An algorithm for the identification of autoregressive moving average systems from noisy observations

This paper presents an algorithm for the parameter estimation of minimum-phase autoregressive moving average (ARMA) systems from noise-corrupted observations. In order to estimate the AR parameters of the ARMA system, an enhanced autocorrelation function (ACF) of the observed data is employed in a modified form of least-squares Yule-Walker equations. For the estimation of the MA parameters, first, a noise-subtraction algorithm is proposed to reduce the effect of noise from the residual signal which is obtained by filtering the noisy ARMA signal via the estimated AR parameters. The MA parameters are then estimated by using the spectral factorization corresponding to the noise-compensated residual signal. Computer simulations are carried out for ARMA systems of different orders and simulation results demonstrate a superior identification performance in terms of estimation accuracy and consistency under noisy conditions.