Dual Quaternion Matrices in Precise Formation Flying of Satellite Clusters

Dual quaternions are essential for the precise formation flying of satellite clusters and for the Relative Navigation and Positioning (RNP). In this paper, we investigate dual quaternion matrices within the contexts of the precise formation and the RNP. We begin by reformulating the graph model of the formation flying problem using dual quaternion unit gain graphs. Following this, we study the dual quaternion incidence matrix to characterize the balance of these unit gain graphs. We also show that the Perron-Frobenius theorem holds for balanced dual quaternion unit gain graphs. As an application, we study a pose graph optimal problem in the RNP.