Objectives Aiming at significant systematic errors and serious coordinate coupling in the traditional deep-space network measurement for lunar lander positioning, a joint orbit determination and positioning method for lunar relay satellites and lunar probes is proposed. Based on four-way relay measurement, the proposed method fuses local and global parameters, thereby breaking the accuracy bottleneck of lunar positioning.

Methods We elaborate the application principle of four-way relay measurement data in joint orbit determination and positioning, and quantitatively analyze its potential in improving positioning accuracy. A local-global parameter fusion optimization scheme is constructed to make full use of long-term observation data and realize the global optimal estimation of parameters to be solved. Simulation tests are designed to compare the orbit determination and positioning performance of lunar landers under independent and alternating observation modes. Moreover, the observation geometry and tracking arc differences caused by different landing areas are analyzed.

Results Four-way relay measurement effectively suppresses system errors and coordinate coupling existing in traditional ground-based ranging. The local-global parameter fusion strategy improves the utilization efficiency of observation data and speeds up parameter convergence. Alternating observation mode significantly improves the accuracy of relay satellite orbit determination and lander positioning compared with independent observation. Different landing regions lead to different observation geometries, which bring measurable differences in final orbit determination and positioning accuracy. With the increase of observation arc segments, lander positioning accuracy gradually stabilizes at the meter level.

Conclusions The proposed joint orbit determination and positioning method provides an effective technical solution for high-precision orbit control and precise landing positioning of lunar probes. Four-way relay measurement and alternating observation mode optimize observation geometry and shorten the parameter convergence period. Regional differences among landing sites should be fully considered in mission design. This method can be extended to more complex deep-space exploration scenarios, and supports the construction of high-precision lunar telemetry, tracking and command networks and fine-scale lunar surface positioning.