On component-wise conditionally unbiased linear Bayesian estimation

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 work we extend the findings on component-wise conditionally unbiased (CWCU) linear Bayesian estimation for linear data models. We discuss the construction and properties of CWCU estimators for parameter vectors consisting of mutually independent elements, and we give a derivation of the CWCU linear minimum mean square error (CWCU LMMSE) estimator for zero mean and nonzero mean parameter vectors under this condition. No Gaussian assumptions on the probability density functions (PDFs) of the data and the noise have to be made. Finally, the advantageous properties of the CWCU LMMSE estimator are demonstrated with the help of a well-known channel estimation application.