Background and Clutter Mixture Distributions for Active Sonar Statistics

False alarms in active sonar systems arising from physical objects in the ocean (e.g., rocks, fish, or seaweed) are often called clutter. A variety of statistical models have been proposed for representing the sonar probability of false alarm (P
_fa
) in the presence of clutter, including the log-normal, generalized-Pareto, Weibull, and
K
distributions. However, owing to the potential sparseness of the clutter echoes within the analysis window, a mixture distribution comprising one of the clutter distributions and a Rayleigh-distributed envelope (i.e., an exponentially distributed intensity) to represent diffuse background scattering and noise is proposed. Parameter-estimation techniques based on the expectation-maximization (EM) algorithm are developed for mixtures containing the aforementioned clutter distributions. While the standard EM algorithm handles the mixture containing log-normal clutter, the EM-gradient algorithm, which combines the EM algorithm with a one-step Newton optimization, is necessary for the generalized-Pareto and Weibull cases. The mixture containing
K
-distributed clutter requires development of a variant of the EM algorithm exploiting method-of-moments parameter estimation. Evaluation of three midfrequency active-sonar data examples, spanning mildly to very heavy-tailed P
_fa
, illustrates that the mixture models provide a better fit than single-component models. As might be expected, inference on clutter-source scattering based on the shape parameter of the clutter distribution is shown to be less biased using the mixture model compared with a single-component distribution when the data contain both clutter echoes and diffuse background scattering or noise.