# Design of Cislunar Navigation Constellation via Orbits with a Resonant Period
###### Abstract  
With the increasing number of cislunar space missions, real-time and reliable navigation and communication services have become critical. It is necessary to develop the navigation constellations dedicated to cislunar space services. However, there are plenty of orbits in cislunar space providing alternative orbits, which makes constellation design a challenging task. To address this, this paper proposes a method for a cislunar navigation constellations configuration design via orbits with resonant periods. First, a periodic orbit catalog for the Earth-Moon system is constructed. Baseline orbits are selected from different orbital families, and all resonant orbits with periods proportional to the baseline orbits are compiled into a resonant orbit set. Second, a Dilution of Precision (DOP) model for navigation performance and a spatial zoning model are established. Then, resonant orbital combinations are screened based on orbital type composition, followed by resonance constellation generation according to predetermined constellation scales. All constellation configurations are categorized by orbital type to obtain a full resonant constellation set. Finally, the proposed method is applied to design optimal configurations providing navigation services for near-Earth and lunar regions. The simulation results shows that constellations combining L2 southern/northern Near-Rectilinear Halo Orbits (NRHOs) with vertical orbits at L4/L5 points deliver the optimal navigation performance in cislunar regions. The relationships between orbital radius and DOP values in target areas, as well as the DOP evolution patterns over constellation periods, are analyzed. The mean DOP values of the optimal constellation in both the near-Earth region and the lunar region increase as the spatial radius expands. eurm-moon navigation constellation; three-body periodic orbits; resonant constellations; dilution of precision (DOP) analysis 2025154998  
18 April 202528 April 2  
operations, precise orbit determination [2; 3], asteroid detection [4; 5], and deep space exploration missions [6; 7; 8; 9]. Current deep space exploration missions predominantly rely on the existing ground-based Deep Space Network (DSN) infrastructure, while autonomous deep space navigation systems fall far short of the required precision levels [10; 11]. Moreover, surging mission demands risk overwhelming the DSN's operational capacity. This has intensified research into developing navigation and positioning systems for deep space missions through leveraging cislunar periodic orbits or lunar orbital architectures. [PERSON] et al. [12] first proposed deploying navigation and communication satellites at Earth-Moon libration points to construct constellations. [PERSON] et al. [13] analyzed the navigation and coverage capabilities of constellations near the Earth-Moon L2 point for lunar orbiters, demonstrating that four libration point satellites at L2 could achieve higher navigation accuracy than the Deep Space Network. [PERSON] and [PERSON] [14] introduced a Lunar Global Positioning System (LGPS) and Lunar Global Communication System (LGCS), utilizing Lissajous orbits at Earth-Moon L1/L2 points. [PERSON] [15] extended this work to Halo orbits, proposing LGPS architectures using northern/southern Halo orbit families near L1/L2. Chinese scholars have also contributed extensively to cislunar constellation research. [PERSON] et al. [16] suggested deploying cislunar communication constellations on retrograde periodic orbits near Earth-Moon L2/L3/L4/L5 points to achieve full coverage of Earth and lunar surfaces. [PERSON] and [PERSON] [17] conducted a comprehensive design and analysis of libration point navigation constellations, considering orbital selection, spatial coverage, Geometric Dilution of Precision (GDOP), signal transmission, and navigation accuracy.