Reliable underwater multi-target direction of arrival estimation with optimal transport using deep models

Multi-target direction of arrival (DoA) estimation is an important and challenging task for sonar signal processing. In this study, we propose a method called learning direction of arrival with optimal transport (LOT) to accurately estimate the DoAs of multiple sources with a single deep model. We model the DoA estimation problem as a multi-label classification task and introduce an optimal transport (OT) loss based on the OT theory to capture the intrinsic continuity within the angular categories. We design a cost matrix for the OT loss in LOT approach to characterize the order and periodicity of the angular grid. The LOT approach encourages reliable predictions closer to the ground truth and suppresses spurious targets. We also propose a lightweight channel mask data augmentation module for deep models that use items related to the covariance matrix as input. The proposed methods can be seamlessly integrated with different model architectures and we indicate the portability with experiments on several typical network backbones. Experiments across various scenarios using different measurements show the effectiveness and robustness of our approaches. Results on SwellEx-96 experimental data demonstrate the practicality in real applications.