Direction of arrival estimation with neural networks via test time self-supervised optimization and array manifold sensing

Adaptive beamformers such as the minimum-variance distortionless response (MVDR) are highly sensitive to mismatches in both the sample covariance matrix (SCM) and the array steering vector. This paper proposes a closed-loop Neural-MVDR framework for direction-of-arrival estimation that enforces a distortionless constraint consistent with a physically parameterized array model. The method requires no offline supervised pretraining on external labeled datasets. Instead, it performs per-frame, self-supervised adaptation at test time. For each incoming snapshot, it alternates among steering-vector refinement, robust SCM reconstruction parameterized by a lightweight neural module, and analytical MVDR spectral estimation. Experiments on synthetic data and the SWellEx-96 S5 event demonstrate improved robustness compared with the conventional beamformer, conventional MVDR, and representative robust MVDR variants based on eigenspace suppression, covariance matrix tapering, and oracle-approximating shrinkage, respectively.