# ToF-Wheel Odometry: Navigating Degeneration of Localization With Limited Sensing Capabilities

arXiv: https://arxiv.org/abs/2610.14590 · HTML: https://mlsanity.com/paper/2610.14590/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 13 of 13)

- [FAST-LIO2: Fast Direct LiDAR-inertial Odometry](https://mlsanity.com/paper/2107.06829/) (2021)
- [X-ICP: Localizability-Aware LiDAR Registration for Robust Localization in Extreme Environments](https://mlsanity.com/paper/2211.16335/) (2022)
- [Efficient and Probabilistic Adaptive Voxel Mapping for Accurate Online LiDAR Odometry](https://mlsanity.com/paper/2109.07082/) (2021)
- [Observability-Aware Intrinsic and Extrinsic Calibration of LiDAR-IMU Systems](https://mlsanity.com/paper/2205.03276/) (2022)
- [Wheel-SLAM: Simultaneous Localization and Terrain Mapping Using One Wheel-mounted IMU](https://mlsanity.com/paper/2211.03174/) (2022)
- [LIWO: Lidar-Inertial-Wheel Odometry](https://mlsanity.com/paper/2302.14298/) (2023)
- [Tightly-Coupled LiDAR-IMU-Wheel Odometry with Online Calibration of a Kinematic Model for Skid-Steering Robots](https://mlsanity.com/paper/2404.02515/) (2024)
- [C3P-VoxelMap: Compact, Cumulative and Coalescible Probabilistic Voxel Mapping](https://mlsanity.com/paper/2406.01195/) (2024)
- [I2EKF-LO: A Dual-Iteration Extended Kalman Filter Based LiDAR Odometry](https://mlsanity.com/paper/2407.02190/) (2024)
- [WING: Wheel-Inertial Neural Odometry with Ground Manifold Constraints](https://mlsanity.com/paper/2407.10101/) (2024)
- [Joint State and Noise Covariance Estimation](https://mlsanity.com/paper/2502.04584/) (2025)
- [AKF-LIO: LiDAR-Inertial Odometry with Gaussian Map by Adaptive Kalman Filter](https://mlsanity.com/paper/2503.06891/) (2025)
- [Towards Robust Sensor-Fusion Ground SLAM: A Comprehensive Benchmark and A Resilient Framework](https://mlsanity.com/paper/2507.08364/) (2025)

## Abstract (arXiv)

Wheel odometry provides an efficient motion prior for ground robots but is prone to transient violations such as wheel slip or terrain-induced tilt. In filtering-based odometry, these violations frequently trigger divergence when they coincide with constrained geometric observability (e.g., featureless corridors). We address this challenge by proposing ToF-Wheel Odometry (TWO), a tightly-coupled filtering framework that integrates wheel kinematics with geometric constraints from Time-of-Flight (ToF) cameras. The primary contribution of this work is a degeneracy-aware, directional covariance-shaping strategy that replaces heuristic online covariance tuning with geometry-conditioned inflation. The core idea is to infer process noise from geometric corrections with a strict reliability check. We decompose the posterior-to-prior correction into a wheel-explainable subspace and an orthogonal remainder. The process covariance is anisotropically adjusted according to the observability of the ToF update: if the geometry is degenerate in non-kinematic directions, the remainder is suppressed as sensor noise; if the geometry is distinct, it is admitted as a valid kinematic violation. Additionally, we introduce an intra-frame feedback loop that retrospectively repairs the process covariance within the current frame to reduce structural lag during bursty disturbances. Extensive experiments on challenging scenarios demonstrate that TWO improves trajectory accuracy and robustness compared to static and adaptive Gaussian filtering, robustly navigating the trade-off between kinematic reliability and limited sensing capabilities.