A UNIFYING MAXIMUM-LIKELIHOOD VIEW OF CUMULANT AND POLYSPECTRAL MEASURES FOR NON-GAUSSIAN SIGNAL CLASSIFICATION AND ESTIMATION

Classification and estimation of non-Gaussian signals observed in additive Gaussian noise of unknown covariance is addressed using cumulants or polyspectra. By integrating ideas from pattern recognition and model identification, asymptotically optimum maximum-likelihood classifiers and ARMA parameter estimators are derived without knowledge of the data distribution. Identifiability of noncausal and nonminimum phase ARMA models is established using a finite number of cumulant or polyspectral lags of any order greater than two. A unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms. Tentative order determination and model validation tests for non-Gaussian ARMA processes are described briefly. Illustrative simulations are also presented.