One of the primary applications of higher order statistics has been for detection and estimation of nonGaussian signals in Gaussian noise of unknown covariance. This is motivated eby the fact that higher order cumulants of Gaussian processes vanish. In the present work we study the opposite problem, namely, detection and estimation in nonGaussian noise. We estimate cumulants of nonGaussian processes in the presence of unknown deterministic and/or Gaussian signals, which allows either parametric or nonparametric estimation of the covariance of the nonGaussian process via its cumulants. This in turn motivates a study of detection in colored nonGaussian noise. Our approach is to augment existing second-order detection methods using cumulants. We propose solutions for detection of deterministic signals based on matched filters and the generalized likelihood ratio test which incorporate cumulants, where the resulting solutions are valid under either detection hypothesis. This allows for single record detection and obviates the need for noise-only training records. The problem of estimating signal strength in the presence of nonGaussian noise of unknown covariance is also considered, and a cumulant-based solution is proposed which uses a single data record. Examples are used throughout to illustrate our proposed methods.
Bibliographical noteFunding Information:
Manuscript received December 13, 1992; revised February 5, 1994. This work was supported by ONR grants N00014-92-5-1086 and N00014-93-14485. . The associate editor coordinating the review of this paper and approving it for publication was Prof. Jose A. R. Fonollosa. B. M. Sadler is with the Army Research Laboratory, Adelphi, MD 20783-1197 USA. G. Giannakis is with the Department of Electrical Engineering, University of Virginia, Charlottesville. VA 22903-2442 USA. K.3. Lii is with the Department of Statistics, University of California, Riverside, CA 92502 USA. IEEE Log Number 9403737.
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