A general synchronization method is proposed for a class of nonlinear chaotic systems involving uncertain parameters and nonlinear transmitted signals. Under some mild conditions, it shows 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 the observed output. Synchronization can be achieved by using Kalman filtering technology. 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 in the observed output.
The paper presents new methodology how to find and estimate the main features of time series to achieve the reduction of their components (dimensionality reduction) and so to provide the compression of information contained in it under keeping the selected features invariant. The presented compression algorithm is based on estimation of truncated time series components in such a way that the spectrum functions of both original and truncated time series are sufficiently close together. In the end, the set of examples is shown to demonstrate the algorithm performance and to indicate the applications of the presented methodology.