Improved Noise Reduction Method for Chaotic Time Series Using Neural Network and Singular Spectrum Analysis

An improved method for noise reduction from a time series obtained from a chaotic system is presented. This improved method is based on a noise reduction technique presented by Schreiber and Grassberger that has good performance and less complexity compared to other noise reduction methods from chaotic data. Here a global model created using a neural network has been used as a prediction model for chaotic time series. This global prediction model performs better compared to the local prediction model used in the original method. The improved method also takes advantage of the singular spectrum analysis reconstruction technique. Both of these improvements led to a more accurate noise reduction method while preserving the unique properties of the original. The improved method is applied to a time series obtained from the chaotic state of Lorenz equations that is polluted with Gaussian noise. The final results show a 33 percent reduction in mean absolute error values compared to the original method. Also, the error of calculating the correlation dimension from the data has been reduced to 2 percent after applying the improved method.