Decoding chaotic secure communication system with extended Kalman filter based observers

This paper presents two methods to codec exact messages with an expended matrix representation of linear multivariable systems whose parameters are used to describe three-port chaotic secure communications networks. The matrix representation includes an optimal extended Kalman filter based observer, which is in linearization with time. The observer and its input can be regarded as a transmitting agent; several messages are received from them. First, the optimal linearization technique is used to find the exact linear models of the chaotic system at operating states of interest. Then, an extended Kalman filter (EKF) algorithm is used to estimate both the parameters and states where the message is already embedded. By using the EKF together with the optimal linear model, the message can be adequately recovered at the receiver´s end. Numerical examples and simulation results demonstrate the effectiveness of the proposed methodology.