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

Haoming Zhang

TL;DR

The paper tackles robust vehicle localization under GNSS outliers and non-Gaussian noise typical of urban canyons. It combines continuous-time factor graph optimization with learning-based components: a TE-LSTM for offline outlier (NLOS) detection and an online variational Bayesian GMM to approximate pseudorange noise, all within a generalized multisensor state estimator. Key contributions include a sensor-agnostic, time-centric FGO using Gaussian-process trajectory representations, the TE-LSTM architecture for NLOS detection, and online GMM adaptation integrated into the optimization, with empirical validation in urban campaigns showing improved robustness and accuracy. The work sets the stage for a federated framework that jointly leverages offline and online learning for robust, scalable GNSS-based localization in challenging environments.

Abstract

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.

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

TL;DR

The paper tackles robust vehicle localization under GNSS outliers and non-Gaussian noise typical of urban canyons. It combines continuous-time factor graph optimization with learning-based components: a TE-LSTM for offline outlier (NLOS) detection and an online variational Bayesian GMM to approximate pseudorange noise, all within a generalized multisensor state estimator. Key contributions include a sensor-agnostic, time-centric FGO using Gaussian-process trajectory representations, the TE-LSTM architecture for NLOS detection, and online GMM adaptation integrated into the optimization, with empirical validation in urban campaigns showing improved robustness and accuracy. The work sets the stage for a federated framework that jointly leverages offline and online learning for robust, scalable GNSS-based localization in challenging environments.

Abstract

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.

Paper Structure

This paper contains 9 sections, 3 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Multisensor Fusion
  3. Outlier Rejection
  4. Robust Error Modeling
  5. Learning-based Methods
  6. Continuous-Time Factor Graph Optimization
  7. Offline Learning for Outlier Prediction
  8. Online Learning for Noise Distribution Approximation
  9. Conclusion and Future Work

Figures (3)

  • Figure 1: Schema of all proposed methods embedded in an embodied system, where the red contents indicate future work.
  • Figure 2: Vehicle Localization in Urban Area in Düsseldorf with NLOS Exclusion. The GNSS reference solution is shown in blue. a) presents the estimated trajectory without NLOS exclusion and the solution by fusing GNSS observations and lidar odometry in a tight coupling (Section \ref{['sec: fgo']}). b) and c) illustrate the estimated trajectories with NLOS exclusion using different learning models.
  • Figure 3: Demonstration of the online-approximated GMM distributions for different satellites while driving through a tree-rich area in Aachen.