Synchronization of Chaotic Communication Systems via Kalman Filtering

A general synchronization method is proposed for a class of nonlinear chaotic systems where the uncertain parameters are present, and the nonlinearities involve the transmitted signal. Under some mild conditions, it is shown that the class of nonlinear chaotic systems can be treated as linear time-varying systems, driven by the additive white noise contaminated at the receiver, or observed output. The synchronization is tackled via optimal filtering to which the results of Kalman filtering can be applied. We present some sufficient conditions under which the states of the driven system are able to track the states of the drive system asymptotically, and good tracking performance can be obtained in the presence of the additive white noise involved at the observed output.