Quaternion-Based Two-Dimensional DOA Estimation for Coherent Underwater Sources Without Eigendecomposition

For scenarios of coherent underwater sources at low signal-to-noise ratio (SNR), a novel quaternion-based DOA algorithm without eigendecomposition is proposed using a linear vector-hydrophone array. We construct four quaternion models by judiciously arranging the received data to fully utilize the statistical information of the incident signals. To avoid the high computational complexity caused by the eigenvalue decomposition (EVD), we introduce the computationally efficient propagator method (PM) to estimate the elevation angles of the observed signals. In the quaternion algebra framework, we statistically eliminate the additive noise, which makes the PM method exhibit a robust performance in low SNR. By fully exploiting the direction information embedded in the velocity components, we achieve a high-resolution two-dimensional (2-D) DOA estimation result with a linear vector-hydrophone array. The simulations demonstrate that the proposed method offers stable estimation performance compared with the existing non-quaternion schemes without the need for any pair matching between the estimated azimuth and elevation angles.