The report contains an analysis of an active sonar detection model. A k-out-of-n positive signal excess criterion determines echo detection. The analysis is based on encounter simulations in which signal excess fluctuations are described by either a Gauss-Markov process or a lambda-sigma jump process. For both processes, encounter probability estimates generated by the simulations suggest that the probability of detection during an encounter is maximum when the relaxation time for the process is in the neighborhood of the time required to generate k consecutive pings given the time between pings remains constant. Keywords: Active sonar detection models; Signal excess fluctuation models. (RH)