CWCU LMMSE Estimation Under Linear Model Assumptions

The classical unbiasedness condition utilized e.g. by the best linear unbiased estimator (BLUE) is very stringent. By softening the ”global” unbiasedness condition and introducing component-wise conditional unbiasedness conditions instead, the number of constraints limiting the estimator’s performance can in many cases significantly be reduced. In this paper we extend the findings on the component-wise conditionally unbiased linear minimum mean square error (CWCU LMMSE) estimator under linear model assumptions. We discuss the CWCU LMMSE estimator for complex proper Gaussian parameter vectors, and for mutually independent (and otherwise arbitrarily distributed) parameters. Finally, the beneficial properties of the CWCU LMMSE estimator are demonstrated in two applications.