# RIO: Rotation-equivariance supervised learning of robust inertial odometry

arXiv: https://arxiv.org/abs/2111.11676 · HTML: https://mlsanity.com/paper/2111.11676/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 23 Nov 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Unsupervised Learning of Depth and Ego-Motion from Video](https://mlsanity.com/paper/1704.07813/) (2017)
- [Learning to See by Moving](https://mlsanity.com/paper/1505.01596/) (2015)
- [On-Manifold Preintegration for Real-Time Visual-Inertial Odometry](https://mlsanity.com/paper/1512.02363/) (2015)
- [How Useful is Self-Supervised Pretraining for Visual Tasks?](https://mlsanity.com/paper/2003.14323/) (2020)
- [RoNIN: Robust Neural Inertial Navigation in the Wild: Benchmark, Evaluations, and New Methods](https://mlsanity.com/paper/1905.12853/) (2019)
- [Cross-Domain Self-supervised Multi-task Feature Learning using Synthetic Imagery](https://mlsanity.com/paper/1711.09082/) (2017)
- [IONet: Learning to Cure the Curse of Drift in Inertial Odometry](https://mlsanity.com/paper/1802.02209/) (2018)
- [TLIO: Tight Learned Inertial Odometry](https://mlsanity.com/paper/2007.01867/) (2020)
- [RIDI: Robust IMU Double Integration](https://mlsanity.com/paper/1712.09004/) (2017)
- [IDOL: Inertial Deep Orientation-Estimation and Localization](https://mlsanity.com/paper/2102.04024/) (2021)
- [OxIOD: The Dataset for Deep Inertial Odometry](https://mlsanity.com/paper/1809.07491/) (2018)
- [Inertial Odometry on Handheld Smartphones](https://mlsanity.com/paper/1703.00154/) (2017)

## Built on by (most cited first, 14 of 14)

- [EgoDistill: Egocentric Head Motion Distillation for Efficient Video Understanding](https://mlsanity.com/paper/2301.02217/) (2023)
- [Deep Learning for Inertial Positioning: A Survey](https://mlsanity.com/paper/2303.03757/) (2023)
- [EqNIO: Subequivariant Neural Inertial Odometry](https://mlsanity.com/paper/2408.06321/) (2024)
- [AirIO: Learning Inertial Odometry with Enhanced IMU Feature Observability](https://mlsanity.com/paper/2501.15659/) (2025)
- [AirIMU: Learning Uncertainty Propagation for Inertial Odometry](https://mlsanity.com/paper/2310.04874/) (2023)
- [SM/VIO: Robust Underwater State Estimation Switching Between Model-based and Visual Inertial Odometry](https://mlsanity.com/paper/2304.01988/) (2023)
- [Learning IMU Bias with Diffusion Model](https://mlsanity.com/paper/2505.11763/) (2025)
- [RIOT: Recursive Inertial Odometry Transformer for Localisation from Low-Cost IMU Measurements](https://mlsanity.com/paper/2303.01641/) (2023)
- [NeurIT: Pushing the Limit of Neural Inertial Tracking for Indoor Robotic IoT](https://mlsanity.com/paper/2404.08939/) (2024)
- [Piggyback Camera: Easy-to-Deploy Visual Surveillance by Mobile Sensing on Commercial Robot Vacuums](https://mlsanity.com/paper/2507.04910/) (2025)
- [IONext: Unlocking the Next Era of Inertial Odometry](https://mlsanity.com/paper/2507.17089/) (2025)
- [X-IONet: Cross-Platform Inertial Odometry Network for Pedestrian and Legged Robot](https://mlsanity.com/paper/2511.08277/) (2025)
- [MARIO: Motion-Augmented Real-Time Multi-Sensor Inertial Odometry](https://mlsanity.com/paper/2606.02996/) (2026)
- [GINIO: A Geometric SO(3)-Equivariant Interface for Neural Inertial Odometry](https://mlsanity.com/paper/2609.25338/) (2026)

## Abstract (arXiv)

This paper introduces rotation-equivariance as a self-supervisor to train inertial odometry models. We demonstrate that the self-supervised scheme provides a powerful supervisory signal at training phase as well as at inference stage. It reduces the reliance on massive amounts of labeled data for training a robust model and makes it possible to update the model using various unlabeled data. Further, we propose adaptive Test-Time Training (TTT) based on uncertainty estimations in order to enhance the generalizability of the inertial odometry to various unseen data. We show in experiments that the Rotation-equivariance-supervised Inertial Odometry (RIO) trained with 30% data achieves on par performance with a model trained with the whole database. Adaptive TTT improves models performance in all cases and makes more than 25% improvements under several scenarios.