Versatility of constrained CRB for system analysis and design

Provided that one keeps in mind the Craḿer-Rao bound (CRB) limitations, that is, to become an overly optimistic lower bound when the observation conditions degrades, the CRB is a lower bound of great interest for analysis and design of a system of measurement in the asymptotic region. As a contribution, we introduce an original framework taking into account most (and possibly all) of the factors impacting the asymptotic estimation performance of the parameters of interest via equality constraints, leading to direct algebraic computations of constrained CRB. For complex systems, derivation of analytical expression of CRB is either impossible or inefficient. For application to active systems of measurement such as radar, we provide the general form of the Fisher information matrix (FIM) for multiple conditional models, which generally precludes the derivation of an analytical expression of the CRB for scenarios including interference and sensors modelling errors. We show that the proposed framework can also be used efficiently to generate new closed-form expressions of CRB, although this is not its main aim.