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NeRC: Neural Ranging Correction through Differentiable Moving Horizon Location Estimation

Xu Weng, K. V. Ling, Haochen Liu, Bingheng Wang, Kun Cao

TL;DR

This work addresses the challenge of GNSS localization in urban environments where multipath and NLOS effects degrade accuracy. It introduces NeRC, a two-stage framework that first uses an upstream neural network to estimate pseudorange errors from a horizon of GNSS measurements and then feeds these estimates into a differentiable Moving Horizon Estimator to recover a trajectory, allowing end-to-end training on location losses. A key innovation is enabling learning from unlabeled data via Euclidean Distance Field supervision, which couples predicted trajectories to reference map routes without requiring precise ground truth. Evaluations on public benchmarks and real-time edge tests demonstrate state-of-the-art localization performance and practical feasibility for mobile devices.

Abstract

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.

NeRC: Neural Ranging Correction through Differentiable Moving Horizon Location Estimation

TL;DR

This work addresses the challenge of GNSS localization in urban environments where multipath and NLOS effects degrade accuracy. It introduces NeRC, a two-stage framework that first uses an upstream neural network to estimate pseudorange errors from a horizon of GNSS measurements and then feeds these estimates into a differentiable Moving Horizon Estimator to recover a trajectory, allowing end-to-end training on location losses. A key innovation is enabling learning from unlabeled data via Euclidean Distance Field supervision, which couples predicted trajectories to reference map routes without requiring precise ground truth. Evaluations on public benchmarks and real-time edge tests demonstrate state-of-the-art localization performance and practical feasibility for mobile devices.

Abstract

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.

Paper Structure

This paper contains 27 sections, 21 equations, 18 figures, 2 tables.

Table of Contents

  1. Introduction
  2. NeRC Design
  3. Upstream Network for Ranging Correction
  4. Downstream Location Estimator
  5. Structured Learning Mechanism
  6. Moving Horizon Estimation
  7. Differentiable Formulation of MHE
  8. Unification and Profiling
  9. Unification
  10. Forward profiling
  11. Forward profiling
  12. Backward profiling
  13. Training NeRC
  14. Supervised Learning
  15. Unleashing the Power of Unlabeled Data
  16. ...and 12 more sections

Figures (18)

  • Figure 1: (a) Pervasive multipath/NLOS-induced ranging errors in urban environment. (b) Ranging errors of visible satellites observed at the same site and time across multiple days.
  • Figure 2: Categories of data-driven ranging error regression
  • Figure 3: Performance of SOTA end-to-end methods in cities
  • Figure 4: Principle diagram of NeRC.
  • Figure 5: Principle diagram of differentiable MHE. It comprises three layers: the cost computation layer, the differentiable optimizer layer, and the state covariance update layer.
  • ...and 13 more figures