Computationally enabled alternatives to Gaussian classification and tracking—A survey.
John R. Sacha · The Journal of the Acoustical Society of America · 2010
The normal distribution is a good model of physical phenomena in numerous situations where central limit theorem effects come into play. It has a prominent place historically because the many special properties of the Gaussian PDF often yield mathematically elegant closed-form solutions to problems. This role was especially important when numeric calculation was expensive. Normality is not a valid assumption in many applications of modern acoustical signal processing, perhaps especially involving classification and tracking. For pattern recognition, Gaussian classifiers are a straightforward methodology requiring mean and covariance estimates of the class distributions. However, in many cases, feature PDFs themselves are not multivariate-Gaussian; even if they are, estimating parameters in large feature spaces with limited data is difficult. In tracking, the Kalman filter is the canonical formulation, but it requires normally distributed process noise and measurement errors. The advent of cheap computation power has made practical a host of alternative models. In classification, this includes empirical PDF estimation via binning, fuzzy logic, neural nets, support vector machines, featureless classification, Bayesian belief nets, and decision trees. For tracking, particle filters are used to model densities as clouds of point estimates; although computationally expensive, they admit arbitrary densities and are amenable to parallel implementation. [Portions of this work were sponsored by ONR.]