Unscented Kalman Filter and Particle Filter for Chaotic Synchronization

The first and foremost step in developing a chaotic communication system is to establish synchronization of the chaotic systems/maps at the transmitter and receiver. Extended Kalman filter (EKF) is a widely studied nonlinear observer for chaotic synchronization. Since this scheme depends on the first order Taylor series approximation of the nonlinear function, it may introduce large errors in the state estimates causing the trajectories to diverge and eventually resulting in desynchronization. This has adverse effect especially when synchronizing chaotic maps with non-hyperbolic chaotic attractors (NCA). To overcome this behaviour, the unscented Kalman filter (UKF) and particle filter (PF) are proposed and studied for synchronizing chaotic systems/maps. The Lorenz and Mackey-Glass (MG) systems as well as the Ikeda map (IM) are considered for the numerical evaluation. The normalized mean square error (NMSE), total normalized mean square error (TNMSE), and normalized instantaneous square error (NISE) are computed numerically for performance evaluation