Relative navigation for satellites in close proximity using angles-only observations

In performing relative navigation for satellites in close proximity, two methods of observation are typically used. These are cameras and range sensors on the satellites. The problem that is examined here is a case where the only orbit determination tools are cameras. This means the only information known is the angles one satellite exhibits in the frame of the other, usually represented as a Line-Of-Sight (LOS) unit vector. Woffinden and Geller 1 stated that the unique relative orbit cannot be found using angles-only measurements when a linear model of relative motion is used to model the dynamics and there are no thrusting maneuvers, due to lack of observability. They showed that a family of trajectories whose state histories are proportional to one another (i.e. differ by only a constant scalar multiple) will possess a common LOS history. Figure 1 shows what is meant by a family of relative orbits. This implies that while the unique relative state cannot be determined, it should be possible to determine a basis vector for the trajectory. This can be thought of as the direction of the state vector, whereas its magnitude is unobservable. The goal of this paper is to develop a technique for determining the basis vector of a relative trajectory given angles-only measurements.