Using McDaniel\u27s model to represent non-Rayleigh active sonar reverberation

Reverberation in active sonar systems has often been observed to follow non-Rayleigh distributions. Current statistical models tend to be either too restrictive, leading to significant mismatch error, or too general, leading to large estimation error. McDaniel\u27s model has shown promise as having reasonably tight representation in terms of skewness and kurtosis for reverberation from a variety of sonar systems. This dissertation intensively explores capability and effectiveness of the generalized McDaniel\u27s model in representing non-Rayleigh reverberation when minimal data are available. ^ Three major topics are covered in this dissertation. First, derivation and computation of the cumulative distribution function of McDaniel\u27s model is addressed. Two approaches, one based on direct integration and the other via characteristic function inversion, are both shown to achieve adequate precision with the former leading to a closed-form solution and the latter requiring significantly less computational effort. Second, parameter estimators using both method of moments (MM) and maximum likelihood (ML) algorithms are developed. The MM estimator has the advantage of a simple and rapid implementation, but the disadvantage of a non-zero probability of a solution not existing. Bootstrap/pruning techniques are proposed to partially deal with the failure of this method. The ML estimator will always provide a solution; however, it requires multivariate optimization. The expectation-maximization (EM) algorithm iteration is also derived for obtaining the ML estimates and compared with the simplex method and quasi-Newton multivariate optimization routines. Furthermore, the ability of various statistical models to represent the probability of false alarm is evaluated as a function of sample size. It is demonstrated that when minimal data are available, McDaniel\u27s model can more accurately represent non-Rayleigh reverberation than the K or Rayleigh mixture models. Third, detection performance of McDaniel\u27s model is analyzed through testing statistical hypotheses. This thesis provides a sensible approach to the derivation of a target model for McDaniel\u27s reverberation, which involves also the derivation of the non-central gamma distribution. The likelihood ratio, locally optimal and Bayes tests are developed and the receiver operating characteristic (ROC) curves are generated at different signal-to-reverberation power ratios for performance evaluation.