Threshold estimation in least-squares error functions: Application to impedance spectroscopy

Abstract

Least-squares error functions are widely used in the determination of the parameters of models of a system. When this procedure is iterative, the problem of deciding when to stop iterating arises. Usually a threshold is defined, so that when the error function falls below this value, the least-squares error procedure can be stopped and the solution is found. However, this threshold depends on the uncertainty of the measurements. In this paper, the cost function PDF (probability density function) is analyzed to obtain a closed-form expression for the estimation of this threshold, in the framework of impedance spectroscopy.