Neural Inertial Odometry from Lie Events

Neural displacement priors (NDP) can reduce the drift in inertial odometry and provide uncertainty estimates that can be readily fused with off-the-shelf filters. However, they fail to generalize to different IMU sampling rates and trajectory profiles, which limits their robustness in diverse settings. To address this challenge, we replace the traditional NDP inputs comprising raw IMU data with Lie events that are robust to input rate changes and have favorable invariances when observed under different trajectory profiles. Unlike raw IMU data sampled at fixed rates, Lie events are sampled whenever the norm of the IMU pre-integration change, mapped to the Lie algebra of the SE(3) group, exceeds a threshold. Inspired by event-based vision, we generalize the notion of level-crossing on 1D signals to level-crossings on the Lie algebra and generalize binary polarities to normalized Lie polarities within this algebra. We show that training NDPs on Lie events incorporating these polarities reduces the trajectory error of off-the-shelf downstream inertial odometry methods by up to 21% with only minimal preprocessing. We conjecture that many more sensors than IMUs or cameras can benefit from an event-based sampling paradigm and that this work makes an important first step in this direction.