An approach to ARMA system identification at a very low signal-to-noise ratio

A new approach for the identification of minimum-phase autoregressive moving average (ARMA) systems in the presence of heavy noise is presented in this paper. A damped sinusoidal (DS) model for the autocorrelation function of a noise-free ARMA signal is proposed to estimate the AR parameters, which overcomes the failure of conventional correlation based techniques in estimating the AR parameters of an ARMA system at a very low signal-to-noise ratio (SNR). The MA parameters of the ARMA system are then estimated by using Durbin´s method along with an optimum order selection criterion. Both white noise and periodic impulse train excitations are considered for the application of the proposed method to system identification as well as to speech processing. Computer simulations are carried out based on both synthetic ARMA systems and natural speech signals, showing superior identification results even at an SNR of -5 dB for which most of the existing methods would fail.