Solving the sonar equations with fluctuating signals in noise

Fluctuations of signals and noise are commonplace in sonar and have profound effects on the detectability of sonar targets. In this paper, "transition curves", giving probability of detection vs "signal excess", are derived for three theoretical fluctuation models and their use in making sonar performance predictions by means of the sonar equations is described. Some detection results from fleet exercises are presented. They seem to show that the handy and oft-assumed log-normal fluctuation model, with a σ of 6 to 8 dB, provides as good a fit as any to the sparse and scattered field data.