An Identification Technique for Noisy ARMA Systems in Correlation Domain

In this paper, an identification technique for the minimum-phase autoregressive moving average (ARMA) systems using only the noise-corrupted observations is presented. In order to obtain a more accurate estimate of the AR parameters in the noisy environment, a repeated autocorrelation function (RACF) of the observed data is employed in the modified least-squares Yule-Walker equations. It has been found that at a very low signal-to-noise ratio (SNR), the effect of the additive noise can be significantly reduced if a twice-RACF is employed instead of the conventional ACF. Prior to the MA part identification, a noise-compensation scheme is proposed which operates on the noise-contaminated residual signal. The MA parameters are extracted from the noise-compensated power spectrum of the residual signal using the spectral factorization. ARMA systems of different orders and some natural speech signals are tested and computer simulations demonstrate a superior identification results even at a very low SNR.