A Simple Derivation of the Constrained Multiple Parameter CramerRao Bound

Recently Gorman and Hero obtained a remarkable extension to tbe classical multiple parameter Cramer-Rao (CR) lower bound tbat accounts for deterministic, nonlinear equality constraints on the parameters. The virtue of Gorman and Hero's new result is that the constrained CR bound on all of the parameters is obtained by a subtracting an easily computed nonnegative definite correction matrix from the unconstrained CR bound matrix. This correspondence presents a new, simple derivation of the constrained CR bound and a new necessary condition for an estimator to satisfy the constrained CR bound with equality.