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.