Observability-Aware Manifold Flow Matching for Degradation-Resilient Radar-Inertial-Visual UAV Odometry

Reliable metric odometry for small unmanned aerial vehicles is difficult when vision is degraded and radar returns have limited directional coverage. We present Observability-Aware Manifold Flow Matching (OAM-FM), a self-supervised radar-inertial-visual odometry framework that learns conditional transport in local pose coordinates and maps its outputs to SE(3). A calibrated Doppler Jacobian supplies a directional training metric; its undamped information matrix characterizes instantaneous radar constraints without conflating numerical regularization with physical observability. The objective combines flow matching, robust Doppler residuals, and IMU preintegration over poses, velocities, and sensor biases. Optional visual features provide complementary constraints without being required at inference. A separate covariance head estimates local prediction uncertainty, whose calibration is evaluated against reference poses. The formulation distinguishes this uncertainty from the spread of flow samples: a deterministic sensor-based training endpoint alone does not establish a multimodal posterior. The method requires no dense depth or pose labels during training and is evaluated on real-world UAV odometry under radar sparsity, visual degradation, aggressive motion, and inertial bias, together with onboard latency.