Classifying Complex, Deterministic Signals

Abstract

When attempting to analyze, model, or predict time series, one often finds that the data is so complex or noisy that the presence or location of a desired signal or signals is unknown. Therefore, the first step in such an analysis is often to implement some scheme for detecting or classifying signals in otherwise long stretches of noisy background. Detection/classification of signals is thus one of the principal areas of signal processing, and the utilization of nonlinear information has long been considered as a way of improving performance beyond standard linear (e.g., spectral) techniques. Here, we develop a method for using global models of chaotic dynamical systems theory to define a signal classification processing chain which is sensitive to nonlinear correlations in the data. We use it to demonstrate classification in high noise regimes, using short data segments which mimic real-world processing restrictions, and also show that classification probabilities can be directly computed from ensemble statistics in the model coefficient space. We also develop a modification for non-stationary signals (i.e. pulses) using non-autonomous ODEs. Finally, we demonstrate the technique by analyzing actual open ocean acoustic data from marine biological sources such as whales and dolphins.