抗差最小二乘法在水准网平差中的应用  

Application of Robust Least Squares Method on Leveling Network Adjustment

作　　者：叶林 王文佩 王奉林 李帅 郭力娜 YE Lin;WANG Wen-pei;WANG Feng-lin;LI Shuai;GUO Li-na(College of Mining Engineering, North China University of Science and Technology, Tangshan Hebei 063210, China)

机构地区：[1]华北理工大学矿业工程学院

出　　处：《华北理工大学学报（自然科学版）》2019年第3期41-46,共6页Journal of North China University of Science and Technology：Natural Science Edition

基　　金：数字唐山地理空间框架基础数据建库(20180120)

摘　　要：因最小二乘法的平差结果具有最优线性和无偏性,故水准网平差计算时多采用最小二乘法,当数据中存在粗差时,平差精度降低,结果失实。稳健估计通常用于消除或减弱观测值中的粗差,提高计算精度,又因不同稳健估计方法的稳健性不同,该项目使用经典的最小二乘法与几种常见的稳健估计方法分别对水准网数据进行平差处理,并对几种稳健估计方法的抗差效果进行分析。结果表明,在数据含有粗差的情况下稳健估计方法优于最小二乘法,Danish法较其它几种稳健估计方法抗差性更好,能有效地消除或减弱粗差对水准网平差带来的影响。Because the adjustment result of the least square method has the best linearity and unbiasedness, the least square method is often used in the calculation of the leveling network. When there are errors difference in the data, the adjustment accuracy is reduced and the result is inaccurate. Robust estimation was usually used to eliminate or weaken the error in the observations, to improve the calculation accuracy, and because of the different robustness of the different robust estimation methods, compared the classical least squares method with several common robust estimation methods to process the leveling network data, and the robust effects of several robust estimation methods was also compared and analyzed. The results show that the robust estimation method is much better than the least squares method when the data contains errors. Compared with several other robust estimation methods, the Danish method has better resistance and can effectively eliminate or reduce the influence of error on the leveling network adjustment.

关 键 词：稳健估计 水准网 方法比较 选权迭代法 

分 类 号：P207.2[天文地球—测绘科学与技术]