Autonomous orbit determination (AOD) based on inter-satellite link (ISL) measurements may lead to the dilution of constellation datum performing constellation rotation and drift. Thus, the maintenance of constellation space datum is the main purpose and one of the core problems of AOD. This paper mainly discusses the maintenance of coordinate system for satellite AOD, and systematically analyzes the estimation method of satellite orbit parameters and the maintenance of the datum under different observation modes using ground-satellite link (GSL) measurements, combined measurements (GSL and ISL measurements), and ISL measurements, respectively. The concepts of "strong datum" and "weak datum" are proposed. The "strong datum" means that the datum of satellite constellation provided by AOD method aligns to the datum of the exis-ting datum of ground stations with good precision using GSLs or combined measurements (ISLs and GSLs). The "weak datum" means that the ISL-only measurements are employed in AOD method but the parameter estimation is constrained with a priori orbit information, and the satellite constellation datum is consistent to the geometric gravity center of the constellation corresponding to satellite a priori orbits. The "strong datum" uses all kinds of observations in inter-satellite and ground-satellite observation networks. The result is stable and reliable. The "weak datum" maintains space datum reliably without ground-based observations, but with a priori satellite orbits which is achieved through precise orbit determination based on ground tracking network. The computation for the "weak datum" is much easier than that of the "strong datum". With observations of the demonstration constellation of global BeiDou satellite navigation system, AOD is conducted with different datum including no datum, "weak datum" and "strong datum". The results show that, for the "weak datum", the constellation rotation can be compensated with a priori orbit inclination angle and the right ascension of ascending node constraints. However, the AOD precision is worse than that of "strong datum". When no ground tracking system can be used, "weak datum" is recommended to realize the real AOD.