A vectorial bootstrapping approach for integrated GNSS-based relative positioning and attitude determination of spacecraft

Traditionally in multi-spacecraft missions (e.g. formation flying, rendezvous) the GNSS-based relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibility to use multi-antenna data from each spacecraft, not only for attitude determination, but also to improve the relative positioning between spacecraft. Both for ambiguity resolution and accuracy of the baseline solution, we will show the theoretical improvement achievable as a function of the number of antennas on each platform. We concentrate on ambiguity resolution as the key to precise relative positioning and attitude determination and will show the theoretical limit of this kind of approach. We will use mission parameters of the European Proba-3 satellites in a software-based algorithm verification and a hardware-in-the-loop simulation. The software simulations indicated that this approach can improve single epoch ambiguity resolution up to 50% for relative positioning applying the typical antenna configurations for attitude determination. The hardware-in-the-loop simulations show that for the same antenna configurations, the accuracy of the relative positioning solution can improve up to 40%.