On the application of Cramer-Rao type lower bounds for constrained estimation

Using limiting forms of the Chapman-Robbins (1951) version of the Barankin bound, a study is made of the effect of parameter constraints on local lower bounds on estimator covariance. One such limiting form is the Cramer-Rao bound, for which constraints are seen to induce an oblique projection of the columns of the inverse Fisher information matrix onto a linear subspace tangent to the parameter constraint set. Another limiting form is the Bhattacharyya bound, which is defined in terms of higher-order Fisher information. For the Bhattacharyya bound, parameter constraints induce a transformation of the higher-order Fisher information that depends on the tangent space projection operator and its derivatives