Because of the autonomous underwater vehicles' (AUVs') slow motion and insufficient excitations, monocular visual-inertial odometry (VIO) systems for AUVs still have large-scale errors and a lengthy initialization period. In this paper, we present a relative-depth-aided monocular visual-inertial odometry (RD-VIO) system based on two innovative methods: Inertial Measurement Unit (IMU)-depth joint initialization and relative depth tightly coupled with visual-inertial. The RD-VIO performs reprojection bundle adjustment with dynamic weight factors for visual residuals. Depth measurements acquired by depth gauge or pressure sensor are compensated with reliable inter-image IMU pre-integration to account for different sensor frequencies. Also, we adopt an IMU-depth joint initialization using relative depth measurements and IMU excitations to estimate the scale and gravity direction together, which captures the complete AUV motion changes, improving scale estimation and decreasing initialization time. To reduce scale drift and improve global accuracy and consistency, a tight coupling of relative depth and visual-inertial in the RD-VIO is employed to optimize the AUV pose from depth measurements. Using two open-source datasets and our experiments from Sanya, we evaluated the performance of RD-VIO. The evaluation results show that the proposed system can achieve a more accurate trajectory than the state-of-the-art algorithms with less system initialization time and scale error.
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