An efficient approach for computing non-Gaussian ARMA model coefficients using Pisarenko's method

Abstract

This paper addresses the problem of estimating the coefficients of a general autoregressive moving average (ARMA) model from only third order cumulants (TOCs) of the noisy observations of the system output. The observed signal may be corrupted by additive coloured Gaussian noise. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian sequence. The input is not observed. The unknown model coefficients are obtained using eigenvalue–eigenvector decomposition. The derivation of this procedure is an extension of Pisarenko harmonic autocorrelation-based (PHA) method to third order statistics. It will be shown that the desired ARMA coefficients vector corresponds to the eigenvector associated with the minimum eigenvalue of a data covariance matrix of TOCs. The proposed method is also compared with well-known algorithms as well as with the PHA method. Copyright © 2005 John Wiley & Sons, Ltd.