# Exploiting Lunar Navigation Constellation for GNC Enhancement in Landing Missions
## 1 Introduction
[11] utilised a sequential Extended Kalman Filter (EKF) to highlight the system complexity benefits of implementing the LNS infrastructure over traditional visual-based navigation sensors and ground-tracking techniques. Their work revealed that a formal horizontal dilution of precision below 30 metres can be achieved with a minimum of three satellites in view. Another case study is provided by [12], where the LNS system is used coupled with a high-fidelity Digital Elevation Model (DEM) to navigate a rover under various service availability conditions. Conversely, ref. [13] employed a Batch filter to fuse LNS signals with IMU and altimeter readings, resulting in navigation errors below 30 metres. In both cases, the kinematic approach used for the estimation implies that navigation errors would rapidly diverge during signal outages. The advantages of a dynamic estimation process were discussed in [14; 15]. The attained performance significantly depends on the accuracy of the onboard dynamical model, necessitating precise Sun and Earth ephemerides and harmonic coefficients for the spherical expansion of the lunar gravity field. However, these demands might conflict with low-cost hardware and Commercial-Off-The-Shelf (COTS) components, especially when the filter must operate at high frequencies, which is why a proper navigation architecture is fundamental (see [16]). Comprehensive introductions to the dynamic state estimation theory, together with a description of the main algorithms and comparisons between sequential and batch filtering techniques, can be found in [17; 18; 19]. The current paper is intended as a continuation of a series of successive articles in the framework of lunar constellations. Indeed, the first two studies proposed a method to design an LNS constellation to provide communication and navigation services to different users, optimising the orbital configuration considering multiple objectives. In particular, in [20] we focused on surface users only, and multi-objective optimisation was used to service different Moon regions. Then, in [14], we focussed our attention on orbital users in polar inclinations. Also in this case, an optimisation combining different clashing objectives was performed in order to derive optimal constellation architectures. The deriving navigation performance for the orbital user was assessed in accordance with a proposed filtering architecture, which has been tested under different conditions also in [16]. From the set of optimal configurationsextracted in [14], the best performing one was selected to be used for further assessments, such as in this current work. In our previous analyses and in the investigated literature, however, only the navigation task was taken into consideration. Even the works concerning landers or rovers considered the dynamics of the user as defined independently from the navigation tasks, thus excluding a complete GNC scheme. The goal of this paper is to evaluate the behaviour of the LNS architecture when inserted into a more dynamically challenging scenario. Indeed, testing the final performance of the GNC in closed loop provides a testbed to understand if, even with a reduced constellation, the critical tasks of a landing operation can be completed successfully. In particular, the main braking phase of the landing is considered here, as the last phase in a landing which could be handled with an absolute navigation strategy, before handover to a relative one for the final (or terminal) descent. The results in a nominal scenario are presented, after the description of the added guidance and control algorithms are provided. After that, a Monte Carlo analysis with dispersion in the initial state is performed and the overall results collected. After this introduction, the complete modelling environment used for spacecraft dynamics and sensor simulation is presented in Section 2. The description of the core of the employed GNC algorithms is provided in Section 3.