Analysis of Fitting GNSS Data Provided by Stationary Receiver to Non-Gaussian distributions

Understanding dataset characterisation is fundamental to achieving accurate statistical modelling, particularly in the context of Global Navigation Satellite System (GNSS) data analysis. GNSS data exhibit heavy-tailed and skewed distributions, prompting this study to evaluate non-Gaussian models (Cauchy, Student's t, lognormal, skew-normal) in modelling GNSS data collected from a stationary receiver. This study uses maximum likelihood estimation for parameter estimation with a confidence interval. It evaluates the model's performance using log-likelihood analysis, the Akaike Information Criterion, the Bayesian Information Criterion, and the Root Mean Squared Error. The comparative assessment of these models highlights that lognormal and skew-normal outperform in capturing extreme deviations and provide a better fit than the normal distribution. These findings underscore the importance of selecting appropriate statistical models to enhance uncertainty quantification in GNSS-based measurements.