Parameter Estimation of the FitzHugh–Nagumo Neuron Model Using Integrals Over Finite Time Periods

Abstract

This paper proposes two methodologies for estimating the parameters of the FitzHugh–Nagumo (FHN) neuron model. The identification procedures use only measurements of the membrane potential. The first technique is named the identification method based on integrals and wavelets (IMIW), which combines a parameterization based on integrals over finite time periods and a wavelet denoising technique for removing the measurement noise. The second technique, termed as the identification method based only on integrals (IMOI), does not use any wavelet denoising technique and attenuates the measurement noise by integrating the IMIW parameterization two times more over finite time periods. Both procedures use the least squares algorithm for estimating the FHN parameters. Integrating the FHN model over finite time periods allows eliminating the unmeasurable recovery variable of this model, thus obtaining a parameterization based on integrals of the measurable membrane potential variable. Unlike an identification technique recently published, the proposed methods do not rely on the time derivatives of the membrane potential and are not limited to continuously differentiable input current stimulus. Numerical simulations show that both the IMIW and IMOI have a good and a similar performance, however, the implementation of the latter is simpler than the implementation of the former.