Robust fitting of the Cole-Cole permittivity equation
Since there are several applications of Electrical Bioimpedance (EBI) that use the Cole parameters as base of the analysis, to fit EBI measured data onto the Cole equation is a very common practice within Multifrequency-EBI and spectroscopy. The aim of this paper is to compare different fitting methods for EBI data in order to evaluate their suitability to fit the Cole equation and estimate the Cole parameters. Three of the studied fittings are based on the use of Non-Linear Least Squares on the Cole model, one using the real part only, a second using the imaginary part and the third using the complex impedance. Furthermore, a novel fitting method done on the Impedance plane, without using any frequency information has been implemented and included in the comparison. Results show that the four methods perform relatively well but the best fitting in terms of Standard Error of Estimate is the fitting obtained from the resistance only. The results support the possibility of measuring only the resistive part of the bioimpedance to accurately fit Cole equation and estimate the Cole parameters, with entailed advantages.