Gaussian-Pareto overbounding of DGNSS pseudoranges from CORS

This paper presents a novel approach for overbounding unknown distribution functions called the Gaussian-Pareto overbounding. This extends the current practice of using Gaussian distributions for overbounding, but combines it with methods from Extreme Value Theory for modeling tails. Hence, this approach uses a Gaussian distribution to overbound the core of the distribution and generalized Pareto distributions for the tails. Furthermore, this approach is applied to Differential Global Navigation Satellite System (DGNSS) pseudorange data collected from two Continuously Operating Reference Stations (CORS) and compared to Gaussian overbounding. It is shown that Gaussian-Pareto Overbounding more closely matches the empirical distribution than the simpler Gaussian overbounding approach in the case where there is significant heavy-tailedness of DGNSS data. This approach also highlights the ability of the flexible Gaussian-Pareto model to become less conservative in the tail region as more data is collected.