Identification of autoregressive moving average systems based on noise compensation in the correlation domain

This study presents a new scheme for the identification of minimum-phase autoregressive moving average (ARMA) systems from noise-corrupted observations. From the autocorrelation function (ACF) of the observed data, exploiting the characteristics of the zero lag, the authors develop a set of equations containing the lower lags of the ACF and solve the corresponding quadratic eigenvalue problem in order to estimate simultaneously the AR parameters and the observation noise variance. In the proposed identification technique, both the white noise and the periodic impulse-train excitations are considered for the purpose of practical applications. In order to estimate the MA parameters, first, a residual signal is obtained by filtering the noisy observations via the estimated AR parameters. A noise-subtraction algorithm is proposed utilising the estimated noise variance and the AR parameters to reduce the effect of noise from the ACF of the residual signal. The MA parameters are then estimated by using the spectral factorisation corresponding to the noise-compensated ACF of the residual signal. In order to demonstrate the effectiveness of the proposed method, extensive experimentations are performed considering synthetic ARMA systems of different orders in the presence of noise and results are compared with those of some of the existing methods. Computer simulations demonstrate a superior identification results in terms of estimation accuracy and consistency even under heavy noisy conditions. Simulation results are also provided for the identification of a human vocal-tract system using natural speech signals showing a superior performance of the proposed technique in terms of the power spectral density of the synthesised speech signal.