IMPROVED MANEUVER-FREE APPROACH TO ANGLES-ONLY NAVIGATION FOR SPACE RENDEZVOUS

This work introduces a novel strategy for improving angles-only relative navigation for distributed space systems. Instead of relying on orbit or attitude maneuvers to reconcile the known observability issues, a rigorous state comparison and observability assessment is conducted to provide new insight into the benefits gained from improved dynamic and measurement modeling. First of all, a new method is described to derive a J(2)-perturbed state transition matrix in mean quasi-nonsingular relative orbit elements. In particular, Floquet theory is used to solve the resulting set of time-varying, periodic differential equations under the assumption of small state components. The presented formulation enables the seamless derivation of computationally efficient state transition matrices valid for different regimes of orbit eccentricity (from near-circular to arbitrary). Second, this research shows how the inclusion of nonlinearities in the measurement model vastly improves the condition number of the system's observability Gramian by increasing the accuracy of modeled bearing measurements. The results of this assessment lead to the design of a novel architecture for angles-only relative navigation which is comprised of an initial batch relative orbit determination algorithm used to initialize a sequential extended Kalman filter. The initialization method leverages the relative orbital element description to decouple the range uncertainty from the observable relative geometry, and a series of navigation filters are built using different combinations of the derived dynamics and measurement models. The prototype navigation algorithms are tested and validated in high-fidelity simulations which show that improved dynamics modeling has little effect on observability, whereas preserving nonlinearities in the measurement model reconciles the range ambiguity issues without necessarily requiring maneuvers.