Complex Mean and Variance of Linear Regression Model for High-Noised Systems by Kriging

TL;DR

The paper addresses estimation in high-noise linear-regression contexts by deriving a complex-valued least-squares estimator for bias-noise mean and variance within a kriging framework. It develops the kriging weights and the best linear unbiased estimator for a background trend, showing asymptotic unbiasedness and zero mean-squared error as sample size grows, and extends these results to complex-valued bias-noise mean and variance with closed-form expressions for the complex mean $\hat{m}$ and variance $\hat{σ}^2$ that include an imaginary component. The approach yields explicit formulas for the complex estimators and demonstrates how slope terms in the bias influence the estimation, which enhances robustness in noisy, potentially complex-valued signal-processing settings. Overall, the work provides a principled method to obtain complex-valued mean and variance estimates in high-noise linear systems using kriging-based BLU techniques.

Abstract

The aim of the paper is to derive the complex-valued least-squares estimator for bias-noise mean and variance.