在测绘领域,关于整体最小二乘法的应用研究刚刚开始,受到众多学者的关注,如何提高测量数据处理的精确度与稳定性是目前面临的根本任务,将整体最小二乘法应用于GPS高程的拟合中,对拟合函数进行参数求解,并且该方法解算结果与传统最小二乘法解算结果进行对比分析,研究得出:模型以二次曲面模型为依据,对测量数据进行计算,计算结果与传统的最小二乘法相比,整体最小二乘法建立的模型更加合理、更加严密;对具体数据进行算例解算分析,并应用于平面模型与曲面模型中,然后通过整体最小二乘法与传统最小二乘法进行对比分析,采用整体最小二乘法进行GPS高程拟合得到的拟合结果更加贴近实际情况、更加准确。
In the field of surveying and mapping,the application research on the global least squares method has just begun,and it has attracted the attention of many scholars. How to improve the accuracy and stability of measurement data processing was the fundamental task at present,and the application of the global least squares method to GPS elevation In the middle,the fitting function was solved,and the solution result was compared with the traditional least squares solution. The research results showed that the model was based on the quadric model and the measurement data was calculated. Compared with the traditional least squares method,the model established by the global least squares method was more reasonable and more rigorous; the specific data was solved and analyzed in the plane model and the surface model,and then the whole least squares method and the tradition were adopted. The least squares method was used for comparative analysis. The fitting result obtained by GPS elevation fitting using the overall least squares is closer to the actual situation and more accurate.
In the field of surveying and mapping,the application research on the global least squares method has just begun,and it has attracted the attention of many scholars. How to improve the accuracy and stability of measurement data processing was the fundamental task at present,and the application of the global least squares method to GPS elevation In the middle,the fitting function was solved,and the solution result was compared with the traditional least squares solution. The research results showed that the model was based on the quadric model and the measurement data was calculated. Compared with the traditional least squares method,the model established by the global least squares method was more reasonable and more rigorous; the specific data was solved and analyzed in the plane model and the surface model,and then the whole least squares method and the tradition were adopted. The least squares method was used for comparative analysis. The fitting result obtained by GPS elevation fitting using the overall least squares is closer to the actual situation and more accurate.
引文
[1]楚彬,范东明.基于比例整体最小二乘的GPS高程拟合[J].测绘工程,2014,23(4):37-39.Chu Bin,Fan Dongming. GPS elevation fitting based on proportional global least squares[J]. Engineering of Surveying and Mapping,2014,23(4):37-39.
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[3]张鹏杰,郑晓晨,孟祥用,等.加权整体最小二乘在GPS高程拟合中的应用[J].城市勘测,2017(3):86-89.Zhang Pengjie,Zheng Xiaochen,Meng Xiangyong,et al. Application of weighted whole least squares in GPS height fitting[J]. Urban Geotechnical Investigation&Surveying,2017(3):86-89.
[4]鲁铁定,周世健,张立亭,等.基于整体最小二乘的地面激光扫描标靶球定位方法[J].大地测量与地球动力学,2009,29(4):102-105.Lu Tieding,Zhou Shijian,Zhang Liting,et al. Global laser scanning target ball localization method based on global least squares[J].Journal of Geodesy and Geodynamics,2009,29(4):102-105.
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[6]李明飞,郇敏,秦川.基于遗传算法的加权最小二乘支持向量机GPS高程拟合法[J].全球定位系统,2016,41(6):98-101.Li Mingfei,Xun Min,Qin Chuan. Weighted least square support vector machine GPS elevation fitting method based on genetic algorithm[J]. GNSS World of China,2016,41(6):98-101.
[7]李献民,李夕明.基于二次曲面半参数模型的GPS高程拟合及应用研究[J].测绘与空间地理信息,2013(10):117-119.Li Xianmin,Li Ximing. GPS height fitting based on semi-parametric model of conicoid and its application[J]. Geomatics&Spatial Information Technology,2013(10):117-119.
[8]魏玉明,张永志.基于抗差最小二乘配置法的GPS高程拟合[J].工程勘察,2017,45(3):40-43.Wei Yuming,Zhang Yongzhi. GPS height fitting based on robust least square collocation method[J]. Geotechnical Investigation&Surveying,2017,45(3):40-43.
[9]杨会军.基于整体最小二乘的GNSS高程拟合研究[J].全球定位系统,2015(6):99-101.Yang Huijun. Research on GNSS height fitting based on global least squares[J]. GNSS World of China,2015(6):99-101.
[10]官云兰,刘绍堂,周世健,等.基于整体最小二乘的稳健点云数据平面拟合[J].大地测量与地球动力学,2011,31(5):80-83.Guan Yunlan,Liu Shaotang,Zhou Shijian,et al. Robust point could data plane fitting based on global least squares[J]. Journal of Geodesy and Geodynamics,2011,31(5):80-83.
[11]熊风光,李希,韩燮.基于整体最小二乘的椭圆拟合方法[J].微电子学与计算机,2017,34(1):102-105.Xiong Fengguang,Li Xie,Han Xie. Ellipse fitting method based on global least squares[J]. Microelectronics&Computer,2017,34(1):102-105.
[12]辛明真,翟敏,褚恒滨.基于整体最小二乘的平面坐标转换模型比较[J].工程勘察,2015,43(5):24-28.Xin Mingzhen,Zhai Min,Chu Hengbin. Comparison of plane coordinate transformation models based on global least squares[J].Geotechnical Investigation&Surveying,2015,43(5):24-28.
[13]宋会龙.整体最小二乘算法在直线拟合中的应用[J].四川水泥,2016(1):77-78.Song Huilong. Application of global least squares algorithm in straight line fitting[J]. Sichuan Cement,2016(1):77-78.
[14]黄德双.基于整体最小二乘的单次快拍线性预测空域谱估计方法分析[J].系统工程与电子技术,1991(11):35-40.Huang Deshuang. Analysis of spatial spectrum estimation of single fast linear prediction based on global least squares[J]. Systems Engineering and Electronics,1991(11):35-40.
[15]武艳强,江在森,杨国华,等.利用最小二乘配置在球面上整体解算GPS应变场的方法及应用[J].地球物理学报,2009,52(7):1707-1714.Wu Yanqiang,Jiang Zaisen,Yang Guohua,et al. Method and application of calculating GPS strain field on the sphere with least squares allocation[J]. Chinese Journal of Geophysics,2009,52(7):1707-1714.
[16]李延成,李军,刘慧霞,等.基于最小二乘法的区域整体最优匹配选取控制点的方法[J].测绘科学,2012,37(6):94-97.Li Yancheng,Li Jun,Liu Huixia,et al. Method of selecting control points based on the least square method in the whole region optimal matching[J]. Science of Surveying and Mapping,2012,37(6):94-97.
[17]张冬菊,黄声享.基于整体最小二乘的灰色模型在大坝变形分析中的应用[J].工程勘察,2017,45(12):55-59.Zhang Dongju,Huang Shengxiang. Application of gray model based on whole least square in dam deformation analysis[J]. Geotechnical Investigation&Surveying,2017,45(12):55-59.
[18]叶珉吕,花向红,陈西江,等.基于正交整体最小二乘平面拟合的点云数据去噪方法研究[J].测绘通报,2013(11):37-39.Ye Minlü,Hua Xianghong,Chen Xijiang,et al. Research on point cloud data denoising method based on orthogonal global least squares plane fitting[J]. Bulletin of Surveying and Mapping,2013(11):37-39.
[19]杨勇喜,贾东振,何秀凤.基于选权迭代法的抗差整体最小二乘及其应用[J].测绘工程,2014,23(12):56-59.Yang Yongxi,Jia Dongzhen,He Xiufeng. Anti-difference whole least squares based on the weighted iteration method and its application[J]. Engineering of Surveying and Mapping,2014,23(12):56-59.
[20]吴开岩,张献州,马龙,等.基于多元整体最小二乘优化的多点灰色动态变形分析模型[J].大地测量与地球动力学,2016,36(8):682-685.Wu Kaiyan,Zhang Xianzhou,Ma Long,et al. Multi-point gray dynamic deformation analysis model based on multivariate global least squares optimization[J]. Journal of Geodesy and Geodynamics,2016,36(8):682-685.
[21]杨仕平,范东明,龙玉春.整体最小二乘法平面坐标转换在基坑水平位移监测中的应用[J].测绘与空间地理信息,2012,35(9):221-223.Yang Shiping,Fan Dongming,Long Yuchun. Application of whole least squares plane coordinate transformation in monitoring pit horizontal displacement[J]. Geomatics&Spatial Information Technology,2012,35(9):221-223.
[22]丁克良,欧吉坤,赵春梅.正交最小二乘曲线拟合法[J].测绘科学,2007,32(3):18-19.Ding Keliang,Ou Jikun,Zhao Chunmei. Orthogonal least squares curve fitting method[J]. Science of Surveying and Mapping,2007,32(3):18-19.
[23]贺建清,刘秀军.基于最小二乘法的边坡稳定性分析[J].岩土力学,2012,33(6):128-133.He Jianqing,Liu Xiujun. Slope stability analysis based on least squares method[J]. Rock and Soil Mechanics,2012,33(6):128-133.
[2]鲁铁定,陶本藻,周世健.基于整体最小二乘法的线性回归建模和解法[J].武汉大学学报(信息科学版),2008,33(5):504-507.Lu Tieding,Tao Benzao,Zhou Shijian. Linear regression modeling and solution based on global least square method[J]. Geomatics and Information Science of Wuhan University,2008,33(5):504-507.
[3]张鹏杰,郑晓晨,孟祥用,等.加权整体最小二乘在GPS高程拟合中的应用[J].城市勘测,2017(3):86-89.Zhang Pengjie,Zheng Xiaochen,Meng Xiangyong,et al. Application of weighted whole least squares in GPS height fitting[J]. Urban Geotechnical Investigation&Surveying,2017(3):86-89.
[4]鲁铁定,周世健,张立亭,等.基于整体最小二乘的地面激光扫描标靶球定位方法[J].大地测量与地球动力学,2009,29(4):102-105.Lu Tieding,Zhou Shijian,Zhang Liting,et al. Global laser scanning target ball localization method based on global least squares[J].Journal of Geodesy and Geodynamics,2009,29(4):102-105.
[5]赵辉,张书毕,张秋昭.基于加权总体最小二乘法的GPS高程拟合[J].大地测量与地球动力学,2011,31(5):88-90.Zhao Hui,Zhang Shubi,Zhang Qiuzhao. GPS height fitting based on weighted overall least squares method[J]. Journal of Geodesy and Geodynamics,2011,31(5):88-90.
[6]李明飞,郇敏,秦川.基于遗传算法的加权最小二乘支持向量机GPS高程拟合法[J].全球定位系统,2016,41(6):98-101.Li Mingfei,Xun Min,Qin Chuan. Weighted least square support vector machine GPS elevation fitting method based on genetic algorithm[J]. GNSS World of China,2016,41(6):98-101.
[7]李献民,李夕明.基于二次曲面半参数模型的GPS高程拟合及应用研究[J].测绘与空间地理信息,2013(10):117-119.Li Xianmin,Li Ximing. GPS height fitting based on semi-parametric model of conicoid and its application[J]. Geomatics&Spatial Information Technology,2013(10):117-119.
[8]魏玉明,张永志.基于抗差最小二乘配置法的GPS高程拟合[J].工程勘察,2017,45(3):40-43.Wei Yuming,Zhang Yongzhi. GPS height fitting based on robust least square collocation method[J]. Geotechnical Investigation&Surveying,2017,45(3):40-43.
[9]杨会军.基于整体最小二乘的GNSS高程拟合研究[J].全球定位系统,2015(6):99-101.Yang Huijun. Research on GNSS height fitting based on global least squares[J]. GNSS World of China,2015(6):99-101.
[10]官云兰,刘绍堂,周世健,等.基于整体最小二乘的稳健点云数据平面拟合[J].大地测量与地球动力学,2011,31(5):80-83.Guan Yunlan,Liu Shaotang,Zhou Shijian,et al. Robust point could data plane fitting based on global least squares[J]. Journal of Geodesy and Geodynamics,2011,31(5):80-83.
[11]熊风光,李希,韩燮.基于整体最小二乘的椭圆拟合方法[J].微电子学与计算机,2017,34(1):102-105.Xiong Fengguang,Li Xie,Han Xie. Ellipse fitting method based on global least squares[J]. Microelectronics&Computer,2017,34(1):102-105.
[12]辛明真,翟敏,褚恒滨.基于整体最小二乘的平面坐标转换模型比较[J].工程勘察,2015,43(5):24-28.Xin Mingzhen,Zhai Min,Chu Hengbin. Comparison of plane coordinate transformation models based on global least squares[J].Geotechnical Investigation&Surveying,2015,43(5):24-28.
[13]宋会龙.整体最小二乘算法在直线拟合中的应用[J].四川水泥,2016(1):77-78.Song Huilong. Application of global least squares algorithm in straight line fitting[J]. Sichuan Cement,2016(1):77-78.
[14]黄德双.基于整体最小二乘的单次快拍线性预测空域谱估计方法分析[J].系统工程与电子技术,1991(11):35-40.Huang Deshuang. Analysis of spatial spectrum estimation of single fast linear prediction based on global least squares[J]. Systems Engineering and Electronics,1991(11):35-40.
[15]武艳强,江在森,杨国华,等.利用最小二乘配置在球面上整体解算GPS应变场的方法及应用[J].地球物理学报,2009,52(7):1707-1714.Wu Yanqiang,Jiang Zaisen,Yang Guohua,et al. Method and application of calculating GPS strain field on the sphere with least squares allocation[J]. Chinese Journal of Geophysics,2009,52(7):1707-1714.
[16]李延成,李军,刘慧霞,等.基于最小二乘法的区域整体最优匹配选取控制点的方法[J].测绘科学,2012,37(6):94-97.Li Yancheng,Li Jun,Liu Huixia,et al. Method of selecting control points based on the least square method in the whole region optimal matching[J]. Science of Surveying and Mapping,2012,37(6):94-97.
[17]张冬菊,黄声享.基于整体最小二乘的灰色模型在大坝变形分析中的应用[J].工程勘察,2017,45(12):55-59.Zhang Dongju,Huang Shengxiang. Application of gray model based on whole least square in dam deformation analysis[J]. Geotechnical Investigation&Surveying,2017,45(12):55-59.
[18]叶珉吕,花向红,陈西江,等.基于正交整体最小二乘平面拟合的点云数据去噪方法研究[J].测绘通报,2013(11):37-39.Ye Minlü,Hua Xianghong,Chen Xijiang,et al. Research on point cloud data denoising method based on orthogonal global least squares plane fitting[J]. Bulletin of Surveying and Mapping,2013(11):37-39.
[19]杨勇喜,贾东振,何秀凤.基于选权迭代法的抗差整体最小二乘及其应用[J].测绘工程,2014,23(12):56-59.Yang Yongxi,Jia Dongzhen,He Xiufeng. Anti-difference whole least squares based on the weighted iteration method and its application[J]. Engineering of Surveying and Mapping,2014,23(12):56-59.
[20]吴开岩,张献州,马龙,等.基于多元整体最小二乘优化的多点灰色动态变形分析模型[J].大地测量与地球动力学,2016,36(8):682-685.Wu Kaiyan,Zhang Xianzhou,Ma Long,et al. Multi-point gray dynamic deformation analysis model based on multivariate global least squares optimization[J]. Journal of Geodesy and Geodynamics,2016,36(8):682-685.
[21]杨仕平,范东明,龙玉春.整体最小二乘法平面坐标转换在基坑水平位移监测中的应用[J].测绘与空间地理信息,2012,35(9):221-223.Yang Shiping,Fan Dongming,Long Yuchun. Application of whole least squares plane coordinate transformation in monitoring pit horizontal displacement[J]. Geomatics&Spatial Information Technology,2012,35(9):221-223.
[22]丁克良,欧吉坤,赵春梅.正交最小二乘曲线拟合法[J].测绘科学,2007,32(3):18-19.Ding Keliang,Ou Jikun,Zhao Chunmei. Orthogonal least squares curve fitting method[J]. Science of Surveying and Mapping,2007,32(3):18-19.
[23]贺建清,刘秀军.基于最小二乘法的边坡稳定性分析[J].岩土力学,2012,33(6):128-133.He Jianqing,Liu Xiujun. Slope stability analysis based on least squares method[J]. Rock and Soil Mechanics,2012,33(6):128-133.