# Physics-Regularized Machine Learning for Proprioceptive Vehicle Localization Using Onboard Sensors

arXiv: https://arxiv.org/abs/2607.05663 · HTML: https://mlsanity.com/paper/2607.05663/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Deep Learning for Time Series Classification and Extrinsic Regression: A Current Survey](https://mlsanity.com/paper/2302.02515/) (2023)
- [Backprop KF: Learning Discriminative Deterministic State Estimators](https://mlsanity.com/paper/1605.07148/) (2016)
- [Particle Filter Recurrent Neural Networks](https://mlsanity.com/paper/1905.12885/) (2019)
- [Multimodal Sensor Fusion with Differentiable Filters](https://mlsanity.com/paper/2010.13021/) (2020)
- [AI-IMU Dead-Reckoning](https://mlsanity.com/paper/1904.06064/) (2019)
- [Deep Learning for Inertial Positioning: A Survey](https://mlsanity.com/paper/2303.03757/) (2023)
- [An Unscented Kalman Filter-Informed Neural Network for Vehicle Sideslip Angle Estimation](https://mlsanity.com/paper/2303.05238/) (2023)
- [Three-Dimensional Vehicle Dynamics State Estimation for High-Speed Race Cars under varying Signal Quality](https://mlsanity.com/paper/2408.14885/) (2024)
- [Uncertainty-Aware Hybrid Machine Learning in Virtual Sensors for Vehicle Sideslip Angle Estimation](https://mlsanity.com/paper/2504.06105/) (2025)
- [A Hybrid Adaptive Velocity Aided Navigation Filter with Application to INS/DVL Fusion](https://mlsanity.com/paper/2211.01329/) (2022)

## Abstract (arXiv)

Accurate and robust localization is essential for autonomous mobility systems in real-world environments. While fusing Inertial Measurement Unit (IMU) data with satellite-based correction signals provides precise vehicle pose estimates, performance degrades substantially during outages. Recent studies indicate that Machine Learning (ML) can improve IMU-based proprioceptive localization, highlighting untapped potential for onboard sensors readily available in production vehicles. This paper introduces Physics-Regularized Machine Learning for Localization (PRML2), a hybrid framework that combines the complementary strengths of Kalman filtering and data-driven learning to estimate vehicle pose directly from onboard sensors. A key aspect of PRML2 is its physics-regularized learning, enabled by end-to-end training of an ML model through a differentiable Kalman filter. This improves consistency with vehicle motion models, thereby enhancing both localization accuracy and generalization across driving conditions. We evaluate the performance limits of ML-enhanced onboard odometry on a publicly available dataset and show that PRML2 achieves superior localization accuracy and demonstrates real-time capability. This work also introduces a novel dataset to support vehicle localization research under low-friction conditions. The proposed framework provides a robust and cost-effective solution for vehicle localization under degraded sensing conditions by integrating learning with physics-based priors.