Comparison of some algorithms for identifying autoregressive signals in the presence of observation noise

Several methods have been proposed for identifying autoregressive (AR) signals in noise. These include, e.g. : 1) solving a set of appropriately shifted Yule-Walker equations, and 2) compensation for the noise power (in the case of a white observation noise) using an iterative procedure. - However, small errors in the estimated correlations of the observation may cause the AR parameter estimates to be of rather poor quality or to correspond to an unstable model. Other methods can be developed, where the errors in the serial, or computed, correlations are taken into account. One example is the approach taken by Cadzow. An alternative modelization of these errors is presented in this paper, where a random noise is supposed to have been added to the correlation coefficients. The solution is obtained as the eigen-vector of a particular covariance matrix. Experimentation has shown that the last two methods result in more "robust" and stable estimators than those approaches where serial correlation errors are not modelized. On the other hand they entail a somewhat higher computational cost.