一种基于LS-WTLS的稳健平面拟合方法  

A robust methods of fitting plane based on LS-WTLS

作　　者：欧江霞 邓雄文 蔡茂欣 邱敏 OU Jiangxia;DENG Xiongwen;CAI Maoxin;QIU Min(Gedogical Survey of Guangzhou, Guangzhou 510663, China)

机构地区：[1]广州市地质调查院,广州510440

出　　处：《激光技术》2020年第6期784-788,共5页Laser Technology

基　　金：国家自然科学基金资助项目(41974214)。

摘　　要：为了解决平面数据点位精度差异性及平面模型常数项解算精度较低的问题,提出了一种基于最小二乘-加权总体最小二乘(LS-WTLS)的稳健平面拟合方法。该方法采用加权最小二乘模型与稳健估计IGGⅢ方案相结合的方式对平面模型误差项参量进行解算,然后通过设置阈值剔除粗差数据,利用最小二乘法对平面模型常数项进行解算,以此进一步提高了平面模型各参量的解算精度。结果表明,新方法相对于最小二乘(LS)法、总体最小二乘(TLS)法、LS-TLS法、IGGⅢ-LS-TLS法,其单位权中误差分别提高了53.6%,195.0%,47.5%和5.1%,平面拟合精度分别提高了49.4%,179.3%,48.7%和46.99%,表现出了良好的抗粗差干扰能力。该研究验证了新方法在平面拟合领域的优越性和可靠性。In order to solve the positional accuracy difference of plane data and the low calculation precision of plane model’s constant term,a robust plane fitting method based on least squares-weighted total least square(LS-WTLS)was proposed.This method uses least squares model and robust estimation of IGGⅢscheme to calculate the error parameters of plane model.Meanwhile,after rejecting the gross error data by setting the threshold,the constant term of plane model was calculated by using least square model.And based on this model,the accuracy of plane parameters was further improved.The new method shows favorable resistant to gross errors in experiments of fit the simulated plane data,meanwhile,the observed plane data fitting experiments show that compared with LS method,TLS method,LS-TLS method,IGGⅢ-LS-TLS method,the new method’s mean square error of unit weight increased by 53.6%,195.0%,47.5%,and 5.1%,respectively,and its plane fitting accuracy increased by 53.6%,195.0%,47.5%,and,5.1%,respectively.The results effectively verify this new method’s superiority and reliability in the field of plane fitting.

关 键 词：测量与计量 稳健平面拟合方法 加权总体最小二乘 稳健估计 IGGⅢ方案 

分 类 号：P207[天文地球—测绘科学与技术]