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

AimThis study proposed a revision to the Rosensteins method of numerical calculation of largest Lyapunov exponent (LyE) to make it more robust to noise.\n\nMethodsTo 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 Rosensteins method), 2, 3, 4, 5, 10, 15, 20, 25, and 30 data points.\n\nResultsThe 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.\n\nConclusionThe proposed method could be used to calculate LyE more reliably in experimental time series acquired from biological systems where noise is omnipresent.