Reconstructing nonlinear dynamics by extended Kalman filtering

We investigate the use of the extended Kalman filter as a tool for the parameter estimation of radial basis function models. We show that the method is best used as an add-on to other estimation techniques such as subset selection of the centers using a minimum description length criterion rather than as a stand-alone method. We also show that the covariance matrix returned by the extended Kalman filter can be used to calculate Rissanen's minimum description length criterion more easily. Illustrative examples are given for data from the Ikeda map and two time series of real world experimental systems.