Weighted Orthogonal Distance Regression for Tire Models Parameters Identification

Determining the parameters in existing tire models (e.g. Magic Formula (MF)) for calculating longitudinal and lateral forces depending on the tire slip is often based on standard least squares techniques. This type of optimization minimizes the vertical differences in the ordinate axis between the test data and the chosen tire model. Although the practice is to use this type of optimization in adjusting those model parameters, it should be noted that this approach disregards the errors that have been committed in the measurement of tire slips. These inaccuracies in the measured data affect the optimum parameters of the model, producing non optimum models. This paper presents a methodology to improve the fitting of mathematical tire models on available test data, taking into account the vertical errors together with errors in the independent variable.