Logistic-aided Huber M-estimator for robust GNSS positioning

TL;DR

This paper introduces a logistic-aided Huber M-estimator for robust GNSS positioning, improving accuracy and error spike suppression under long-tailed measurement errors by leveraging logistic error assumptions.

Contribution

It establishes a novel approximation linking logistic-based loglikelihood and Huber kernel, providing closed-form tuning rules for enhanced GNSS robustness.

Findings

LAH reduces 2D RMSE/STD by 28.03%/38.83% in simulations.

LAH decreases 3D RMSE/STD by 4.85%/16.68% in real-world data.

LAH suppresses large positioning error spikes by up to 51%.

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%.