Upper bound estimation of positioning error for ground-based augmentation system

Ground-based augmentation systems (GBAS) calculate protection levels (PL), which are bounds of the GBAS positioning errors associated with given integrity levels. In practice, PLs calculated using a Gaussian overbound method tend to be overestimated when the actual (non-Gaussian-distributed) GBAS ranging errors exhibit heavy tails. We propose a stable distribution-based method to overcome this problem. The heavy-tailed stable distribution gives a more appropriate representation of the GBAS ranging error. Based on a symmetric stable distribution, the overbound of the GBAS ranging error is estimated using numerical computations. The stable overbound can tightly bound both the core and the tails of the GBAS ranging error. The PL calculated using this stable overbound is less conservative than that calculated using the Gaussian overbound, although both methods have similar computational complexity. A performance evaluation based on simulated measurements collected from a GBAS prototype shows that the proposed approach increases the availability of GBAS.