Signal separation for nonlinear dynamical systems

The problem of signal separation for nonlinear dynamical systems, particularly chaotic systems, is considered. These systems are characterized by a stretching and folding within state space and by the presence of an attractor. Signal separation involves the separation of a received signal into two components, one of which is modeled as the output of a nonlinear dynamical system. The authors review previous approaches to this problem and present results from the application of Kalman filtering to the signal separation problem. A Cramer-Rao bound on the performance of a signal separation algorithm in white noise is presented. The special properties of nonlinear dynamical systems allow state estimation that improves exponentially with the number of observations but requires special processing techniques to achieve