Analysis of signals under compositional noise with applications to SONAR data

We consider the problem of estimation and classification of signals in presence of compositional noise, where the traditional techniques do not provide either a consistent estimator for signals or a robust distance for classification. We use a recently introduced comprehensive framework that: (1) uses a distance-based objective function for data alignment leading to a consistent estimator of signals, (2) combines the classical data and smoothness terms for signal registration in a natural fashion, obviating the need for an arbitrary relative weight, and (3) leads to warping-invariant distances between signals for robust clustering and classification. We use this framework to introduce two pairwise distances that can be used for signal classification: (1) a y-distance which is the distance between the aligned signals and (2) an x-distance, that measures the amount of warping needed to align the signals. This problem is motivated by automatic target recognition in underwater acoustic data, where the task of clustering and classifying objects using acoustic spectrum is complicated by the uncertainties in aspect angles at data collections. Small changes in the aspect angles corrupt signals in a way that amounts to compositional noise. We demonstrate the use of this framework in classification of spectral signatures in acoustic data and highlight improvements in signal classification over current methods.