A general extreme value-based Gaussian global navigation satellite systems measurement error distribution for mission-critical applications

Abstract Global Navigation Satellite Systems (GNSS) positioning and integrity monitoring models and algorithms currently generically assume that measurement errors follow a Gaussian distribution. As this is not always the case, there is a trade-off affecting system safety and availability, emphasising the need for better error characterisation in mission-critical applications. Research to date has shown advantages of Generalised Extreme Value (GEV) distribution for mapping extreme events. However, it is more complex than the Gaussian distribution, especially in the error convolution process. This paper derives a distribution, referred to as the GEV-based Gaussian distribution , that benefits from the advantages of both the GEV and Gaussian distributions in mapping extreme events and simplicity, respectively. The proposed distribution is tested against Gaussian, GEV and Generalised t distribution. The results show that the proposed distribution can provide a better bound for extreme events than the tested distribution both for pseudorange and carrier phase errors.