Numerical Techniques for the Maximum Likelihood Toeplitz Covariance Matrix Estimation: Part I. Symmetric Toeplitz Matrices

TL;DR

This paper explores numerical methods for estimating symmetric Toeplitz covariance matrices, emphasizing their ability to be accurately estimated despite phase errors, which is crucial for applications requiring phase calibration.

Contribution

It introduces techniques specifically tailored for symmetric Toeplitz matrices, highlighting their robustness against phase errors and their potential for improved covariance estimation.

Findings

Symmetric Toeplitz matrices can be estimated accurately despite phase errors.

The proposed methods outperform traditional approaches in phase error scenarios.

Symmetric Toeplitz matrices offer unique advantages in covariance estimation applications.

Abstract

In several applications, one must estimate a real-valued (symmetric) Toeplitz covariance matrix, typically shifted by the conjugated diagonal matrices of phase progression and phase "calibration" errors. Unlike the Hermitian Toeplitz covariance matrices, these symmetric matrices have a unique potential capability of being estimated regardless of these beam-steering phase progression and/or phase "calibration" errors. This unique capability is the primary motivation of this paper.