Discrete-Time Detection Modelling for Unsaturated Ocean Acoustic Propagation

The basic problem in ocean acoustic detection is formulated under the assumption of unsaturated sound propagation. The latter essentially amounts to a constant signal plus Gaussian noise. Detection is defined as occurring whenever ρ, the root mean square pressure at the receiver, exceeds a specified threshold level ρ₀. A two‐state, discrete‐time Markov model is derived, and closed‐form expressions for the probability mass functions of the number of time steps separating two successive detections (interarrival time) or one detection and the first subsequent ‘‘downcrossing’’ (holding time) are presented. Expressions for the joint probability density function of ρ at two different points in time are obtained and used to determine the relevant one‐step transition probabilities of the Markov model. Sample results using the model are finally presented.