Impact of non-Gaussian noise on position accuracy provided by Global Navigation Satellite Systems (GNSS)

Accurate positioning obtained from the Global Navigation Satellite System (GNSS) is crucial for many applications; however, environmental and instrumental factors, such as satellite geometry, signal multipath, and atmospheric delays, often degrade its accuracy. Traditional uncertainty quantification and filtering methods, such as the Kalman Filter (KF), assume that the measurement noise follows a Gaussian distribution. In practice, real-world GNSS data often violate this assumption, showing skewness, heavy tails, and outliers that distort the estimates and reduce the accuracy. This study systematically evaluates the impact of non-Gaussian noise on GNSS positioning accuracy and introduces a unified framework that integrates robust statistical methods and nonlinear filtering. Specifically, we compared the performance of the KF, Median Absolute Deviation (MAD), and Particle Filter (PF) on stationary GNSS data. The evaluation used comprehensive accuracy and uncertainty diagnostics, including the root mean square error (RMSE), probable circular error (CEP), estimated position error at 95% (R95), covariance analysis, and nonparametric bootstrapping. The results demonstrate that Gaussian-based models fail under heavy-tailed noise, whereas MAD and PF achieve superior reliability by suppressing outlier influence and capturing complex error distributions. The proposed framework advances GNSS uncertainty quantification by bridging robust statistics and nonlinear filtering. It offers a statistically sound and practical approach for real-world environments in which non-Gaussian noise is prevalent.