On some detection and estimation problems in heavy-tailed noise
Signal Processing - Signal processing with heavy-tailed models
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We consider detection and estimation in correlated impulsive noise. The non-Gaussian impulsive noise is modeled as the sum of two linear processes: a nominal part and an impulsive part. This model admits correlated impulsive bursts lasting many data samples. Identifiability of the noise model is established using fourth- and second-order cumulants. Under this model, the correlated time series can be whitened and an appropriate memoryless nonlinearity applied to attenuate the impulsive events. A detection statistic is then formed from the output of the nonlinearity. In the threshold detection case, the use of cumulants allows identification of the noise in the presence of the signal to be detected, obviating the need for noise-only training records. Simulation results with a sample size of 512 show small loss in detector performance versus an ideal detector with no impulsive part present