Rayleigh-non-Rayleigh mixtures for active sonar clutter.
Douglas A. Abraham, James M. Gelb, Andrew W. Oldag · The Journal of the Acoustical Society of America · 2010
False alarms in active sonar systems commonly come from natural and man-made inhomogeneities in the ocean environment. For example, fish, mud-volcanoes, rock outcrops, and ship-wrecks can all cause target-like false alarms called clutter. The sparse nature of the physical sources of clutter can lead to data most appropriately represented statistically as a mixture of two probability distribution functions (PDFs). The Rayleigh PDF is a natural choice for the background scattering, while there are many options to represent the clutter-source scattering. Expectation-maximization (EM) based algorithms are presented to estimate parameters for a Rayleigh-distributed background mixed with log-normal, generalized Pareto, Weibull, or K PDFs representing the clutter. The EM algorithm requires maximization of a weighted log-likelihood function, similar to maximum-likelihood parameter estimation. While the log-normal distribution yields closed-form estimates, the other PDFs do not. Thus, an EM-gradient algorithm is implemented for the generalized-Pareto and Weibull PDFs, while a method-of-moments algorithm is necessary for the K. Application of the estimation algorithm on real data ranging from near-Rayleigh to very-heavy-tailed illustrates the various models’ efficacy. [Work sponsored by ONR under Contract nos. N00014-09-C-0318 and N00014-06-G-0218-34.]