Denoising chaotic time series using an evolutionary state estimation approach

Abstract

This work presents a method for denoising chaotic time series when the structure of the underlying dynamics is known, albeit not the associated initial conditions and parameters. The strategy relies on finding the initial conditions and free parameters that minimize deviations - in the mean-squared error sense - from the noisy observations, thus providing the means to identify the original model that engenders the noise-free chaotic signal. To accomplish this purpose, an evolutionary immune-inspired approach was adopted. The reason for choosing this approach was its significant global search potential and the fact that it does not demand cost function manipulations. The proposal can be applied to general contexts, but a most promising perspective is its use in communications systems employing chaotic signals, for which the existence of knowledge about the underlying dynamics is a reasonable assumption.