| 正交最小二乘曲线拟合法 |
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| 引用本文： | 丁克良,欧吉坤,赵春梅.正交最小二乘曲线拟合法[J].测绘科学,2007,32(3):18-19,17. |
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| 作者姓名： | 丁克良 欧吉坤 赵春梅 |
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| 作者单位： | 北京建筑工程学院,测绘和城市信息学院,测绘工程系,北京,100044;中国科学院测量与地球物理研究所,武汉,430077;中国测绘科学研究院,大地测量与地球动力学研究所,北京,100039 |
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| 基金项目： | 国家自然科学基金项目(40504003) |
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| 摘 要： | 在最小二乘曲线拟合中,自变量的误差常常被略而不计,提出采用正交最小二乘法拟合曲线。该方法以正交距离残差平方和极小为准则,同时顾及了因变量和自变量的误差;基于间接平差原理详细推导了相关模型和算法。实际计算表明,采用正交最小二乘法拟合曲线,拟合效果整体上优于普通最小二乘法。
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| 关 键 词： | 最小二乘 曲线拟合 正交最小二乘 精度评定 |
| 文章编号： | 1009-2307（2007）03-0018-03 |
| 修稿时间： | 2006-11-07 |
Methods of the least- squares orthogonal distance fitting |
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| DING Ke-liang,OU Ji-kun,ZHAO Chun-mei.Methods of the least- squares orthogonal distance fitting[J].Science of Surveying and Mapping,2007,32(3):18-19,17. |
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| Authors: | DING Ke-liang OU Ji-kun ZHAO Chun-mei |
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| Abstract: | For curve fitting, the errors of independent variable are usually ignored. In this paper, the model of Least-Squares orthogonal distance fitting of curves is presented, whose criterion is to minimize the square sum of the orthogonal distance, and the errors of independent variable and dependent variable are considered at the same time. The arithmetic is derived in detail based on indirect adjustment. The results of experiments show that the effect of the Least-Squares orthogonal distance fitting is better than that of ordinary least squares curve fitting on the whole. |
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| Keywords: | ordinary least squares curve fitting least-squares orthogonal distance fitting accuracy |
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