This paper focuses on assessing the precision of carrier phase relative positioning using GPS-only, BDS-only and GPS/BDS measurements. A zero baseline is used in order to achieve this. Software for GPS and BDS processing has been developed, allowing static and kinematic data processing, as well as the combined GPS and BDS processing. Ionospheric and tropospheric delays are significantly reduced by double differencing between satellites and receivers, but the Multipath signals are still a major source of error for the various general GNSS baseline applications. In this paper, two Multi-GNSS receivers are connected to one antenna by an antenna splitter. This strategy results in all the delays or errors being mitigated, leaving only the random measurement noises resulted from the double difference processing. The time series of the final baseline error reveal that both GPS and BDS can achieve a precision of millimetres, but GPS performs better than BDS. Results from the combined processing of GPS and BDS demonstrate that the integration of GPS and BDS can significantly improve the precision, compared with the GPS-only and BDS-only results.