Novel Method of Fitting a Nonlinear Function to Data of Measurement Based on Linearization by Change Variables, Examples and Uncertainty

Abstract

This paper presents a novel method for determining parameters and uncertainty bands of nonlinear functions fitted to data obtained from measurements. In this procedure, one or two new variables are implemented to linearize this function for using the linear regression method. The best parameters of the straight-line in new variables are adjusted to the transformed coordinates of tested points according to the weighted total mean square criterion WTLS, or WTLS-C of data points are also correlated. Uncertainties of measured points are found according to the rules of the GUM Guide. The parameters and the uncertainty band of the nonlinear function result from the parameters of this straight line and of its uncertainty band. A few examples determining the parameters and uncertainty bands of different types of nonlinear functions are presented. There are also examples of measurements using the presented method and conclusions.

Keywords

• linear regression of nonlinear functions
• fit to data of measured points
• WTLS weighted total least squares criterium
• correlation
• covariance matrix
• band of uncertainty