Neural Inertial Odometry from Lie Events

Abstract: 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.

Neural Inertial Odometry from Lie Events

The paper "Neural Inertial Odometry from Lie Events" by Royina Karegoudra Jayanth et al. presents a methodological advancement in the field of inertial odometry, aiming to address key challenges associated with neural displacement priors (NDP). Traditional NDPs, while proficient at reducing drift and providing uncertainty estimates for odometry applications, suffer from limitations in generalization across varying Inertial Measurement Unit (IMU) sampling rates and trajectory profiles. This paper introduces an innovative approach by integrating Lie algebra-based event sampling into the training of NDPs.

Methodological Overview

The authors propose substituting raw IMU data, typically challenged by rate variability and diverse motion profiles, with Lie events. These Lie events leverage concepts from event-based vision, where events are triggered based on significant changes as opposed to fixed-rate sampling. Specifically, events are generated when the norm of the change in IMU pre-integration, expressed in the Lie algebra of the $SE(3)$ group, surpasses a defined threshold. This approach is akin to level-crossing in event-based vision but adapted to the multidimensional Lie algebra framework. Furthermore, the paper generalizes binary polarities to "Lie polarities," which are more informative and conducive to higher-dimensional manifolds.

Numerical Results and Implications

By training NDPs using these enriched Lie events, the paper demonstrates substantial improvements in trajectory accuracy, with an up to 21% reduction in trajectory error for downstream inertial odometry methods. The minimal preprocessing requirements for generating these events suggest a promising avenue for enhancing NDP robustness without significant computational overhead.

The implications of this research are twofold:

1. Practical Advancements: The improved generalization of NDPs may bolster the efficacy of various systems relying on inertial odometry, such as autonomous vehicles and robotics, particularly in scenarios involving disparate sampling rates or motion conditions.
2. Theoretical Contributions: The formalism introduced for Lie events extends to a vast range of applications in sensor data processing beyond IMUs, proposing a broader event-based sensor paradigm that may revolutionize data handling in dynamic and variable-rate environments.

Future Developments

This work lays a foundation for future exploration into event-based methodologies across various sensing modalities. By demonstrating the feasibility of event-based adaptations for IMU data, a potential exists for similar methodologies to influence the design and operation of other dynamic systems reliant on sensor data integration, thereby enhancing the overall robustness and accuracy of automated and real-time systems.

In summary, "Neural Inertial Odometry from Lie Events" convincingly argues for the viability and advantages of using Lie algebra-based events to advance the capabilities and applicability of neural displacement priors in inertial odometry. This approach not only mitigates current limitations but also suggests new frontiers for event-based sensor technologies in artificial intelligence and robotics.