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| 任意阶次多项式最小二乘拟合不确定度计算方法与最佳拟合阶次分析 | |
| 引用本文： | 许金鑫,由强. 任意阶次多项式最小二乘拟合不确定度计算方法与最佳拟合阶次分析[J]. 计量学报, 2020, 41(3): 388-392. DOI: 10.3969/j.issn.1000-1158.2020.03.23 |
| 作者姓名： | 许金鑫 由强 |
| 作者单位： | 1. 中国计量科学研究院, 北京100029 2. 清华大学 电机工程与应用电子技术系, 北京100084 |
| 摘 要： | 阐述了一种采用矩阵方程表示的任意阶次多项式最小二乘拟合的不确定度计算方法,同时通过仿真研究了该方法的特性。通过该方法,可以得到拟合不确定度最小的拟合阶次,也就是最佳的拟合阶次。仿真得到的最佳拟合阶次与仿真模型的原函数阶次都为5阶,从而验证了该方法的有效性。 |
| 关 键 词： | 计量学,不确定度 最小二乘拟合,最佳拟合阶次,多项式拟合,矩阵方程, |
Uncertainty Calculation for Arbitrary Order Polynomial Least-square Fitting and Analysis of the Best Fitting Order |
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| XU Jin-xin,YOU Qiang. Uncertainty Calculation for Arbitrary Order Polynomial Least-square Fitting and Analysis of the Best Fitting Order[J]. Acta Metrologica Sinica, 2020, 41(3): 388-392. DOI: 10.3969/j.issn.1000-1158.2020.03.23 | |
| Authors: | XU Jin-xin YOU Qiang |
| Affiliation: | 1. National Institute of Metrology, Beijing 100029, China 2. Department of Electrical Engineering, Tsinghua University, Beijing 100084, China |
| Abstract: | A matrix-calculation method for evaluating the uncertainty of the polynomial fitting data is derived and the properties of this method are studied by simulation.Based on this,the optimal fitting order can be obtained with minimum fitting uncertainty.The optimal fitting order obtained in the simulation is the same as that of the original function of the simulation model.Hence,the effectiveness of this method is verified. |
| Keywords: | metrology uncertainty ordinary least-square fitting best fitting order polynomial fit matrix equation |
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