Observer-based Tracking and Identification of Chaotic Systems with Application to Chaotic Communication Through Noisy Channel

A novel observer for tracking and identifying a chaotic system with time-varying bifurcation parameters via an observation signal contaminated by additive white Gaussian noise (AWGN) is developed in this paper. It is realized by an adaptive algorithm which takes advantage of the good approximation capability of the Radial Basis Function (RBF) neural network and the ability of the Extended Kalman Filter (EKF) for tracking a time-varying dynamical system. It is demonstrated that, provided the bifurcation parameter varies slowly in a time window, a chaotic dynamical system can be tracked and identified continuously, and the time-varying bifurcation parameter can also be retrieved in a sub-window of time via a simple least-square-fit method. The proposed tracking and parameter retrieval method can be used in a chaotic modulation/demodulation system where a message is represented by the parameter variation and carried by a wideband chaotic signal.