Robust Statistics vs. Machine Learning vs. Bayesian Inference: Insights into Handling Faulty GNSS Measurements in Field Robotics

TL;DR

This paper tackles the challenge of faulty GNSS measurements in field robotics by evaluating three robust paradigms: M-estimators for robust error weighting, learning-based outlier prediction, and online variational Bayesian inference for noise distribution modeling. It leverages a continuous-time factor-graph fusion framework and real-world datasets to compare these approaches under varying LOS/NLOS and urban multipath conditions. Key findings indicate that soft-redescending M-estimators (e.g., Cauchy, GM) offer favorable robustness-efficiency trade-offs, while learning-based methods excel in pre-processing tasks like NLOS detection and fault prediction, though generalization across environments remains nontrivial. The variational MH-GMM approach with MPMA demonstrates substantial accuracy gains, but challenges with trajectory smoothness and online adaptation persist, motivating future work on local versus global models and online tuning for robust, long-term GNSS-based localization.

Abstract

This paper presents research findings on handling faulty measurements (i.e., outliers) of global navigation satellite systems (GNSS) for vehicle localization under adverse signal conditions in field applications, where raw GNSS data are frequently corrupted due to environmental interference such as multipath, signal blockage, or non-line-of-sight conditions. In this context, we investigate three strategies applied specifically to GNSS pseudorange observations: robust statistics for error mitigation, machine learning for faulty measurement prediction, and Bayesian inference for noise distribution approximation. Since previous studies have provided limited insight into the theoretical foundations and practical evaluations of these three methodologies within a unified problem statement (i.e., state estimation using ranging sensors), we conduct extensive experiments using real-world sensor data collected in diverse urban environments. Our goal is to examine both established techniques and newly proposed methods, thereby advancing the understanding of how to handle faulty range measurements, such as GNSS, for robust, long-term vehicle localization. In addition to presenting successful results, this work highlights critical observations and open questions to motivate future research in robust state estimation.

Figures (7)

• Figure 1: GNSS delays and interference.
• Figure 2: Learning models studied in this work.
• Figure 3: Concept of nested estimation with noise model update using variational Bayesian inference following phd_Pfeifer.
• Figure 4: Results of pseudorange error prediction of all models using the HK data.
• Figure 5: Feature Permutation Importance for NLOS classification (reproduced from te_lstm).