Orthogonal Ray Projection: A Tangent-Space Visual Measurement Model for Robust Visual-Inertial Odometry

The reprojection error in Visual-Inertial Odometry (VIO) suffers from high nonlinearity due to perspective division, which degrades estimator consistency and robustness, particularly under large depth uncertainty. To address this, we propose a novel visual measurement model, the Orthogonal Ray Projection Error (ORPE), which is formulated in the tangent space of the observation ray. By minimizing the orthogonal distance between the estimated landmark and the measurement ray, ORPE decouples the measurement error from the scalar depth, rendering the residual function linear with respect to the feature position. We derive the exact analytical Jacobians and an uncertainty propagation model, integrating ORPE into both the MSCKF-based OpenVINS and the optimization-based ORB-SLAM3 frameworks. Simulations confirm that ORPE achieves geometric linearity for features, while significantly reducing the system nonlinearity with respect to camera pose. Extensive real-world experiments demonstrate that the proposed method significantly improves trajectory accuracy and estimator consistency in challenging weak-parallax scenarios, while maintaining computational efficiency comparable to standard approaches. To facilitate reproducibility and further research, we release our source code implemented in both OpenVINS and ORB-SLAM3 frameworks at our public repository.