Prediction of Chaotic Time Series Using Bilinear Adaptive Filter

Based on the delay-coordinate reconstruction and bilinear expressions in the phase space of a chaotic system, a bilinear adaptive filter was designed to predict low-dimensional chaotic time series. Experiments conducted on two examples of low-dimensional chaotic series show that, using the bilinear adaptive filter, the prediction process converges after about 50 samples are processed and the relative prediction error is less than 0.001.