Statistical characterization of active sonar reverberation using extreme value theory

The statistics of reverberation in active sonar are characterized by non-Rayleigh distributed amplitudes in the normalized matched filter output. Unaccounted for, this property can lead to high false-alarm rates in fixed-threshold detectors. A new approach to modeling threshold-crossing statistics based on extreme value theory is proposed, which uses the generalized Pareto distribution as the unique asymptotic model of the tail distribution, valid at large thresholds. Methods of parameter estimation are discussed and applied to active sonar reverberation collected on a hull-mounted sonar system. The statistics of reverberation in active sonar are found to generally have a power-law behavior in the tails with a shape parameter that is persistent in time and bandwidth dependent. The threshold needed for accurate parameter estimation is generally found to be well below that of typical fixed-threshold detectors.