I am quite interested to know the significance of using kalman filter,unscented kalman filter and extended kalman filter in chaos synchronization when infact the very basics of chaos synchronization(physics perspective) never mentions about using kalman filter!However, these papers KF1 and alike use kalman filter for synchronization. There are various methods of chaos synchronization viz generalized, phase, projective, adaptive Boccaletti_Kurths et al and wikipedia considered to be the bible in thi field, do not mention about using kalman filtering and alike methods. Would be obliged if the role of this technique is explained since I think I am missing on important theory. Thank you
Kalman filters are useful if one is dealing with noisy systems, when one either has no knowledge about the source of the noise or the noise is created by a high-dimensional nonlinear system with many positive Lyapunov exponents.
Chaos synchronization is dealing with small low-dimensional systems which usually posses only one or two positive Lyapunov exponents. Applying a Kalman filter does not make much sense, since many better suited methods exist to deal with such systems, as one knows, that the system is not a stochastic one.