Coherent DOA Estimation Using Symmetric KLD on the Hermitian Positive Definite Manifold

Since the space of covariance matrices forms a nonlinear manifold, conventional spatial smoothing techniques, which are formulated within Euclidean frameworks, are unable to fully exploit the intrinsic geometric properties of the data. This limitation leads to performance degradation in DOA estimation, particularly in scenarios involving coherent sources. In this letter, we propose a method based on symmetric Kullback–Leibler divergence (SKLD), which reformulates DOA estimation as a divergence minimization problem on the manifold of Hermitian positive definite (HPD) matrices. Theoretically, we demonstrate that minimizing the divergence is equivalent to maximizing the similarity between two matrices on the manifold, with the searching angle precisely matching the true incident direction. Simulation results show that the proposed method achieves superior signal decorrelation and enhanced robustness to noise, significantly outperforming conventional spatial smoothing approaches under low signal-to-noise ratio (SNR) and limited snapshot conditions.