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%.

翻译：本文提出了一种Logistic辅助的Huber（LAH）M-估计器，用于在长尾、多路径影响的测量误差下实现鲁棒GNSS定位。核心思想是利用Logistic测量误差假设，并通过匹配其得分函数，在基于Logistic的对数似然（即准log-cosh函数）与Huber核之间建立一一对应近似关系。由此导出了基于Logistic误差统计特性的Huber估计器中尺度参数与阈值参数的闭式调优规则。我们进一步证明，所提出的LAH估计器在与相关的基于Logistic的最小准log-cosh（LQLC）估计器相比时，保持了可比的效率与鲁棒性。基于长尾测量误差的蒙特卡洛仿真以及一小时的城区GNSS数据集均证实，基于Logistic统计的调优方法在抑制大幅误差尖峰的同时，提升了定位精度与准确度。具体而言，在仿真中，相较于传统的基于95%效率的Huber调优，LAH将二维RMSE/STD分别降低了28.03%/38.83%；在实际实验中，将整体三维RMSE/STD分别降低了4.85%/16.68%，同时将大幅定位误差尖峰抑制了高达51%。