Linear Fitting in Gas Measurement

Various calibration methods such as single-point, double-point, and linear can be used in gas composition measurements, and linear calibration can be divided into various subdivision methods such as ordinary linear least squares and weighted bivariate least squares linear fitting. In this paper, the above two methods introduced in different literatures are compared and analyzed, and the matters that should be noted in the weighted bivariate least squares linear fitting are introduced. When the uncertainty of the measured signal is already close to or even lower than the uncertainty level of the gas standard, it is more reasonable to use the weighted bivariate least squares linear fitting method to process the measurement results. When using the weighted bivariate least squares linear fit, the weights are the reciprocal of the squared standard uncertainty, and the values of the intercept and slope can be calculated using the two-step iterative method; the standard uncertainty of the intercept and slope is calculated using the numerical differentiation method. Both analytical and calibration functions can be used for weighted bivariate least squares linear fitting. For the calculation of the measured sample concentration and its uncertainty, the results obtained by using these two functions are the same, but it is easier to use the analytical function when calculating the uncertainty.