Jayawardena A W, Xu Pengcheng, Li W K
International Centre for Water Hazard and Risk Management under the auspices of UNESCO, Public Works Research Institute, Tsukuba, Japan.
Chaos. 2008 Jun;18(2):023115. doi: 10.1063/1.2903757.
An attempt is made in this study to estimate the noise level present in a chaotic time series. This is achieved by employing a linear least-squares method that is based on the correlation integral form obtained by Diks in 1999. The effectiveness of the method is demonstrated using five artificial chaotic time series, the Henon map, the Lorenz equation, the Duffing equation, the Rossler equation and the Chua's circuit whose dynamical characteristics are known a priori. Different levels of noise are added to the artificial chaotic time series and the estimated results indicate good performance of the proposed method. Finally, the proposed method is applied to estimate the noise level present in some real world data sets.
本研究尝试估计混沌时间序列中存在的噪声水平。这是通过采用一种线性最小二乘法来实现的，该方法基于迪克斯在1999年获得的相关积分形式。使用五个已知先验动力学特征的人工混沌时间序列（即亨农映射、洛伦兹方程、杜芬方程、罗斯勒方程和蔡氏电路）来证明该方法的有效性。向人工混沌时间序列中添加不同水平的噪声，估计结果表明所提出的方法具有良好的性能。最后，将所提出的方法应用于估计一些实际数据集里存在的噪声水平。
