An algorithm for ARMA model parameter estimation from noisy observations

This paper presents a new 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, based on a repeated autocorrelation function (ACF) of the observed data, a set of zero lag compensated equations has been developed. For the estimation of the MA parameters, first, a noise-subtraction algorithm is proposed to reduce the effect of noise from the ACF of 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 a spectral factorization corresponding to the noise-compensated ACF of the residual signal. Computer simulations are carried out for ARMA systems of different orders under noisy environments and simulation results demonstrate a superior identification performance in terms of estimation accuracy and consistency.