Bayesian classifier performance for realistically randomized signals

Acoustic, seismic, radio-frequency, optical, and other types of signals in complex real-world environments are randomized by processes such as multipath reflections from buildings and hills, surface scattering from rough terrain, and volume scattering by turbulence and vegetation. Bayesian classifier methods have the ability to incorporate physically realistic distributions for the random signal variations caused by these processes, and thus enable quantitative assessments of the uncertainty in the target classifications. This paper formulates a Bayesian classifier for problems involving strongly scattered signals with partially correlated features, as would be appropriate for situations involving observations of multiple signal features (e.g., spectral bands) at multiple sensor locations. In this case, the appropriate formulation of the likelihood function is a complex Wishart distribution. We simulate the classifier performance for two- and three-target problems involving multiple spectral signal features, for cases involving moderate and strong correlations between the signal features. The results illustrate the challenges of performing reliable classification based on a small number of samples of a strongly scattered signal, particularly when the target features are similar in strength. When there exist strong correlations between the feature data, full Bayesian classifiers decisively outperform naive classifiers.