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 noninvertible 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 a, 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.