Application of risk-sensitive optimal filtering equations to excitable noise system

In this work the risk-sensitive optimal filtering equations for systems of third grade with linear observations and mean square cost criterion to be minimized had been applied to the Fitz Hugh-Nagumo model. This special model represents a excitable system. The performance of the obtained risk-sensitive estimator for third degree stochastic systems with polynomial linear drift terms with polynomial observations equations is verified, comparing the mean-square criteria values in final time for the optimal risk-sensitive estimator and polynomial filtering equations. The goal of this work is to experiment applying both filtering equations: risk-sensitive and polynomial to third degree polynomial systems, comparing the results obtained in this special model. It is observed that when the value of D is greater than 1, the risk-sensitive equations present a singularity. However, the estimates are better than the polynomial filtering equations with respect to the values of the proposed mean square cost criterion to be minimized.