K-Rayleigh mixture model for sparse active sonar clutter

The mixture of a Rayleigh probability density function (PDF) and a K PDF is proposed for representing active sonar data comprising clutter sparsely observed in a Rayleigh-distributed background. While both the Rayleigh and K distributions have been shown to accurately represent the statistics of certain types of active sonar data, it is common to observe data containing both echoes from distinct clutter objects and more diffuse, Rayleigh-distributed reverberation. While the K distribution can often still capture the behavior of such data, the K-Rayleigh mixture is seen to provide improved PDF fits and inference on the clutter statistics. A parameter estimation algorithm for the K-Rayleigh mixture PDF based on the expectation-maximization (EM) technique is proposed and shown to provide adequate performance in representing the PDF of very heavy tailed real sonar data.