This letter extends the Yule-Walker method to the estimation of ARMA parameters from output measurements corrupted by noise. In the proposed method it is assumed that the noise variance and the input are unknown. An algorithm for the estimation of noise variance is, therefore, given. The use of the variance estimation method proposed here together with the Yule-Walker equations allow the estimation of the parameters of a minimum phase ARMA model based only on noisy measurements of its output. Moreover, using this method it is not necessary to slove a set of nonlinear equations for MA parameter estimation as required in the conventional correlation based methods.

In many applications involving the processing of noisy signals, it is desired to know the noise variance. This paper proposes a new method for estimating the noise variance from the signals of autoregressive (AR) and autoregressive moving-average (ARMA) systems corrupted by additive white noise. The method proposed here uses the low-order Yule-Walker (LOYW) equations and the lattice filter (LF) algorithm for the estimation of noise variance from the noisy output measurements of AR and ARMA systems, respectively. Two techniques are proposed here: iterative technique and recursive one. The accuracy of the methods depends on SNR levels, more specifically on the inherent accuracy of the Yule-Walker and lattice filter methods for signal plus noise system. The estimated noise variance is used for the blind indentification of AR and ARMA systems. Finally, to demonstrate the effectiveness of the method proposed here many numerical results are presented.