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| The Measurement Uncertainty Evaluation of Linear Regression Fitting |
| XIA Yu-guo1,PENG You-zhi1,2,3 ,LIU Zheng-hua1,2,3,SONG Xiao1,ZENG Zhuo1 |
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1. Wuhan Seismic Metrological Verification & Surveying Engineering Institute, Wuhan, Hubei 430071, China
2. Key Laboratory of Earthquake Geodesy, China Earthquake Administration, Wuhan, Hubei 430071, China
3. Hubei Earthquake Agency, Wuhan, Hubei 430071, China |
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Abstract The measurement uncertainty of the least squares linear regression fitting results was evaluated by GUM method, and a general formula of standard uncertainty was proposed to estimate the influence of error of independent variable in coefficient matrix and dependent variable simultaneously. Firstly, the linear regression fitting model and least squares estimation results were described.Secondly, considering the influence of coefficient matrix, the general formulas for fitting parameters, fitting values, sensitivity coefficients on independent and dependent variables, and standard uncertainty were derived. At the same time, considering the correlation, a general formula for standard uncertainty after special treatment of variable correlation is given. Finally, the sensitivity of linear displacement sensor (without considering the correlation) and the additive multiplying constant of geodimeter (considering the correlation) were taken as examples to compare with the Monte Carlo method (MCM).The research results showed that the calculation results of the GUM method were basically consistent with the results of the MCM method.
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Received: 20 September 2022
Published: 18 April 2023
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2023, Vol. 44 
