EKF and UKF based synchronization of hyperchaotic systems

Abstract

Noise like yet deterministic behavior of chaotic systems has led the researchers to show a great interest in developing secure communication schemes based on chaotic systems. In the field of secure communication, hyperchotic systems are preferred to traditional chaotic systems because they have more complicated dynamical behavior. More recently, the focus has been on developing hyperchaotic systems with higher dimensions such as novel 5D hyperchaotic systems. Such systems offer more complicated topological structures which makes them an even better candidate in the field of secure communication. In such applications, synchronization and control of two identical chaotic systems with random initial conditions is a real challenge that too in presence of process and measurement noises. This paper presents a synchronization mechanism for novel 5D hyperchaotic systems in probabilistic state space framework. At transmitter end, a novel 5D hyperchaotic system is used as the master system which transmits some of the states as synchronization signal via additive white Gaussian noise (AWGN) channel whereas at the receiver end, two stochastic nonlinear dynamic state estimators viz. Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are employed as slave system to reconstruct the master system states using noisy synchronization signal and random initialization. Performance of both the estimators is tested and the comparative study is illustrated with numerical examples and simulation results. Analysis shows that UKF based estimator was better for meeting out synchronization requirements.