Title :
Estimation and detection in non-Gaussian noise using higher order statistics
Author :
Sadler, Brian M. ; Giannakis, Georgios B. ; Lii, Keh-Shin
Author_Institution :
Army Res. Lab., Adelphi, MD, USA
fDate :
10/1/1994 12:00:00 AM
Abstract :
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 by the fact that higher order cumulants of Gaussian processes vanish. 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 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 hypotheses. 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
Keywords :
estimation theory; filtering and prediction theory; matched filters; maximum likelihood estimation; nonparametric statistics; parameter estimation; random noise; signal detection; statistical analysis; Gaussian noise; Gaussian processes; Gaussian signals; covariance; deterministic signals; generalized likelihood ratio test; higher order cumulants; higher order statistics; matched filters; nonGaussian noise detection; nonGaussian noise estimation; nonparametric estimation; parametric estimation; second-order detection methods; signal strength; single record detection; Colored noise; Gaussian noise; Gaussian processes; Higher order statistics; Low-frequency noise; Matched filters; Signal detection; Signal processing; Testing; Working environment noise;
Journal_Title :
Signal Processing, IEEE Transactions on