Best Widely Linear Unbiased Estimator for Real Valued Parameter Vectors

TL;DR

This paper introduces a novel widely linear estimator tailored for real-valued parameter vectors in complex measurement scenarios, outperforming traditional BLUE and BWLUE estimators in variance reduction.

Contribution

A new unbiased widely linear estimator is derived that explicitly accounts for real-valued parameters, improving estimation accuracy over existing methods.

Findings

The proposed estimator is unbiased and outperforms BLUE and BWLUE in variance.

It effectively incorporates the real-valued nature of parameters in complex measurement models.

The estimator demonstrates superior performance in variance reduction.

Abstract

For classical estimation with an underlying linear model the best linear unbiased estimator (BLUE) is usually utilized for estimating the deterministic but unknown parameter vector. In the case of real valued parameter vectors but complex valued measurement matrices and noise vectors, the BLUE results in complex valued estimates, introducing a systematic error. In recent years widely linear estimators have been investigated for complex estimation. In this work a novel widely linear classical estimator is derived which incorporates the knowledge that the parameter vector is real valued. The proposed estimator is unbiased in the classical sense and it outperforms the BLUE and the best widely linear unbiased estimator (BWLUE) in terms of the variances of the vector estimator's elements.