Riemannian Covariance Fitting for Direction-of-Arrival Estimation

TL;DR

This paper introduces a Riemannian geometry-based approach to covariance fitting for DoA estimation, improving robustness and accuracy over traditional Euclidean methods by leveraging the affine-invariant and Log-Euclidean metrics.

Contribution

It presents a novel covariance fitting method using Riemannian metrics, especially the Log-Euclidean metric, and develops a new beamformer with enhanced spatial characteristics and robustness.

Findings

LE-based beamformer outperforms classical beamformers in noisy conditions

Riemannian metrics improve covariance fitting accuracy

Enhanced robustness with small sample sizes and interference

Abstract

Covariance fitting (CF) is a comprehensive approach for direction of arrival (DoA) estimation, consolidating many common solutions. Standard practice is to use Euclidean criteria for CF, disregarding the intrinsic Hermitian positive-definite (HPD) geometry of the spatial covariance matrices. We assert that this oversight leads to inherent limitations. In this paper, as a remedy, we present a comprehensive study of the use of various Riemannian metrics of HPD matrices in CF. We focus on the advantages of the Affine-Invariant (AI) and the Log-Euclidean (LE) Riemannian metrics. Consequently, we propose a new practical beamformer based on the LE metric and derive analytically its spatial characteristics, such as the beamwidth and sidelobe attenuation, under noisy conditions. Comparing these features to classical beamformers shows significant advantage. In addition, we demonstrate, both theoretically and experimentally, the LE beamformer's robustness in scenarios with small sample sizes and in the presence of noise, interference, and multipath channels.