The Constrained CramÉr–Rao Bound From the Perspective of Fitting a Model

Stoica and Ng (1998) presented a simple expression for the constrained Cramer-Rao bound (CCRB) when the constraints are given by a differentiable function of the parameter to be estimated. This letter considers the parallel case in developing the CCRB when the parameters are locally fitted to a lower-dimensional parametric model, i.e., the parameters are locally assumed to be functions of a distinct reduced parameter vector. We employ classical elements of CRB theory on the locally fitted model to present a very simple derivation of the CCRB, conditions for attaining the bound, and a regularity condition. Examples illustrate the key ideas.