On the Cramér-Rao bound of autoregressive estimation in noise

The problem of noise-compensated autoregressive estimation has not been sufficiently explored especially with regard to the variance of the estimation. This paper explores this important aspect, presenting the asymptotic Cramer-Rao bound thereto. This valuable result is achieved by using a frequency- domain perspective of the problem as well as an unusual parametrization of an autoregressive model. One interesting finding is that the Fisher information matrix turns out to be built with the Wiener filter rule. Despite the power spectral density of the noise is assumed to be available in advance, the variance of the best estimator thereto is proven to be larger than that of the classical (noiseless) autoregressive estimation. The theoretical analysis has been validated with simulation experiments involving stationary colored noise.