Using McDaniel's model to represent non-Rayleigh reverberation

Reverberation in low-frequency active sonar systems operating in shallow wa ter has often been observed to follow non-Rayleigh statistical distribution s. McDaniel's model, generalized to allow noninteger valued parameters, has shown promise as being capable of accurately representing real data with a minimal parameterization. This paper first derives an exact analytical exp ression for the cumulative distribution function (CDF) of the generalized M cDaniel model and then compares it with numerical inversion of the characte ristic function. Both methods are seen to provide adequate and equivalent p recision; however, the characteristic function inversion method is signific antly faster. The latter CDF evaluation technique is then applied to the an alysis of simulated and real data to show that, when minimal data are avail able, McDaniel's model can more accurately represent a wide variety of non- Rayleigh reverberation than the K or Rayleigh mixture models. This result a rises from the generality of McDaniel's model with respect to the K-distrib ution (i.e., the K-distribution P-fa estimate can be dominated by model mis match error) and to its compact parameterization with respect to the Raylei gh mixture (i.e., the Rayleigh mixture model P-fa estimate is usually domin ated by parameter estimation error).