On some detection and estimation problems in heavy-tailed noise

  • Authors:

  • Ananthram Swami;Brian M. Sadler

  • Affiliations:

  • Army Research Laboratory, Adelphi, MD;Army Research Laboratory, Adelphi, MD

  • Venue:
  • Signal Processing - Signal processing with heavy-tailed models
  • Year:
  • 2002

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Abstract

We consider the problem of estimating the parameters of a linear process with stable innovations; the linear system may be non-causal and have mixed-phase (i.e., poles and/or zeros may be inside or outside the unit circle). We show that self-normalized fourth-order moments exist, can be consistently estimated, and lead to consistent estimates of the ARMA model parameters. In the context of estimating the parameters of finite variance (or deterministic) signals observed in alpha-stable noise, we show that conventional correlation-based schemes can be used provided that the noisy data have been pre-processed by passing them through a generic zero-memory non-linearity which serves to clip the noise. We demonstrate this through applications to harmonic retrieval and direction of arrival estimation. The idea is also seen to be useful in estimating the underlying correlation matrix of a sub-Gaussian stable process. These pre-processing ideas are also shown to be useful in the context of detection and classification, and to outperform standard approaches. Numerical results related to the Fisher information and Cramer-Rao bounds are also presented.