# Learning-based GNSS Uncertainty Quantification using Continuous-Time Factor Graph Optimization

arXiv: https://arxiv.org/abs/2503.04933 · HTML: https://mlsanity.com/paper/2503.04933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping](https://mlsanity.com/paper/2007.00258/) (2020)
- [Super Odometry: IMU-centric LiDAR-Visual-Inertial Estimator for Challenging Environments](https://mlsanity.com/paper/2104.14938/) (2021)
- [GVINS: Tightly Coupled GNSS-Visual-Inertial Fusion for Smooth and Consistent State Estimation](https://mlsanity.com/paper/2103.07899/) (2021)
- [Graph-based Multi-sensor Fusion for Consistent Localization of Autonomous Construction Robots](https://mlsanity.com/paper/2203.01389/) (2022)
- [Tightly-coupled Fusion of Global Positional Measurements in Optimization-based Visual-Inertial Odometry](https://mlsanity.com/paper/2003.04159/) (2020)
- [GNSS/Multi-Sensor Fusion Using Continuous-Time Factor Graph Optimization for Robust Localization](https://mlsanity.com/paper/2309.11134/) (2023)
- [Learning-based NLOS Detection and Uncertainty Prediction of GNSS Observations with Transformer-Enhanced LSTM Network](https://mlsanity.com/paper/2309.00480/) (2023)
- [GNSS Outlier Mitigation Via Graduated Non-Convexity Factor Graph Optimization](https://mlsanity.com/paper/2109.00667/) (2021)
- [Rail Vehicle Localization and Mapping with LiDAR-Vision-Inertial-GNSS Fusion](https://mlsanity.com/paper/2112.08563/) (2021)
- [Uncertainty-aware Gaussian Mixture Model for UWB Time Difference of Arrival Localization in Cluttered Environments](https://mlsanity.com/paper/2307.16848/) (2023)

## Abstract (arXiv)

This short paper presents research findings on two learning-based methods for quantifying measurement uncertainties in global navigation satellite systems (GNSS). We investigate two learning strategies: offline learning for outlier prediction and online learning for noise distribution approximation, specifically applied to GNSS pseudorange observations. To develop and evaluate these learning methods, we introduce a novel multisensor state estimator that accurately and robustly estimates trajectory from multiple sensor inputs, critical for deriving GNSS measurement residuals used to train the uncertainty models. We validate the proposed learning-based models using real-world sensor data collected in diverse urban environments. Experimental results demonstrate that both models effectively handle GNSS outliers and improve state estimation performance. Furthermore, we provide insightful discussions to motivate future research toward developing a federated framework for robust vehicle localization in challenging environments.