Statistical Characterisation of GNSS Data for a Stationary Receiver using Non-Gaussian Distributions

Abstract

Accurately characterising datasets is crucial for effective statistical modelling, particularly when analysing Global Navigation Satellite System (GNSS) data. While traditional approaches often assume a Gaussian distribution, real-world GNSS datasets frequently exhibit heavy-tailed and skewed properties, prompting the need to explore alternative statistical models. The study examines the suitability of non-Gaussian distributions, specifically the Laplace, skew-normal, skew-t, and generalised hyperbolic (GH) distributions, for modelling GNSS data obtained from a stationary receiver. Using empirical GNSS datasets, we estimate parameters within confidence intervals (CIs) through weighted maximum likelihood estimation (WMLE). Model performance is assessed using log-likelihood analysis, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and root mean squared error (RMSE). Our comparative analysis  shows that heavy-tailed and skewed distributions, particularly those offering greater flexibility in capturing extreme deviations, consistently out-perform the conventional normal distribution. Among the non-Gaussian models considered, the GH distribution provides the best overall performance. These results emphasise the importance of selecting appropriate statistical models to improve uncertainty quantification in GNSS-based measurements.