Noise in chaotic data: Diagnosis and treatment

A prominent limiting factor in the analysis of chaotic time series are measurement errors in the data. We show that this influence can be quite severe, depending on the nature of the noise, the complexity of the signal, and on the application one has in mind. Theoretical considerations yield general upper bounds on the tolerable noise level for dimension, entropy and Lyapunov estimates. We discuss methods to detect and analyze the noise present in a measured data set. We show how the situation can be improved by nonlinear noise reduction. (c) 1995 American Institute of Physics.