# Equi-RO: A 4D mmWave Radar Odometry via Equivariant Networks

arXiv: https://arxiv.org/abs/2509.20674 · HTML: https://mlsanity.com/paper/2509.20674/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 20 of 20)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [KISS-ICP: In Defense of Point-to-Point ICP -- Simple, Accurate, and Robust Registration If Done the Right Way](https://mlsanity.com/paper/2209.15397/) (2022)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registration](https://mlsanity.com/paper/1905.04153/) (2019)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [Self-Supervised Scene Flow Estimation with 4-D Automotive Radar](https://mlsanity.com/paper/2203.01137/) (2022)
- [4D Millimeter-Wave Radar in Autonomous Driving: A Survey](https://mlsanity.com/paper/2306.04242/) (2023)
- [E2PN: Efficient SE(3)-Equivariant Point Network](https://mlsanity.com/paper/2206.05398/) (2022)
- [NTU4DRadLM: 4D Radar-centric Multi-Modal Dataset for Localization and Mapping](https://mlsanity.com/paper/2309.00962/) (2023)
- [4D iRIOM: 4D Imaging Radar Inertial Odometry and Mapping](https://mlsanity.com/paper/2303.13962/) (2023)
- [4DRVO-Net: Deep 4D Radar-Visual Odometry Using Multi-Modal and Multi-Scale Adaptive Fusion](https://mlsanity.com/paper/2308.06573/) (2023)
- [A Normal Distribution Transform-Based Radar Odometry Designed For Scanning and Automotive Radars](https://mlsanity.com/paper/2103.07908/) (2021)
- [Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebras](https://mlsanity.com/paper/2310.04521/) (2023)
- [Correspondence-Free SE(3) Point Cloud Registration in RKHS via Unsupervised Equivariant Learning](https://mlsanity.com/paper/2407.20223/) (2024)
- [CAO-RONet: A Robust 4D Radar Odometry with Exploring More Information from Low-Quality Points](https://mlsanity.com/paper/2503.01438/) (2025)

## Built on by (most cited first, 2 of 2)

- [Long-SCOPE: Fully Sparse Long-Range Cooperative 3D Perception](https://mlsanity.com/paper/2604.09206/) (2026)
- [RadarSplat-RIO: Indoor Radar-Inertial Odometry with Gaussian Splatting-Based Radar Bundle Adjustment](https://mlsanity.com/paper/2604.13492/) (2026)

## Abstract (arXiv)

Autonomous vehicles and robots rely on accurate odometry estimation in GPS-denied environments. While LiDARs and cameras struggle under extreme weather, 4D mmWave radar emerges as a robust alternative with all-weather operability and velocity measurement. In this paper, we introduce Equi-RO, an equivariant network-based framework for 4D radar odometry. Our algorithm pre-processes Doppler velocity into invariant node and edge features in the graph, and employs separate networks for equivariant and invariant feature processing. A graph-based architecture enhances feature aggregation in sparse radar data, improving inter-frame correspondence. Experiments on an open-source dataset and a self-collected dataset show Equi-RO outperforms state-of-the-art algorithms in accuracy and robustness. Overall, our method achieves 10.7% and 13.4% relative improvements in translation and rotation accuracy, respectively, compared to the best baseline on the open-source dataset.