Threshold Estimation for Least-Squares Fitting in Impedance Spectroscopy

Abstract

The estimation of circuit component values in impedance spectroscopy applications usually requires the minimization of a least-squares cost function. Independently of the minimization method used, a threshold value should be used as a stopping criteria for the iterative minimization procedure. This paper presents a new estimator for the threshold value to be used in least-squares minimization problems applied to electrical circuit impedance component values estimation. The new estimator is an improvement of a previous work that is more general as it can take into account different measurement system uncertainties for each measured value. Comparison between the threshold obtained with constant uncertainties and with varying uncertainties is presented to show the usefulness of this new method. Simulated impedance responses are used to validate the method, which is further confirmed using measurement results. The effects of correctly choosing a threshold in the fitting of a circuit impedance response to a set of measurements is presented by analyzing the convergence properties and the uncertainties of the estimated component values.