Robust parameter estimation of chaotic systems

Abstract

Reliable estimation of parameters of chaotic dynamical systems is a long standing problem important in numerous applications. We present a robust method for parameter estimation and uncertainty quantification that requires neither the knowledge of initial values for the system nor good guesses for the unknown model parameters. The method uses a new distance concept recently introduced to characterize the variability of chaotic dynamical systems. We apply it to cases where more traditional methods, such as those based on state space filtering, are no more applicable. Indeed, the approach combines concepts from chaos theory, optimization and statistics in a way that enables solving problems considered as ‘intractable and unsolved’ in prior literature. We illustrate the results with a large number of chaotic test cases, and extend the method in ways that increase the accuracy of the estimation results.