Nonlinear observer performance in chaotic synchronization with application to secure communication

This work is on performance comparison of five different nonlinear observers in two chaotic synchronization case studies and their application to secure communications. Extended Kalman filter, state dependent Riccati equation, Thau's observer, high-gain observer, and covariance upper bound assignment techniques are used in state reconstruction of two chaotic nonlinear systems, namely Chua and Lorenz systems. We show that synchronization of chaotic systems can be effectively achieved by using any of the above techniques. However they exhibit different performances. A comparative robustness study involving performance under different measurement noise levels is also included. The above methods are then applied to introduce a method of secure communications, by chaotic masking, where the message is injected into the chaotic signal generated by Chua's circuit in the transmitter where they are simultaneously transmitted over a noisy channel to the receiver. The proposed observers are then applied in the receiver and the performances are compared based on Monte-Carlo simulations in order to demonstrate the relative effectiveness of these techniques.