Error analysis of same-beam differential VLBI technique using two SELENE satellites

The Japanese SELENE project consists of a main satellite, a relay sub-satellite (Rstar), and a VLBI sub-satellite (Vstar). Rstar will relay the Doppler ranging signal between the main satellite and the ground station for the world's first direct measurement of the gravity field on the far side of the Moon. The differential VLBI radio sources onboard Rstar and Vstar will be used to determine the gravity field of the Moon precisely, especially near the rim. Rstar and Vstar only transmit three pairs of carriers in the S-band and one pair of carriers in the X-band, and the difference in phase delays of Rstar and Vstar will be obtained from the relation between correlation phase and frequency of four pairs of carriers. In particular, the difference in correlation phase at each frequency has to be estimated without the 2π ambiguity, and this imposes strict conditions; e.g., the correlation phase error must be lower than 4.3° and the error of differences in total electron content in the ionosphere must be less than 0.23 TECU. To resolve the 2π ambiguity problem, we use the same-beam differential VLBI technique, in which Rstar and Vstar are simultaneously observed by using the same beam of the receiving antenna. In this case, the influences of the atmosphere, ionosphere, and receivers can nearly be canceled in the difference in correlation phases, the difference in delay can be obtained with an accuracy of several picoseconds from the correlation phases, and the relative positions of Rstar and Vstar can be determined with a very high sensitivity (tens of cm). In this paper, we estimate the chance for same-beam differential VLBI observations in SELENE. We give a procedure and conditions for the obtaining differential phase delay, and predict the measurement errors in same-beam differential VLBI by using GPS techniques and by observing three satellites, Shuangxing, Geotail, and a geostationary satellite.