Noise reduction schemes for chaotic time series

Abstract

There has recently been a great deal of interest in the development of noise reduction techniques for noisy trajectories from nonlinear dynamical systems. Particular attention has been shown to their development for use in the analysis of chaotic time series. In this paper we consider the problem in an optimisation context. This allows us to categorise some of the commonly used techniques and to compare the performance of different methods from a theoretical standpoint in order to identify some of the pitfalls that can occur with these methods. Finally this formulation enables us to propose a natural composite method that provides flexibility between speed and stability.