Application of the Extended Kalman Filter for Reconstructing Systems from Chaotic Numerical Time Series

Many hydro-meteorological time series possess chaotic characteristics. In order to study models which can represent this chaotic behavior and their predictability, chaotic time series were generated by the Rossler equations and the parameters of given system models were evaluated by using the Extended Kalman Filter. First, in order to verify the proposed approach, the original structure of the Rossler equations was used as system model. Second, the possibility of reconstructing the system was studied. The results indicate that when a proper system model is given, the Extended Kalman Filter can efficiently evaluate the system parameters from a numerical time series, even when the time series is chaotic.