A Robust Method to Estimate the Largest Lyapunov Exponent of Noisy Signals: A Revision to the Rosenstein’s Algorithm

Aim This study proposed a revision to the Rosenstein’s method of numerical calculation of largest Lyapunov exponent (LyE) to make it more robust to noise. Methods To this aim, the effect of increasing number of initial neighboring points on the LyE value was investigated and compared to the values obtained by filtering the time series. Both simulated (Lorenz and passive dynamic walker) and experimental (human walking) time series were used to calculate LyE. The number of initial neighbors used to calculate LyE for all time series was 1 (the original Rosenstein’s method), 2, 3, 4, 5, 10, 15, 20, 25, and 30 data points. Results The results demonstrated that the LyE graph reached a plateau at the 15-point neighboring condition inferring that the LyE values calculated using at least 15 neighboring points were consistent and reliable. Conclusion The proposed method could be used to calculate LyE more reliably in experimental time series acquired from biological systems where noise is omnipresent.