Analysis of the Cramer-Rao Bound Integrating a Prior-Knowledge

Introducing prior-knowledge of some damped/undamped poles in the estimation of the parameters of a mutlipoles sinusoidal model is an important problem as for instance in bearing estimation or in biomedical signal analysis. The principle is to orthogonally project the data onto the noise space associated with the known poles. As the Cramer-Rao Lower Bound (CRB) gives a benchmark against which algorithms performance can be compared, it is useful to derive the CRB associated with this model, named Prior-CRB (P-CRB). In particular, we analyze this bound in the context of close subspaces context, ie., when the known poles are close to the unknown ones.