Method of Fitting a Nonlinear Function to Measurement Data, Its Uncertainty and as Example the Application in Thermistor Circuits

The paper presents a method of determining parameters and uncertainty bands of a specific non-linear function fitted to given examined measured data. One or both of the variables of this non-linear function are changed so as to linearize it. Using the linear regression method, fined are the most favorable parameters of this straight line for its adjustment to the measured values of the coordinates of points tested according to the weighted total mean square WTLS criterion. Their autocorrelation and cross-correlation coefficients as well as uncertainties estimated according to the rules of the GUM guide [1] are considered. The parameters and the uncertainty band of the non-linear function result from the parameters of this straight line and its uncertainty band. In the part 2 numerical examples of determining the parameters and uncertainty bands for the characteristic of thermistor (two methods) alone and with resistance twoport sensor are given.