Matrix information geometry active DOA estimation method for underwater acoustic sensor array

Since the space of covariance matrices forms a nonlinear manifold, traditional methods based on Euclidean geometry face limitations, as they fail to account for the intrinsic geometric properties of the matrix manifold. This limitation hinders the full extraction of directional information in covariance matrices, thereby reducing the accuracy of direction of arrival (DOA) estimation. In underwater signal transmission scenarios, where significant attenuation and strong interference occur, the received signals are severely distorted, further exacerbating the problem. To address this issue, this paper proposes a DOA estimation method based on a matrix information geometry (MIG) active detection system, which transforms the DOA estimation problem into a divergence measure problem between two Hermitian positive definite (HPD) matrices on a matrix manifold. The algorithm constructs two robust HPD matrices on the matrix manifold and achieves DOA estimation through a divergence minimization criterion. Simulation results demonstrate that the proposed MIG method outperforms traditional DOA estimation approaches, particularly under low signal-to-noise ratio (SNR) conditions and when the number of snapshots is limited. Experimental validations were conducted separately at the anechoic pool of Northwestern Polytechnical University and at Qiandao Lake in Zhejiang Province, with results consistently demonstrating the effectiveness and robustness of the proposed MIG method.