## 4 GNC/FDIR System Design and Analysis
### Navigation  
To ensure the general safe execution of close-proximity operations, the navigation needs to perform a relative position estimation even in the presence of environmental effects that may impact vision-based solutions, as formulated in [11], and summarized as follows:  
* During the Far Rendezvous Phase and within the AZ (including in the KOZ), the servicer must have on-board access to a continuous reliable estimate of the current relative client-servicer position;
* Relative navigation solutions should perform in the presence of external or self-inflicted sources, such as the presence of Earth or other bodies in the background, and different rendezvous illumination conditions.  
In CS-1, the Navigation system is designed to provide an accurate, continuous, and reliable estimate of the relative state of the servicer throughout all Rendezvous phases. The adopted architecture is depicted in Figure 7.  
Figure 6: Abort and Approach corridors, defined within the KOZ. The gray area denotes where an Abort is triggered, the green area denotes where a Cancel is triggered, and the blue area is where no recovery action is needed.  
Figure 7: Navigation system architecture.  
In particular, at far distances, a Narrow-Angle Camera (NAC) is used, facilitating angles-only navigation [28]. As the proximity to the client increases, radar measurements become available, augmenting navigation capabilities for an accurate 3D relative-state estimation. Finally, at close distance, the 6 DOF navigation is initialized using a Wide-Angle Camera (WAC), that allows the system to provide both the relative position and relative attitude estimation. This initialization is performed at the IPP.  
In Far Rendezvous, NAC line-of-sight measurements and Radar distance measurements are processed through a dynamical Kalman filter. The filter state definition is based on relative orbital elements [28], providing an estimate of the translational state.  
In Close Rendezvous, the WAC Pose Estimation provides 6D (relative position and attitude) measurements, processed through a second dynamical Kalman filter. The state definition of this second filter is adapted to short distances and is based on Clohessy-Wiltshire equations, which are a good approximation of the real relative dynamics in low eccentricity orbits [33].  
Therefore, the navigation solution has the necessary sensors to perform in the several operational conditions, to derive the relative position during client phasing, and to compute the relative estimate during Far and Close Rendezvous.  
In CS-1, a robustness against environment perturbations is anticipated in Mission Analysis. Both the navigation initialization and the guidance trajectories should satisfy constraints such as illumination conditions and the avoidance of Earth in the cameras' field of view, so that 6 DOF navigation is operational during the whole path towards the target.  
To this end, the elevation of the Sun in the orbital plane, usually called Beta Angle, is analyzed, together with Eclipse evolution. With a good knowledge of the elevation of the Sun in the orbit plane (Beta Angle) and eclipses cycle, then it is possible to design a trajectory that is compliant with good illumination and that does not have the Earth behind the client, for optimal navigation functioning.  
The analysis of the Beta Angle and of the Eclipse cycle is shown in Figure 8. The figure demonstrates that, for the capture time instant (the transition between the phasing red line and stack green line), the sun Beta Angle is high, and that the eclipse time is short enough to ensure that all capture operations are performed under proper illuminated conditions.  
Figure 8: Evolution of the predicted beta angle (**a**) and eclipse duration (**b**).  
The navigation operation within the complete GNC chain is tested through Monte Carlo campaigns in Section 5.