Achievable MSE lower bounds in non-Bayesian Biased estimation

In this paper, a new structured approach for obtaining uniformly best biased (UBB) estimators, in the mean-square-error (MSE) sense, is established. We show that if a UBB estimator exists, then it is uniquely given by the locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived, and it is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and the UBB estimator is directly obtained from the LBB estimator. The UBB estimator is derived in a non-linear Gaussian estimation problem. In comparison to the maximum-likelihood estimator, we show that the UBB estimator exhibits superior estimation performance in the MSE sense.