Constrained Best Linear and Widely Linear Unbiased Estimation

The least squares estimator (LSE) and the best linear unbiased estimator (BLUE) are two well-studied approaches for the estimation of deterministic but unknown parameters. In situations where the parameter vector is subject to linear constraints, the constrained LSE can be employed. In this paper, we derive the constrained version of the BLUE. In fact, two versions of the constrained BLUE are discussed, one of them with even weaker prerequisites than required for the well-known constrained LSE. In addition, the two corresponding versions of the constrained best widely linear unbiased estimator are presented.