Constrained Best Linear Unbiased Estimation

TL;DR

This paper derives a constrained version of the BLUE estimator that incorporates linear constraints on the parameter vector, extending classical estimation methods for more accurate parameter estimation under known constraints.

Contribution

It introduces the derivation of the constrained BLUE, showing its relation to the constrained LS estimator and addressing the complexity of incorporating linear constraints.

Findings

Derived the constrained BLUE estimator expression.

Showed the relation between constrained BLUE and constrained LS.

Provided insights into estimation under linear constraints.

Abstract

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.