Single point positioning of cis-lunar spacecraft with tri-static common view laser ranging

The challenges of positioning a cis-lunar spacecraft arise from the complex gravitational environment and limited deep space tracking, telemetry and command (TT&C) resources. To address these challenges, this paper proposes a single point positioning (SPP) method based on tri-static common-view laser ranging. Our method enables the rapid determination of the 3D coordinates of spacecraft through simultaneous satellite laser ranging (SLR) from three ground stations. A synchronization and correction algorithm is developed to process asynchronous multi-static observations, ensuring accurate data integration. The performance of the method is validated using real-world SLR data from the LAGEOS-1 satellite, demonstrating a significant improvement in positioning accuracy compared to the initial Two-Line Element (TLE) orbit. The correlation between the positioning error and the Position Dilution of Precision (PDOP) factor lead 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 PDOP data, we formulated the upper and lower error bounds of SPP accuracy. The predicted accuracy range for lunar targets was 6.4 m to 446.5 m, and for L2 targets 7.5 m to 528.2 m. Regarding the SPP ability, the accuracy is comparable to current deep space TT&C technology, implying the tri-static laser ranging as an effective supplement to conventional system. The method typically requires 15 minutes of data and delivers results in several seconds. It provides a new technology for accurate positioning to support commercial lunar exploration.