# Autonomous and Earth-Independent Orbit Determination for a Lunar Navigation Satellite System
## 1 Introduction  
The Moon is going to be very busy over the next decade [1; 2; 3]. In response, major international space players have proposed infrastructure to deliver communication and navigation services to satisfy increasing demand. These include LunaNet by NASA [4], Moonlight from ESA [5], and the Lunar Communication and Navigation Service (LCNS) from JAXA [6]. The performances required by users of this system are demanding, especially in terms of orbit determination, timing, data rates, and others. For LCNS, ten small satellites are being considered, where it is possible to maintain an orbit that meets positioning requirements with minimal orbit maintenance over 3 years [7]. A key performance criterion is an orbit determination accuracy of below 30 m [6], with each satellite transmitting a pseudo-like ranging signal to ground users, to deliver a surface positioning accuracy of 40 m. This performance target is feasible through the use of Earth-based tracking stations, where lunar pathfinder missions have delivered performances below 40 m in three dimensions [8]. However, the use of deep-space tracking networks is expensive, and they have infrequent visibility and a high user demand. They also create a strict dependence on distant Earth-based infrastructure. As an LCNS by any space agency is a critical system for the successful delivery of an increasing number of future lunar missions, orbit determination must be more autonomous. However, meeting this performance is challenging with the current state of the art. Various architectures have been evaluated to deliver this capability. A majority seek to utilize a high-sensitivity Global Navigation Satellite System (GNSS) receiver, relying on the side-lobes of Earth-based GNSS for operation [5; 9]. However, performances areexpected to reach only several 100 m with intermittent availability. A high-sensitivity antenna is also needed with high-pointing requirements to deliver these performances. No successful position fix has been announced yet from recently launched lunar-destined GNSS receivers [10]. Alternative architectures for lunar navigation include using the limb's horizon. This will be demonstrated for satellites in cislunar space, such as Orion [11] and LUMIO [12]. Performances of these instruments alone might only reach up to 1-10 km. Other scenarios have also been studied [13; 14; 15; 16], but most mission concepts have only treated cislunar operations or descent and landing. Fused navigation for a lunar repeating orbit satellite has been considered in [17], where a combination of a horizon-sensing optical navigation unit and a GNSS receiver is treated for a satellite in Near Rectilinear Halo Orbit (NRHO). Estimates at 200 m are expected, but not yet meeting the threshold of 40 m. This result also assumes that the GNSS receiver is measurable and available for all visible periods in NRHO [5]. To aid this estimate, assistance by Inter-Satellite Links (ISLs), a relative positioning method that may only be used in combination with an absolute sensor source, such as GNSS, is proposed [18], achieving an orbit determination performance of 100 m. However, this is still insufficient for the target of JAXA. Some methodologies, such as LiAISON [19], use ISLs between very different orbit and ground surface trajectories. Gravitational asymmetries between the trajectory path of each object provide sufficient absolute information to the Moon's centre for the solution to successfully converge inside a Kalman filter. Such spacecraft may be in lunar or Halo orbits, landing on the Moon or roving the surface. However, this may only work for a dedicated mission architecture that accounts for this variability between vehicles. This work considers fused optical observations, including the lunar horizon, craters, and distant celestial sources, alongside potential inter-satellite links.