The Precise Positioning of Lunar Farside Lander Using a Four-Way Lander-Orbiter Relay Tracking Mode

China is planning to land a spacecraft on the farside of the Moon, a premiere, by 2018. In essence, the traditional tracking modes, based on direct visibility, cannot operate for the lunar farside lander tracking, and therefore a relay satellite, visible at the same time by both the lander and the Earth, will be required, operating in the so-called four-way mode (Earth-relay satellite-lander-relay satellite-Earth). In this paper, we firstly give the mathematical formulation of the four-way relay tracking mode and of its partial derivatives with respect to the relevant parameters, implemented in our POD software WUDOGS (Wuhan University Deep-space Orbit determination and Gravity recovery System). In a second step, in simulation mode, we apply this relay mode to determining lander coordinates, which are absolutely needed for a sample return mission, or to add constraints on rotation models of the Moon. The results show that with Doppler measurements at a 0.1 mm/s error level, the positioning of the farside lander could be done at centimeters level (1-\(\delta\)) in the case of a circumlunar relay satellite; and at a 5 meters level (1-\(\delta\)) in the case of a Lagrange point (L2) Halo relay satellite.