Reparameterization and constraints for CRB: duality and a major inequality for system analysis and design in the asymptotic region

The CRB is a lower bound of great interest for system analysis and design in the asymptotic region (high SNR and/or large number of snapshots), as it is simple to calculate and it is usually possible to obtain closed form expressions. It is from this perspective that the paper highlights, by means of a classical radar estimation problem, two results useful for system analysis and design: a reparameterization inequality and the equivalence between reparameterization and equality constraints.