Cost Function Based on Gaussian Mixture Model for Parameter Estimation of a Chaotic Circuit with a Hidden Attractor

Abstract

In this paper, we introduce a new chaotic system and its corresponding circuit. This system has a special property of having a hidden attractor. Systems with hidden attractors are newly introduced and barely investigated. Conventional methods for parameter estimation in models of these systems have some limitations caused by sensitivity to initial conditions. We use a geometry-based cost function to overcome those limitations by building a statistical model on the distribution of the real system attractor in state space. This cost function is defined by the use of a likelihood score in a Gaussian Mixture Model (GMM) which is fitted to the observed attractor generated by the real system in state space. Using that learned GMM, a similarity score can be defined by the computed likelihood score of the model time series. The results show the adequacy of the proposed cost function.