An Identification Technique for ARMA Systems in the Presence of Noise

This paper presents an approach for the identification of minimum-phase autoregressive moving average (ARMA) systems in the presence of additive noise. For the identification of the AR part of an ARMA system, unlike conventional correlation based methods, we propose to employ a once-repeated autocorrelation function (ORACF) of the observed noisy signal which is capable of reducing the effect of additive noise. The ORACF is used in a modified form of the least-squares Yule-Walker equations which provides an estimate of the AR parameters as a least-squares solution. For the identification of the MA part, the residual signal obtained by filtering the observed signal via the estimated AR polynomial is used. In order to tackle the noise in the residual signal, a noise-compensation scheme is proposed. The MA parameters are estimated by using the spectral factorization corresponding to the noise-compensated power spectrum of the residual signal. Simulation results show the superiority of performance by the proposed method in comparison to some of the existing methods at low levels of SNR.