Global modeling of chaotic time series with applications to signal processing
James B. Kadtke, Jeffrey S. Brush · AIP conference proceedings · 1994
Global modeling of chaotic time series involves the extraction of a set of empirical dynamical equations which describe the evolution of the signal in a reconstructed state space. Each equation models the motion of the observed data along a particular empirical degree of freedom, in contrast to the more popular local methods which construct local mapping rules that vary with position on the ‘attractor’. Although global methods have presented formidable numerical problems in the past, new approaches have recently been proposed which lead to useful results. In this paper, we present an overview of a basic global modeling scheme, as well as a number of numerical methods to improve the quality and stability of extracted models. We also outline a general approach for the use of global models for signal processing applications, and discuss ways of quantifying model quality and expected signal processing performance. Additionally, we present a number of new noise reduction and signal separation algorithms using global models, and discuss a number of outstanding problems and speculations.