Classification of signals in spherically invariant random clutter

Abstract

The generalized likelihood ratio test (GLRT) is derived for the case of a signal subspace in acoustic clutter characterized by a spherically invariant random variable (SIRV). This result is a generalization of two previous results. First, the GLRT for the detection of a one dimensional signal in SIRV clutter has been previously given. However, featureless classification work has previously considered signals that are members of a multidimensional subspace but only in Gaussian clutter. The SIRV model extends that to the non-Gaussian clutter case. A SIRV is the product of two random variables: a non-Gaussian scalar times a complex multivariate Gaussian vector. The general GLRT result is then applied to a generalized gamma distribution for the SIRV scalar. When the generalized gamma exponent parameter is −2 this produces a product SIRV whose acoustic intensity has a generalized Pareto distribution. When the exponent parameter is + 2, the SIRV intensity is k distributed. This demonstrates that two widely used clutter distribution models are special cases of this more general distribution. Methods of parameter estimation for application of the technique are also given. [Work supported by the Office of Naval Research.]