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We show how direct estimation of delay differential equations can be used for time series analysis of observed signals corrupted by noise. The specific application we discuss is to detection (identifying the presence of a deterministic signal) and classification (assignment of a particular signal to a known class). These ideas have potentially widespread application to areas such as remote sensing, voice recognition and image processing.

In Part I of this paper, we described a numerical method for nonlinear signal detection and classification which made use of techniques borrowed from dynamical systems theory. Here in Part II of the paper, we will describe an example of data analysis using this method, for data consisting of open ocean acoustic (SONAR) recordings of marine mammal transients, supplied from NUWC sources. The purpose here is two‐fold: first to give a more operational description of the technique and provide rules‐of‐thumb for parameter choices; and second to discuss some new issues raised by the analysis of non‐ideal (real‐world) data sets. The particular data set considered here is quite non‐stationary, relatively noisy, is not clearly localized in the background, and as such provides a difficult challenge for most detection/classification schemes.

Detection and classification of signals is 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 (negative SNR), and argue 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. transients) using non‐autonomous ODEs. In Part II of this paper, we demonstrate the analysis on actual open ocean acoustic data from marine biologics.