ABSTRACT
Chaotic signals are those produced by nonlinear state mappings defined by a set of differential or difference equations that exhibit some particular characteristics such as strong dependence to initial conditions, aperiodicity, and broadband spectrum. In communication systems based on chaotic synchronization of two systems, it is well known that when additive noise is present on the link between master and slave, the sensitive dependence on initial conditions that characterizes chaotic signals amplifies this error and synchronization is no longer obtained. When the time series being analyzed is produced by a system whose underlying behavior can be characterized as low-dimensional chaos, denoising should be understood as reconstructing the trajectory of the dynamical system from noisy observations, which is, essentially, a state estimation problem. The Kalman filter is a widely known state-space estimator that provides recursive minimum mean-squared error estimates for linear systems embedded in Gaussian noise.
