Optimized Selection of Satellite Subsets for a Multi-Constellation GBAS

In the next generation of Ground Based Augmentation System (GBAS) corrections and integrity parameters for two frequencies and multiple constellations will be provided. However, the capacity of the VDB (VHF Data Broadcast) link providing those parameters to users is strongly limited. Thus providing all those new corrections and parameters would either require a longer update rate of corrections or a limitation on the number of satellites to which corrections are provided. In this paper we propose a new satellite selection method which allows fast selection of a variable sized, quasi-optimal subset of all visible GNSS satellites. The proposed selection heuristic bases on a strong correlation between the third (i. e. vertical) component inside the S -matrix for each satellite and the probability of the related satellite being part of a subset which provides a favorable vertical protection level. Utilizing this correlation we design an algorithm which converges fast and leads to optimal results for a majority of constellations. As the selection can be performed for an arbitrary number of satellites and the complexity is not exponentially scaling with the number of available satellites, as an exhaustive search (brute-force) does, the heuristic is flexible and suitable for different applications even beyond GBAS's. In the context of GBAS these subsets still provide reliable protection levels as the contribution to the accuracy is dropping with every additional satellite. We show the feasibility of using for instance only 14 satellites in global protection level simulations. In a multi-frequency multi-constellation GBAS architecture the approach of selecting only an optimal subset allows to keep the current 2 Hz update rate. This could mitigate problems with VDB capacity or remove the necessity of additional, more frequent integrity messages.