| 稳健整体最小二乘直线拟合 |
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| 引用本文： | 官云兰,周世健,张立亭,鲁铁定. 稳健整体最小二乘直线拟合[J]. 工程勘察, 2012, 0(2): 60-62 |
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| 作者姓名： | 官云兰 周世健 张立亭 鲁铁定 |
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| 作者单位： | [1]东华理工大学测绘工程学院,江西抚州344000 [2]江西省科学院,南昌330029 |
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| 基金项目： | 国家自然科学基金资助（40874010,40940011）;江西省自然科学基金（2008GQC0001,2010GZC0009,2010GZC0008）. |
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| 摘 要： | 针对常用直线拟合方法在数据存在粗差或异常值扰动时,存在拟合结果不稳定的缺点,提出一种稳健的直线拟合方法。该法以整体最小二乘法为基础,在考虑全部观测量存在误差的情况下,通过利用一定的准则删除数据中的粗差或异常值,从而获得稳健的直线参数。实验结果表明,稳健整体最小二乘直线拟合不仅考虑了全部观测值中的误差,而且能剔除数据中的粗差或异常值,精度更高,结果更为可靠。
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| 关 键 词： | 直线拟合 整体最小二乘 粗差 异常值 稳健 |
A robust method for fitting a line to point clouds based on TLS |
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| Guan Yunlan,Zhou Shijian,Zhang Liting,Lu Tieding. A robust method for fitting a line to point clouds based on TLS[J]. Geotechnical Investigation & Surveying, 2012, 0(2): 60-62 |
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| Authors: | Guan Yunlan Zhou Shijian Zhang Liting Lu Tieding |
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| Affiliation: | 1 ( 1. School of Surveying and Mapping Engineering, East China Institute of Technology, Fuzhou 344000, China; 2. Jiangxi Academy of Sciences, Nanchang 330029, China) |
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| Abstract: | In traditional line fitting methods, the gross error and outliers are not considered, and thus the results of parameters estimation are not accurate. In order to overcome this shortcoming, a robust method for line fitting was proposed. The method is based on total least squares （TLS）. In consideration of errors in all observations, by deleting outliers of point clouds according to some criteria, a robust solution to line fitting parameters is obtained. Analytical simulation experiment was conducted, and comparison between the traditional method and TLS method was also implemented. The results show that the method has the capability to overcome bad influence from outliers, and to increase the reliability of parameter estimation. |
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| Keywords: | line fitting total least squares gross error outliers robustness |
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