# NeRC: Neural Ranging Correction through Differentiable Moving Horizon Location Estimation

arXiv: https://arxiv.org/abs/2508.14336 · HTML: https://mlsanity.com/paper/2508.14336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 101 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 22 of 22)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [OrienterNet: Visual Localization in 2D Public Maps with Neural Matching](https://mlsanity.com/paper/2304.02009/) (2023)
- [Differentiable Integrated Motion Prediction and Planning with Learnable Cost Function for Autonomous Driving](https://mlsanity.com/paper/2207.10422/) (2022)
- [Theseus: A Library for Differentiable Nonlinear Optimization](https://mlsanity.com/paper/2207.09442/) (2022)
- [NeRF2: Neural Radio-Frequency Radiance Fields](https://mlsanity.com/paper/2305.06118/) (2023)
- [FIESTA: Fast Incremental Euclidean Distance Fields for Online Motion Planning of Aerial Robots](https://mlsanity.com/paper/1903.02144/) (2019)
- [Hybrid-Prediction Integrated Planning for Autonomous Driving](https://mlsanity.com/paper/2402.02426/) (2024)
- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [Improving GNSS Positioning using Neural Network-based Corrections](https://mlsanity.com/paper/2110.09581/) (2021)
- [HandDGP: Camera-Space Hand Mesh Prediction with Differentiable Global Positioning](https://mlsanity.com/paper/2407.15844/) (2024)
- [Neural Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2206.10397/) (2022)
- [Differentiable Moving Horizon Estimation for Robust Flight Control](https://mlsanity.com/paper/2108.03212/) (2021)
- [Localization with Noisy Android Raw GNSS Measurements](https://mlsanity.com/paper/2309.08936/) (2023)
- [PrNet: A Neural Network for Correcting Pseudoranges to Improve Positioning with Android Raw GNSS Measurements](https://mlsanity.com/paper/2309.12204/) (2023)
- [pyrtklib: An open-source package for tightly coupled deep learning and GNSS integration for positioning in urban canyons](https://mlsanity.com/paper/2409.12996/) (2024)
- [SiTAR: Situated Trajectory Analysis for In-the-Wild Pose Error Estimation](https://mlsanity.com/paper/2308.16813/) (2023)
- [Towards End-to-End GPS Localization with Neural Pseudorange Correction](https://mlsanity.com/paper/2401.10685/) (2024)
- [Data-driven parallel Koopman subsystem modeling and distributed moving horizon state estimation for large-scale nonlinear processes](https://mlsanity.com/paper/2404.06746/) (2024)
- [Fast Decentralized State Estimation for Legged Robot Locomotion via EKF and MHE](https://mlsanity.com/paper/2405.20567/) (2024)
- [Self-tuning moving horizon estimation of nonlinear systems via physics-informed machine learning Koopman modeling](https://mlsanity.com/paper/2408.03653/) (2024)
- [RAG-VR: Leveraging Retrieval-Augmented Generation for 3D Question Answering in VR Environments](https://mlsanity.com/paper/2504.08256/) (2025)
- [Receding Horizon Recursive Location Estimation](https://mlsanity.com/paper/2506.18430/) (2025)

## Abstract (arXiv)

GNSS localization using everyday mobile devices is challenging in urban environments, as ranging errors caused by the complex propagation of satellite signals and low-quality onboard GNSS hardware are blamed for undermining positioning accuracy. Researchers have pinned their hopes on data-driven methods to regress such ranging errors from raw measurements. However, the grueling annotation of ranging errors impedes their pace. This paper presents a robust end-to-end Neural Ranging Correction (NeRC) framework, where localization-related metrics serve as the task objective for training the neural modules. Instead of seeking impractical ranging error labels, we train the neural network using ground-truth locations that are relatively easy to obtain. This functionality is supported by differentiable moving horizon location estimation (MHE) that handles a horizon of measurements for positioning and backpropagates the gradients for training. Even better, as a blessing of end-to-end learning, we propose a new training paradigm using Euclidean Distance Field (EDF) cost maps, which alleviates the demands on labeled locations. We evaluate the proposed NeRC on public benchmarks and our collected datasets, demonstrating its distinguished improvement in positioning accuracy. We also deploy NeRC on the edge to verify its real-time performance for mobile devices.