Estimation of 3D rotation for a satellite from Sun sensors

This paper exposes a method to estimate the rotation of a satellite by means of simple Sun sensors located on its surface. It is shown that a minimal setup of 4 sensors is sufficient to estimate the 3D rotation of the rigid body under some mild assumptions bearing on the inertia parameters of the body and the direction of the Sun. The method is a 3D generalization of an approach originally proposed, using the same setup of sensors, for a rotation restricted to take place about a single axis. Taking into consideration the 3D rotation, the estimation problem is geometrically recast into a simple sources separation problem for the measurement equation. This problem is shown to be feasible through a careful investigation of the free motion dynamics using Jacobi elliptic functions which guarantees sufficient frequency difference between the sources.