Lower bounds on the estimation of harmonics in colored noise

A fast algorithm for the computation of the Fisher information matrix for the parameters of a deterministic signal in Gaussian AR noise is derived. The harmonic signal is studied in detail. In the case of a harmonic signal with random phases, closed-form expressions for the finite-sample posterior Cramer-Rao bounds are established. The fast algorithm is also useful for computing the conditional CRB when the additive noise is a non-Gaussian AR process. It is seen that the asymptotic lower bounds may deviate significantly from the exact bounds even when the data length is moderate. Theoretical results are illustrated via numerical evaluation of the different lower bounds.