Observability Criteria for Angles-Only Navigation

The possibility of implementing angles-only navigation for orbital rendezvous, satellite formation flight, and other relative motion applications possesses great potential that is often discarded because of its inherent and misunderstood limitation in determining range. To formally characterize the conditions required for observability, an analytical expression for the observability criteria for angles-only navigation is derived. As anticipated, the criteria clearly shows that with angle measurements alone, the relative position and velocity cannot be determined for systems with linear dynamics. However, with a calibrated thrust maneuver, observability can be guaranteed for all possible relative trajectories. The solution, intended for relative orbital motion scenarios, is also valid for any system with linear dynamics and line-of-sight (LOS) measurements. An intuitive graphical interpretation is also provided along with several examples related to orbital rendezvous. The derived analytical observability criteria can be extended to include nonlinear systems. It can also be used to derive optimal maneuvers to maximize observability and determine the degree of detectability for a selected relative trajectory when sensor noise is considered.