Improved Assessment of Orbital Stability of Rhythmic Motion with Noise
Fig 2
Estimation of a Floquet multiplier (FM) using the Yule-Walker equation and Burg’s Method.
Time series with different length, n were generated with FM = 0.75. The FM was estimated for each time series using the Yule-Walker equation (A), and Burg’s method (B). In each case, the simulation was repeated 1000 times for each n. For both methods, the mean of the estimated FMs is always smaller than the actual FM though the discrepancy decreases as n increases. H0—the null hypothesis that the estimated orbital stability comes from a normal distribution with mean equal to the actual value—is rejected even when n = 1000. Noise drawn from normal, uniform and lognormal distributions yield similar results.