Expectation Maximization Based FitzHugh-Nagumo Model Identification Under Unknown Gaussian Measurement Noise

This paper applies a new expectation maximization (EM) based identification method to estimate a generic FitzHugh-Nagumo (FHN) model under unknown Gaussian measurement noise. It is well noted that such FHN model is an elementary neuronal dynamics description and plays a significant role in deep understanding and basic analysis for complicated mechanisms of some neural diseases. Different from the most existing relevant identification methods, the applied new method is additionally capable of supplying users with variance estimation for the unknown measurement noise corrupting on the membrane potential apart from model parameter estimates. All unknown parameters can be iteratively estimated by a particle smoothing based EM algorithm, which consists of an expectation (E) step and a maximization (M) step. Smoothed joint-state particles are produced by a new particle smoothing algorithm to evaluate an expectation of a log-likelihood function in the E step, and the model parameters and noise variance can then be efficiently optimized by the gradient based methods in the M step. The resulting estimations own global convergence for a relatively wide range of parameter initializations. Finally, good convergence behaviors of the estimated model parameters and noise variance are demonstrated by a numerical simulation for a classic FHN model by using 10 simulation realizations with random initializations varying within +/- 100% of their respective true values.