Direction of Arrival Estimation using Riemannian Mean and Distance

Abstract

The problem of direction of arrival (DOA) estimation is considered from a geometric point of view. In particular, a new Riemannian geometry direction of arrival (RGDOA) estimation technique based on regularized Burg algorithm (RBA) and Riemannian mean and distance is proposed to maintain robust estimation under low signal-to-noise ratio (SNR) and small sample size. The RBA is exploited on generated Toeplitz Hermitian positive definite (THPD) covariance matrices from the estimates of the reflection coefficients for each radar snapshot. In addition, the Karcher Barycenter is used to calculate the Riemannian mean of THPD covariance matrices. The RGDOA technique is formulated as an optimization problem by minimizing the Riemannian distance between the Riemannian mean and the steering vector Hermitian positive definite covariance matrix. Simulation results indicate the robustness of the RGDOA technique in comparison with MUSIC and MVDR estimation techniques under low SNR and small sample size.