一种拟合GPS高程异常的新方法
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摘要
针对GPS高程异常拟合中观测数据存在粗差和系数矩阵存在误差的情况,提出采用一种新的RTLS迭代算法,同时构造基于标准化残差的IGGIII权函数.RTLS迭代算法顾及了系数矩阵中的常数列不存在误差的特性,仅考虑存在误差的列向量部分.以某市城区的80组GPS水准联测数据为例,设计两种实验方案证该方法的精度和稳健性,其中,拟合数据有43组(四组GPS数据含有粗差),外符合检验数据37组.在拟合数据不含粗差的情况下,RLTS和抗差LS估计效果一致;而在拟合数据存在粗差的情况下,RTLS拟合二次曲面的效果明显抗差LS算法.结果表明:利用RTLS拟合GPS高程异常拟合的二次曲面是最优选择.
Aiming at the situation of errors in observation data and coefficient matric in GPS Height anomaly,a robust total least squares(RTLS) is proposed with a IGGIII weight function based on standardized residuals.The method only takes the parts containing deviation in coefficient matrix into consideration.Taking the 80 groups GPS observation of benchmark as an example,the feasibility and accuracy of TRLS is analyzed compared with two kinds of experiment including 43 groups of data for fitting(4 groups of data with gross error) and 37 groups of data for testing.If the data have no robust,the result of RTLS is equal with robust LS.If the data have robust,the result of RTLS is better than robust LS.The experiment shows that the method of RTLS is the best choice when fitting GPS height anomaly.
Aiming at the situation of errors in observation data and coefficient matric in GPS Height anomaly,a robust total least squares(RTLS) is proposed with a IGGIII weight function based on standardized residuals.The method only takes the parts containing deviation in coefficient matrix into consideration.Taking the 80 groups GPS observation of benchmark as an example,the feasibility and accuracy of TRLS is analyzed compared with two kinds of experiment including 43 groups of data for fitting(4 groups of data with gross error) and 37 groups of data for testing.If the data have no robust,the result of RTLS is equal with robust LS.If the data have robust,the result of RTLS is better than robust LS.The experiment shows that the method of RTLS is the best choice when fitting GPS height anomaly.
引文
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[2]刘经南,曾文宪,徐培亮.整体最小二乘估计的研究进展[J].武汉大学学报(信息科学版),2013,38(5):505-512.LIU Jingnan,ZENG Wenxian,XU Peiliang.Overview of total least squares method[J].Geomatics and Information Science of Wuhan University,2013,38(5):505-512.
[3]孔建,姚宜斌,吴寒.整体最小二乘的迭代解法[J].武汉大学学报信息科学版,2010,35(6):711-714.KONG Jian,YAO Yibiin,WU Han.Iterative method for Total Least Squares[J].Geomatics and Information Science of Wuhan University,2010,35(6):711-714.
[4]鲁铁定,宁津生,周世健,等.最小二乘配置的QR分解解法[J].辽宁工程技术大学学报(自然科学版),2009,28(4):550-553.LU Tieding,NING Jinsheng,ZHOU Shijian,et al.An algorithm of QRdecomposition for least-square collocation[J].Journal of Liaoning Technical University(Natural Science),2009,28(4):550-553.
[5]SCHAFFRIN B,WIESER A.On weighted total least-squares adjustment for linear regression[J].Journal of Geodesy,2008,82(7):415-421.
[6]丁克良,沈云中,欧吉坤.整体最小二乘法直线拟合[J].辽宁工程技术大学学报(自然科学版),2010,29(1):44-47.DING Keliang,SHEN Yunzhong,OU Jikun.Methods of line-fitting based on total least squares[J].Journal of Liaoning Technical University(Natural Science),2010,29(1):44-47.
[7]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.Modeling and algorithm of linear regression based on total least squares[J].Geomatics and Information Science of Wuhan University,2008,33(5):504-507.
[8]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 Total least squares plane coordinate transformation in pit horizontal displacelment monitoring[J].Geomatics&Spatial Information Technology,2012,35(9):221-223.
[9]邓罡.GPS高程拟合代替水准测量研究[D].长沙:中南大学,2012.
[10]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 Yueyang,XU Caijun.Progress in total least squares[J].Geomatics and Information Science of Wuhan University,2013,38(7):850-856.
[11]汪奇生,杨德宏,杨腾飞.线性回归模型的稳健总体最小二乘解算[J].大地测量与地球动力学,2015,35(2):239-242.WANG Qisheng,YANG Hongde,YANG Tengfei.The solution of roubust total least squares for linear regression models[J].Journal of Geodesy and Geodynamics,2015,35(2):239-242.
[12]邱卫宁,陶本藻,姚宜斌,等.测量数据处理理论与方法[M].武汉:武汉大学出版社,2008.
[13]龚循强,李志林.稳健加权总体最小二乘[J].测绘学报,2014,43(9):888-894.GONG Xunqiang,LI Zhiling.A Robust weight total least squares method[J].Acta Geodaetica et Cartographica Sinica,2014,43(9):888-894.