基于稳健总体最小二乘的GPS水准拟合研究  

Study on GPS Height Anomaly Based on Robust Total Least Squares

作　　者：陈振国[1,2] 唐龙江 CHEN Zhenguo;TANG Longjiang(272 Geological Brigade of Jiangsu Nuclear Industry,Nanjing 210000,China;The Nuclear Industry Construction Group Limited Company,Nanjing 210000,China;School of Mapping and Geographical Science,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]江苏省核工业二七二地质大队,江苏南京210000 [2]核工业建设集团有限公司,江苏南京210000 [3]辽宁工程技术大学测绘与地理科学学院,辽宁阜新123000

出　　处：《测绘地理信息》2018年第4期84-87,100,共5页Journal of Geomatics

基　　金：国家青年自然科学基金资助项目(41504030)

摘　　要：针对全球定位系统（global positioning system,GPS）水准拟合中观测数据存在粗差和系数矩阵存在误差的情况,将一种加权稳健总体最小二乘（robust total least squares,RTLS）迭代算法应用于GPS水准拟合。以某市80组联测水准的高程数据为例,以利用抗差最小二乘（least squares,LS）法拟合的高程异常值为参考值,分析了RTLS在GPS水准拟合中的可行性和有效性。结果表明,与LS相比,RTLS不仅考虑了自变量和因变量的误差,同时也顾及了系数矩阵和观测向量中存在的误差。在利用RTLS进行GPS水准拟合时,能较好地去除粗差,合理地估计系数矩阵中含有误差的部分,且二次曲面拟合得到高程异常的精度与利用抗差LS拟合的精度近乎一致。Aiming at the existing errors in observation data and coefficient matric in GPS Height Anomaly,a robust total least squares（RTLS）with weight is proposed.Taking the 80 groups GPS observation of benchmark as an example,the feasibility and accuracy of TRLS is analyzed compared with results from least squares（LS）.The experiment shows that the RTLS considers both errors of independent variables and dependent variables and errors in coefficient matrix and observation vectors,with comparison to LS.During the GPS Height Anomaly,the method of RTLS can remove errors easily and estimate random errors of coefficient matrix correctly.Moreover,the precision is equal with the robust LS.

关 键 词：全球定位系统水准拟合 稳健总体最小二乘 系数矩阵 观测向量 

分 类 号：P207[天文地球—测绘科学与技术] P228.41