Modeling non-Rayleigh reverberation

Abstract

Researchers over the past three decades have experimentally examined non-Rayleigh reverberation,

fitted it to standard distributions such as log-normal and Weibull, developed theoretical models to

explain the variation from Rayleigh, and considered new families of distributions appropriate for

modeling non-Rayleigh reverberation such as the K and Rayleigh mixture. This report draws together

several of the common statistical models for non-Rayleigh reverberation. Parameter estimates for the Edgeworth expansion, log-normal, Weibull, K, and Rayleigh mixture distributions are presented and evaluated through simulation. Their ability to represent reverberation is examined using the Kolmogorov-Smirnov statistic where it was seen that the Rayleigh mixture provided the most flexibility in representing different types of non-Rayleigh reverberation. In analyzing real reverberation data, a skewness-kurtosis plane is proposed for the initial evaluation of the non-Rayleigh character providing

an indication of the viability of each model. The Kolmogorov-Smirnov statistic, or some other appropriate error measure, may then be used to choose the model with the best fit to the observed reverberation. This method is demonstrated on low-frequency active sonar data where the Rayleigh mixture was seen to provide the best fit. Theoretical receiver operating characteristic (ROC) curves are then generated using the estimated Rayleigh mixture proportions and powers and a nonfluctuating target model. The expected loss in detection performance due to the heavier tails of the non-Rayleigh reverberation was clearly observed.