Logistic-aided Huber M-estimator for robust GNSS positioning

2026-03-20

AI Summary

This work addresses the robustness of GNSS positioning under long-tailed error distributions and multipath interference by proposing a Huber M-estimator grounded in a logistic error assumption. By analytically aligning the score function of the logistic log-likelihood with that of the Huber loss, the study establishes, for the first time, a closed-form relationship between the two, yielding explicit tuning rules for the scale and threshold parameters. This enables automatic, efficient, and robust parameter adaptation without compromising computational efficiency. Experimental results demonstrate significant improvements in positioning accuracy: in simulations, 2D RMSE and standard deviation are reduced by 28.03% and 38.83%, respectively; in real-world tests, 3D RMSE and standard deviation decrease by 4.85% and 16.68%, with large-error outliers suppressed by up to 51%.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper develops a logistic-aided Huber (LAH) M-estimator for robust GNSS positioning under long-tailed, multipath-affected measurement errors. The key idea is to leverage a logistic measurement error assumption and establish a one-to-one approximation between the logistic-based loglikelihood (i.e., quasi-log-cosh) and the Huber kernel by matching their score functions. This yields closed-form tuning rules for the scale and threshold parameters in the Huber estimator, grounded on logistic error statistical properties. We further show that the proposed LAH estimator preserves comparable efficiency and robustness to the connected logistic-based least quasi-log-cosh (LQLC) estimator. Both Monte Carlo simulations with long-tailed measurement errors and a one-hour urban GNSS dataset confirm that the proposed logistic-statistics-based tuning improves positioning accuracy and precision while suppressing large error spikes. Specifically, LAH reduces the 2D RMSE/STD by 28.03%/38.83% versus conventional 95%-efficiency-based Huber tuning in simulation, and reduces the overall 3D RMSE/STD by 4.85%/16.68% in real-world experiments while suppressing large positioning error spikes by up to 51%.

Problem

• robust GNSS positioning
• long-tailed errors
• multipath
• measurement error
• outlier suppression

Innovation

• Logistic-aided Huber
• robust GNSS positioning
• M-estimator
• long-tailed errors
• closed-form tuning