Constrained Best Linear Unbiased Estimation

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The least squares (LS) estimator and the best linear unbiased estimator (BLUE) are two well-studied approaches for the estimation of a deterministic but unknown parameter vector. In many applications it is known that the parameter vector fulfills some constraints, e.g., linear constraints. For such situations the constrained LS estimator, which is a simple extension of the LS estimator, can be employed. In this paper we derive the constrained version of the BLUE. It will turn out that the incorporation of the linear constraints into the derivation of the BLUE is not straight forward as for the constrained LS estimator, but the final expression for the constrained BLUE is closely related to that of the constrained LS estimator.