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.
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.
XU Jin-xin,YOU Qiang. Uncertainty Calculation for Arbitrary Order Polynomial Least-square Fitting and Analysis of the Best Fitting Order. Acta Metrologica Sinica, 2020, 41(3): 388-392.
［1］BIPM,IEC,IFCC,ISO,IUPAC,IUPAP,OIML. Guide to the expression of uncertainty in measurement［S］. 1995.
［2］Krystek M, Anton M. A weighted total least-squares algorithm for fitting a straight line ［J］. Meas Sci Technol, 2007, 18: 3438-42.
［3］Willink R. Estimation and uncertainty in fitting straight lines to data: different techniques ［J］. Metrologia, 2008, 45: 290-8.
［4］Higbie J. Uncertainty in a least-square fit ［J］. Am J Phys, 1978, 46: 945.
［5］Zhu L R, Zhang Y. Uncertainty analysis in least square fitting according to next generation of GPS standard system ［C］//The 2nd IEEE Int Conf on Information Management and Engineering (ICIME). 2010, 555-9.
［6］Hibbert D B. The uncertainty of a result from a linear calibration ［J］. Analyst, 2006, 131: 1273-8.
［7］Ren M J, Cheung C F, Kong L B. A task specific uncertainty analysis method for least-squares-based form characterization of ultra-precision freeform surfaces ［J］. Meas Sci Technol., 2012, 23: 54005-14.
［8］Pennecchi F, Malengo A. A weighted total least squares algorithm for any fitting model with correlated variables ［J］. Metrologia, 2013, 50: 654.
［9］Poshusta R D. Spreadsheet error analysis of least-squares fitted models using Monte Carlo simulation［J］. Comput Phys, 1991, 5: 248-52.
［10］Cecchi G C. Error analysis of the parameters of a least-squares determined curve when both variables have uncertainties ［J］. Meas Sci Technol, 1991, 2: 1127-8.
［11］James E. On the Runge example［J］. Amer Math Monthly, 1987, 94: 329-341.
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