title: A method of estimating the noise level in a chaotic time series.
abstract: 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.
authors.affiliation: International Centre for Water Hazard and Risk Management under the auspices of UNESCO, Public Works Research Institute, Tsukuba, Japan. hrecjaw@hkucc.hku.hk
authors.forename: A W
authors.initials: AW
authors.lastname: Jayawardena
authors.forename: Pengcheng
authors.initials: P
authors.lastname: Xu
authors.forename: W K
authors.initials: WK
authors.lastname: Li
mesh_terms: D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012815:Signal Processing, Computer-Assisted; D013598:Systems Theory