Robust fitting of the Cole-Cole permittivity equation

Several problems in engineering and applied sciences require the parameters optimal determination. An example of such problems is the fitting of a Cole-Cole theoretical curve to experimental measurements of the relative permittivity in a biological media. Fitting such curves requires a high level of accuracy to determine the values of its parameters (the so-called Cole-Cole parameters). In this work, a set of algorithms is developed aimed at obtaining the optimal fitting of the Cole-Cole equation for the relative permittivity. The algorithms are implemented in such a way, to achieve a robust fitting, and to reach a relative error suitable for the Cole-Cole parameters, especially for those parameters whose numerical value was decisive for the applications of this equation. The set of algorithms is applied to the fitting of synthetic curves with different noise levels. Then the relative error of the fitted parameters is analysed, compared to that of the reference parameters.