Reliable methods for estimating the K - distribution shape parameter

Parameter estimation for the K distribution is an essential part of the statistical analysis of non-Rayleigh sonar reverberation or clutter for performance prediction, estimation of scattering properties, and for use in signal and information processing algorithms. Computational issues associated with maximum likelihood (ML) estimation techniques for K-distribution parameters often force the use of the method of moments (MoM). However, as often as half the time, MoM techniques will fail owing to a non-invertible equation relating the shape parameter (α) to a particular moment ratio, which is equivalent to the detection index (D) of the matched-filter envelope. In this paper, a Bayesian approach is taken in developing a MoM-based estimator for D, and therefore α, that reliably provides a solution and is less computationally demanding than the ML techniques. Analytical-approximation (AA) and bootstrap-based (BB) approaches are considered for approximating the likelihood function of D and forming a posterior mean estimator, which is compared with the standard MoM and ML techniques. Computational complexity (in the form of execution time) for the Bayes-MoM-AA estimator is on the order of the standard MoM estimator while the Bayes-MoM-BB estimator can be 1–2 orders of magnitude greater, although still less than ML techniques. Performance is seen to be better than the standard MoM approach and the ML techniques, except for very small α (< 3) where the ML techniques remain superior. Advantages of the Bayesian approach are illustrated through the use of alternative priors, the formation of Bayesian confidence intervals, and a technique for combining estimates from multiple experiments.