Development and analysis of echo classification using time delays

The results from an investigation of an analytically based method for determining the performance of echo classifiers are presented. In particular, the problem of classifying echo waveforms reflected from objects that are composed of multiple scatterers is considered. The time delays between the multiple echo returns from the individual scattering centers that characterize an object are investigated as features. A generic stochastic point scatterer model is developed for representing the classes of reflecting objects which are of interest. The model allows for uncertainty in prior knowledge about the exact relative location of the individual component scatterers or uncertainty in the delay measurements. A classifier decision algorithm, in the form of a general optimum Bayesian binary classification decision rule suitable for a large variety of classification problems, is derived for the case when the orientation of the reflecting object is known. The case of unknown aspect angle is addressed through the numerical implementation and analysis of two classifiers. The associated performance for all three classifiers is obtained in terms of the probability of error and tied to standard sonar equation parameters. Example binary classification problems are presented and analyzed and some general observations made. A pragmatic framework is established within which complex echo classification issues can be further examined.