Non-Gaussian and non-homogeneous Poisson models of snapping shrimp noise
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The problem of sonar detection and underwater communication in the presence of impulsive snapping shrimp noise is considered. Non-Gaussian amplitude and nonhomogeneous Poisson temporal statistical models of shrimp noise are investigated from the perspective of a single hydrophone immersed in shallow waters. New statistical models of the noise are devised and used to both challenge the superiority of existing models, and to provide alternative insights into the underlying physical processes.A heuristic amplitude statistical model of snapping shrimp noise is derived from first principles and compared with the Symmetric-α-stable model. The models are shown to have similar variability through the body of the amplitude probability density functions of real shrimp noise, however the new model is shown to have a superior fit to the extreme tails. Narrow-band detection using locally optimum detectors derived from these models show that the Symmetric-α-stable detector retains it's superiority, despite providing a poorer overall fit to the amplitude probability density functions. The results also confirm the superiority of the Symmetric-α-stable detector for detection of narrowband signals in shrimp noise from Australian waters.The temporal nature of snapping from a field of shrimp is investigated by considering the snapping as a point process in time. Point process analysis techniques are drawn from the fields of optics, neuro-physics, molecular biology, finance and computer science, and applied to the problem of snapping shrimp noise. It is concluded that the snapping is not consistent with a homogeneous Poisson process and that correlations exist in the point process on three different time scales. The cause of short time correlations is identified as surface reflected replicas, and models of medium time correlations are investigated. It is shown that a Cox-Ingersoll-Ross driven doubly-stochastic Poisson model is able to describe the medium time correlations observed from the counting process, but a k[superscript]th-order interval analysis reveals that there is more information contained within the snapping than can be described by the model. Analysis of shrimp snap times over a full day provides evidence of correlation between snap events on long time scales. Simulation of ocean noise is conducted to illustrate the use of such temporal models, and implications for their use in detection algorithms are discussed.
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