A bound on mean-square-estimate error

A lower bound on mean-square-estimate error is derived as an instance of the covariance inequality by concatenating the generating matrices for the Bhattacharyya and Barankin bounds; it represents a generalization of the Bhattacharyya, Barankin, Cramer-Rao, Hammersley-Chapman-Robbins, Kiefer, and McAulay-Hofstetter bounds in that all of these bounds may be derived as special cases. The bound is applicable to biased estimates´ of functions of a multidimensional parameter. Termed the hybrid Bhattacharyya-Barankin bound, it may be written as the sum of the mth-order Bhattacharyya bound and a nonnegative term similar in form to the rth-order Hammersley-Chapman-Robbins bound. It is intended for use when small-error bounds, such as the Cramer-Rao bound, may not be tight; unlike many large-error bounds, it provides a smooth transition between the small-error and large-error regions. As an example application, bounds are placed on the variance of unbiased position estimates derived from passive array measurements. Here, the hybrid Bhattacharyya-Barankin bound enters the large-error region at a larger SNR and, in the large-error region, is noticeably greater than either the Hammersley-Chapman-Robbins or the Bhattacharyya bounds