Likelihood Ratios and Signal Detection for Nongaussian Processes.
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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The emphasis is on development of likelihood ratios and detection algorithms for problems involving nonGaussian data. The first problem considered is that of detecting a nonGaussian signal in Gaussian noise. This frequently arises in active sonar it could also be important for passive sonar. General results are presented on nonsingular detection and likelihood ratio. A recursive discrete-time detection algorithm is obtained and is shown to be a likelihood ratio detector when the signal-plus-noise is Gaussian. The second major problem considered is that of detecting a signal in spherically-invariant noise SIN. This is a model which has been proposed for some impulsive-plus-Gaussian environments, and is closely linked to detection problems encountered in some active sonar applications. General results on nonsingular detection and likelihood ratio are first obtained. For detection of a known signal, the behavior of the discrete-time likelihood ratio is analyzed as the sample size increases. Constant-false-alarm-probability detectors are given, and an example based on sonar data illustrates the potential loss due to using a Gaussian model when the noise is actually nonGaussian SIN.
- Statistics and Probability