Asymptotic Cramér-Rao Bound for Noise-Compensated Autoregressive Analysis

Noise-compensated autoregressive (AR) analysis is a problem insufficiently explored with regard to the accuracy of the estimate. This paper studies comprehensively the lower limit of the estimation variance, presenting the asymptotic Cramér-Rao bound (CRB) for Gaussian processes and additive Gaussian noise. This novel result is obtained by using a frequency-domain perspective of the problem as well as an unusual parametrization of an AR model. The Wiener filter rule appears as the distinctive building element in the Fisher information matrix. The theoretical analysis is validated numerically, showing that the proposed CRB is attained by competitive ad hoc estimation methods under a variety of Gaussian color noise and realistic scenarios.