GINIO: A Geometric SO(3)-Equivariant Interface for Neural Inertial Odometry

Chankyo Kim, Minghan Zhu, Tzu-Yuan Lin, Avantika Rattan, Maani Ghaffari

Neural inertial odometry increasingly uses networks as learned measurements inside filtering pipelines. Such measurements should transform consistently under arbitrary IMU mounting conventions: their mean must transform as a vector, and their covariance must transform congruently as a second-order tensor. We present GINIO, a geometric SO(3)-equivariant interface for neural inertial odometry under arbitrary rotations of the IMU measurement frame. Given calibrated IMU windows, our framework predicts a motion measurement and uncertainty obeying these tensorial laws. To support efficient sensor-frame learning, we introduce Last-Frame Alignment (LFA), a deterministic preprocessing step that is provably equivalent to world-frame training for SO(3)-equivariant predictors. The connected estimator tracks sensor-local states such as IMU bias, separating nuisance estimation from the geometric law enforced by the learned measurement. We instantiate the same interface in filter-connected NIO, AirIO-style recurrent aerial prediction, EqNIO-style full-SO(3) canonicalization, and ResNet-style temporal backbones. On TLIO, GINIO achieves 2.018 m ID/SO(3) ATE while EqNIO degrades to 76.389 m, using…