改进权值的加权整体最小二乘法高程拟合应用  

The Elevation Fitting Application of Weighted Total Least Square Method with Improved Weight

作　　者：陈强 岳东杰[1] Chen Qiang;Yue Dongjie(School of Earth Science and Engineering,Hohai University,Nanjing 211100,China)

机构地区：[1]河海大学地球科学与工程学院,江苏南京211100

出　　处：《甘肃科学学报》2020年第5期17-21,41,共6页Journal of Gansu Sciences

摘　　要：GPS高程拟合中二次曲面法应用较广,但传统二次曲面法是基于最小二乘原则,由此引入以变量误差模型(EIV)为基础的整体最小二乘法和加权整体最小二乘法,提出了一种改进的定权方式应用于加权整体最小二乘的高程拟合,并在高程拟合实例中比较了分别基于最小二乘(LS)、基于整体最小二乘(TLS)和基于加权整体最小二乘(WTLS)的二次曲面法。实例表明该定权方法的加权整体最小二乘检核点残差整体减小了约1 mm,外符合精度上提高了1.2%,能够一定程度提高拟合精度。最后将WTLS二次曲面法与多面函数法和BP神经网络进行了实例比较和分析,得出了一些结论和展望。Quadric surface method is widely used in GPS elevation fitting,but the traditional quadric surface method is based on the least square principle.Therefore the total least-square method and weighted total least-square method based on variable error model(EIV)were introduced in this article,and an improved weighting method was applied to the elevation fitting of weighted total least square.In the elevation fitting practices,the quadric surface method based on least square(LS),total least squares(TLS)and weighted total least square(WTLS)were compared respectively to reveal that the check point residual of weighted total least squares by this method decreases by about 1mm on the whole,and the outside coincidence accuracy increases by 1.2%,which can improve the fitting accuracy to a certain extent.Finally,examples of WTLS quadric surface method,multiplane function method and BP neural network were compared and analyzed to arrive at some conclusions and expectations.

关 键 词：加权整体最小二乘 高程拟合 二次曲面法 多面函数法 BP神经网络 

分 类 号：P228.4[天文地球—大地测量学与测量工程]