Identification of autoregressive moving average systems from noise-corrupted observations

In this paper, a new scheme for the identification of minimum-phase autoregressive moving average (ARMA) systems from noise-corrupted observations is presented. Analyzing the characteristics of the autocorrelation function (ACF) of the observed data in the presence of noise, a set of equations has been developed which is capable of estimating the AR parameters of the ARMA system as well as the noise variance. In order to estimate the MA parameters, first, a residual signal is obtained by filtering the noisy observations via the estimated AR parameters. Utilizing the estimated noise variance and the AR parameters, a noise-subtraction algorithm is proposed to reduce the effect of noise from the ACF of the residual signal. The MA parameters are then estimated employing the spectral factorization corresponding to the noise-compensated ACF of the residual signal. Computer simulations on different ARMA systems demonstrate a superior identification results in terms of estimation accuracy and consistency even under a heavy noisy condition.