AR parameter estimation from noisy data using the EM algorithm

This paper considers the problem of parameter estimation of Gaussian autoregressive (AR) processes in the presence of additive white Gaussian noise. The proposed algorithm is based on formulating the estimation problem as an iterative expectation-maximisation (EM) procedure. The observations are seen as the `incomplete´ data and the set formed by the AR process and the noise process represents the `complete´ data. The algorithm is guaranteed to converge in the likelihood function of the parameters. The algorithm is easily generalised to other structures of the covariance matrix of the additive noise. Performance results show that the algorithm is successful in estimating the parameters even at very low signal-to-noise ratios (SNR)