The challenges of positioning a cis-lunar spacecraft arise from the complex gravitational environment, combined with limited deep space tracking, telemetry, and command resources. These challenges can be addressed with a single-point positioning method based on tri-static common-view laser ranging. Our method enables rapid determination of the three-dimensional coordinates of spacecraft using simultaneous satellite laser ranging from three ground stations. We employ a synchronization and correction algorithm to process asynchronous multi-static observations, ensuring accurate data integration. The performance of the method is validated using real-world satellite laser ranging data from the LAGEOS-1 satellite, demonstrating a significant improvement in positioning accuracy, compared with the initial two-line element orbit. The correlation between the positioning error and the position dilution of precision factor leads to a linear empirical formula for error prediction. To investigate error trends, we simulated tri-static ranging scenarios for various cis-lunar orbits using a predefined station group. By fitting the resulting position dilution of precision data, we formulated the upper and lower error bounds of single-point positioning accuracy. The predicted accuracy range for lunar targets was 6.38 m to 446.46 m, and for L2 targets 7.55 m to 528.15 m. The accuracy of the single-point positioning is comparable with current deep space tracking, telemetry, and command technology, suggesting that tri-static laser ranging is an effective supplement to conventional systems. This method typically requires 15~minutes of data and delivers results in several seconds, and provides a new method for accurate positioning to support commercial lunar exploration.
Liang et al. (Thu,) studied this question.