SCIENCE CHINA Physics, Mechanics & Astronomy © Science China Press and Springer-Verlag Berlin Heidelberg 2010 phys.scichina.com www.springerlink.com *Corresponding author (email: liuqh@shao.ac.cn) †Recommended by ZHAO Ming  Research Paper  March 2010 Vol.53 No.3: 571–578 doi: 10.1007/s11433-010-0147-5 Relative position determination of a lunar rover using high-accuracy multi-frequency same-beam VLBI † LIU QingHui 1* , CHEN Ming 1 , XIONG WeiMing 2 , QIAN ZhiHan 1 , LI JinLing 1 , HAO WangHong 1,4 , WANG GuangLi 1 , ZHENG WeiMin 1 , GUAN Di 3 , ZHU RenJie 1 , WANG WeiHua 1 , ZHANG XiuZhong 1 , JIANG DongRong 1 , SHU FengChun 1 , PING JinSong 1 & HONG XiaoYu 1 1 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; 2 Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190, China; 3 Lunar Explorer Engineering General Department, Chinese Academy of Sciences, Beijing 100012, China; 4 Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China Received December 31, 2009; accepted January 9, 2010 Multi-frequency same-beam VLBI means that two explorers with a small separation angle are simultaneously observed with the main beam of receiving antennas. In the same-beam VLBI, the differential phase delay between two explorers and two re- ceiving telescopes can be obtained with a small error of several picoseconds. The differential phase delay, as the observable of the same-beam VLBI, gives the separation angular information of the two explorers in the celestial sphere. The two-dimensional relative position on the plane-of-sky can thus be precisely determined with an error of less than 1 m for a distance of 3.8×10 5 km far away from the earth, by using the differential phase delay obtained with the four Chinese VLBI stations. The relative position of a lunar rover on the lunar surface can be determined with an error of 10 m by using the differential phase delay data and the range data for the lander when the lunar topography near the rover and the lander can be determined with an error of 10 m. same-beam VLBI, differential phase delay, relative position determination, lunar rover PACS: 95.55.Pe, 95.10.Eg, 95.55Jz, 95.10.Jk, 95.55.Br 1 Introduction The moon, which is 3.8×10 5 km far away from the earth averagely, is an ideal springboard and transfer platform for human’s deep space exploration and expansion towards the outer space. The first Chinese lunar explorer, CE-1, was launched on October 24, 2007. According to the long-term schedule, Chinese unmanned lunar exploration plan was divided into three stages: orbiting, landing and returning stages [1]. In the orbiting stage, the CE-1 and CE-2 satel- lites fly around the Moon and take photos about the landing area. In the landing stage, the main task is to softland on the lunar surface and to explore automatically. A lunar lander and a rover are needed in this stage. In fact, SELENE-2, a Japanese lunar project, which consists of three explorers, an orbiter, a lander and a rover, will also be launched in the near future [2]. For the tracking and controlling system, the most obvious difference between the landing stage and the orbiting stage is that multi-explorer must be simultaneously tracked and controlled. For example, there is a problem that is how to precisely determine the relative position of a rover and a lander in the landing stage. In order to determine the position or the orbit of explor- ers, the conventional methods are to measure range, Dop- pler, and angle. In deep space exploration, VLBI (Very Long Baseline Interferometry) is a precise method for the angle measurement. VLBI can give the plane-of-sky posi-