Early work in detection and estimation almost exclusively assumed a Gaussian model for the noise. It has long been known that many important environments exhibit non-Gaussian behavior. For example, an examination of acoustic data from the polar seas suggest that while the noise appears to be Gaussian most of the time, there are also transients and sinusoidal bursts present. Since it is generally impossible to obtain an accurate statistical characterization for the non-Gaussian portion of the noise it is not possible to design optimal detectors. This project will be concerned with the design of detectors to operate in these environments. The detectors will be based on a divide-and- conquer approach. The detectors will use the characteristics of the Gaussian component and minimal information about the impulsive component to identify the impulsive component and eliminate it. Once this has been accomplished the detector will operate on the residual data using standard detection techniques based on Gaussian statistics to determine the presence or absence of signal. The environment will be modeled as consisting of a correlated Gaussian component that is always present and an infrequently occurring impulsive component. Models for impulsive component will include single sample impulses, known transients and sinusoidal bursts (damped and undamped). The detectors considered will be analyzed using asymptotic results if possible and an approximate statistical analysis when necessary. Monte Carlo simulations will be undertaken to identify salient system features and verify analytical results. It is hoped that the detectors designed can be applied to actual arctic sea, acoustic data.
