Analysis of Autonomous Orbit Determination for LEO-Earth-Moon DRO Constellation Using Time-Delayed Inter-satellite Ranging Observation

To address the demand for autonomy and high precision in cislunar space navigation, this study focuses on a heterogeneous constellation composed of Low Earth Orbit (LEO) satellites and Earth-Moon Distant Retrograde Orbit (DRO) satellites. The theoretical method for differential correction of DRO orbits under the Circular Restricted Three-Body Problem (CR3BP) is introduced. In the Barycentric Celestial Reference System (BCRS), a combined observation model for Dual One-Way Ranging (DOWR) is established, and the clock biases caused by light-time delay and general relativistic effects are quantitatively analyzed. Based on numerical simulations, the impact of different uplink-downlink observation intervals on the autonomous orbit determination accuracy of the LEO-Earth-Moon DRO constellation is investigated under non-instantaneous observation conditions. The simulation results show that: (1) In the cislunar space environment, the ranging error in DOWR caused by general relativistic effects reaches the order of 5−30 ns, which is an error term that must be corrected. (2) Autonomous orbit determination for the LEO-Earth-Moon DRO constellation can be achieved using only DOWR observations. Specifically, the three-dimensional positioning accuracy of LEO satellites is better than 10 m. For DRO satellites, the accuracy is better than 50 m, with errors primarily concentrated in the orbital normal direction, while radial and tangential accuracies can reach the meter level in some arc segments. (3) Within the range of 0−20 seconds for uplink-downlink observation time intervals, extending the interval can improve system observability. However, due to the short duration of the interval, the improvement is limited, and the enhancement of overall autonomous orbit determination accuracy is not significant. The accuracy of different schemes is comparable. These results indicate that, subject to maintaining measurement accuracy, the temporal constraints on uplink-downlink observation intervals for the LEO-Earth-Moon DRO constellation orbit determination system can be relaxed. This relaxation contributes to enhanced system robustness and operational redundancy. This study validates the feasibility of high-precision autonomous navigation for LEO-Earth-Moon DRO heterogeneous constellation in cislunar space, providing a theoretical basis and technical reference for the design of future cislunar navigation constellations.