Relative and inertial attitude determination in three-vehicle long formations

This paper addresses a new attitude determination problem for formations. It considers a three-vehicle formation with relative and inertial measurements from sensors, where Constraints limit the relative measurements, which are not available between two of the vehicles, also known as deputies. The other vehicle is called the chief and does not have any limitation. Furthermore, each of the vehicles has an independent inertial measurement, whose references are known. The goal is to determine all attitude relations, both inertial and relative. The solution for this problem is divided into different stages. First, the relative attitude between the chief and the deputies is assessed, which results in two candidates for each of these relations. Then, each candidate yields a candidate for the inertial attitude of the chief. Next, comparing the four inertial candidates gives the solution for their respective relations and consequently for the relative relations as well. The remaining relations derive directly from those already known. The paper also provides some early insights about degeneracies, possible particular cases of the solution, and the effect of sensor noise. Finally, the solution is validated with a simulation, whose results are similar to attitude determination problems in constrained formations.