Fast computation of the exact FIM for deterministic signals in colored noise

A fast algorithm for computing the exact finite-sample Fisher information m atrix (FIM) for the parameters of a deterministic signal observed in Gaussi an AR noise is derived. In the case of a harmonic signal with random phases , closed-form expressions for the finite-sample posterior Cramer-Rao Bound (PCRB) are established, It is shown that 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 CRB mal deviate significantly f rom the exact CRB even when the data length is moderate, whereas the PCRB, which is easy to compute, provides a better approximation. Theoretical resu lts are illustrated via numerical evaluation of the different lower bounds.