## 1 Introduction  
The BeiDou navigation satellite system (BDS) independently developed by China follows three construction phases, including the demonstration system (BDS-1) consisting of three Geostationary Earth Orbit (GEO) satellites, the regional system (BDS-2) composed of five GEO satellites, seven Inclined Geosynchronous Satellite Orbit (IGSO) satellites and three Medium Earth Orbit (MEO) satellites, and the global system (BDS-3) containing three GEO, three IGSO and 24 MEO satellites [1; 2; 3; 4]. With the centralized launch of BDS-3 satellites, all BDS-3 MEO satellites were launched on or before December 16, 2019, and the core constellation deployment of the BDS-3 global system has been completed. The performance of global positioning, navigation and timing (PNT) services will be further improved. With the gradual deployment of the BDS-3 constellation, the BDS constellation will include the satellite systems of BDS-2 and BDS-3. So, the observations of BDS-2 and BDS-3 need to be fully used to take full advantage of the BDS potential. Therefore, it is meaningful for global BDS users to assess the accuracy of BDS-2 and BDS-3 broadcast ephemeris and compare their differences. About the analysis and assessment of BDS broadcast ephemeris, [PERSON] and [PERSON] assessed the GPS, BDS-2, GLONASS, Galileo and QZSS in terms of broadcast orbit errors, clock offsets errors and signal-in-space range error (SISRE), indicating that the SISRE values of BDS-2 are 1.5 m with a monthly scatter of 0.1 m, which is better than GLONASS and the (nonoperational) Galileo IOV system [5]. The initial assessment of BDS-3 broadcast ephemeris in terms of BDS-3 orbit, clock offsets, SISRE and orbit-only SISRE is presented by [PERSON] and [PERSON], concluding that the 3D orbit errors are better than 0.6 m, and the root mean square (RMS) of SISRE and orbit-only SISRE are 0.5 m and 0.1 m, respectively [6]. [PERSON] and [PERSON] used the precise product provided by the GNSS Research Center of Wuhan University (WHU) to evaluate the BDS-2 and BDS-3, which shows that the BDS-3 SISRE is superior to that of BDS-2, and the corresponding values are 0.71 m and 0.97 m, respectively [7]. For the assessment of BDS signal-in-space accuracy, especially for BDS-3, most researchers only use the precise orbit and clock offsets provided by WHU to assess the accuracy of BDS-3 broadcast ephemeris. The RMS of orbit errors and the accuracy of clock offsets and SISRE (including the orbit-only SISRE) used to evaluate the accuracy of BDS broadcast ephemeris will inevitably be affected by the accuracy and the datum of precise product. The conclusions drawn by using the precise satellite product obtained from one analysis center (AC) lack slight reliability. Hence, the precise products provided by the Helmholtz Centre Potsdam German Research Center for Geosciences (GFZ), Wuhan University (WHU) and the International GNSS Monitoring and Assessment System (iGMAS) ACs of Shanghai Astronomical Observatory (SHA) are used to assess the BDS signal-in-space accuracy to draw more scientific and reliable conclusions. In fact, the broadcast ephemeris of BDS-2 and BDS-3 are calculated separately. Although the corrections of unifying the datum of BDS-2 and BDS-3 satellite clock offsets are considered in the BDS information processing, an obvious systematic bias between BDS-2 and BDS-3 is found by comparing the broadcast ephemeris and precise products in terms of satellite orbit and clock offsets. The previous research indicated that there is a pseudorange bias (hardware delay bias) between BDS-2 and BDS-3 in some receivers [8]. The pseudorange bias of the receiver will still produce the inconsistency of the datum of clock offsets for BDS-2 and BDS-3 during the processing of broadcast clock offsets. Most references ignore the inconsistency of the datum of satellite clock offsets in evaluating the accuracy of BDS broadcast ephemeris and positioning [7; 9].