On the computation of an asymptotic bound for estimating autoregressive signals in white noise

The Cramer-Rao lower bound (CRLB) provides a useful reference for evaluating the performance of parameter estimation techniques. This paper considers the problem of estimating the parameters of an autoregressive signal corrupted by white noise. An explicit formula is derived for computing the asymptotic CRLB for the signal and noise parameters. Formulas for the asymptotic CRLB for functions of the signal and noise parameters are also presented. In particular, the center frequency, bandwidth and power of a second order process are considered. Some numerical examples are presented to illustrate the usefulness of these bounds in studying estimation accuracy.