Noise reduction in chaotic time-series data: A survey of common methods

Abstract

This paper surveys some of the methods that have been suggested for reducing noise in time-series data whose underlying dynamical behavior can be characterized as low-dimensional chaos. Although the procedures differ in details, all of them must solve three basic problems: how to reconstruct an attractor from the data, how to approximate the dynamics in various regions on the attractor, and how to adjust the observations to satisfy better the approximations to the dynamics. All current noise-reduction methods have similar limitations, but the basic problems are reasonably well understood. The methods are an important tool in the experimentalist’s repertoire for data analysis. In our view, they should be used more widely, particularly in studies of attractor dimension, Lyapunov exponents, prediction, and control.