# High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Using Multi-Source Observations
## 1 Introduction  
Because GNSSs measure distances and clock offsets by comparing clocks, GNSSs need to provide accurate messages, including their space and time. For BDS-3 open service, BDS-3 calculates the position and velocity of satellites in the Beidou Coordinate System (BDCS) [1], and the satellite clock offsets with respect to Beidou Time (BDT) [2; 3] at first. After that, BDS-3 parameterizes the satellite's orbit and clock offsets to ephemeris and clock offset parameters and uploads them to the satellite for broadcasting [4; 5]. The update frequency of the above messages is often every hour and the predicted time for users to use them is less than 2 h. The influence of their errors on ground users is presented as signal-in-space errors (SISRE) [6; 7]. SISRE is one of the most significant error sources in PNT, which consist of broadcast ephemeris errors and clock offsets parameters errors. Galileo performs the lowest SISRE in \"GSNS Big 4\" at present [8]. The BDS-3 constellation consists of 24 MEOs, 3 IGSSOs, and 3 GEOs, whose SISRE is second to Galileo [9; 10]. Statistical results show that the broadcast ephemeris errors can reach centimeter levels [11; 12], which is at the top level in \"GNSS Big 4\" [8; 9; 10]. However, the clock offsets parameters errors of BDS-3 are 0.35 m (RMS) with respect to BDT, and evaluated by IGS precise clock offsets are more than 0.51 ns, which is larger than the errors of 0.14 m of Galileo. Therefore, the main reason why SISRE of BDS-3 is larger than Galileo is that the clock offsets parameters of BDS-3 with larger errors [9; 10]. Generally, GNSS satellite clock offsets are the differences between the satellite atomic clock onboard and GNSS system time in GNSS conventional reference system. Theirmeasurement is the most crucial step in GNSS generating satellite clock offsets parameters. Orbit determination and time synchronization (ODTS) is GNSS's most proven and widely used clock offsets estimation technology [13; 14]. The ODTS can estimate satellite clock offsets simultaneously when estimating satellite orbit using GNSS downlinks pseudorange and carrier phase measurements from dozens to hundreds of global GNSS stations. For BDS-3, some results suggest that the clock offsets differences between real-time and batch-processed solutions in ODTS are less than 0.15 ns, which is as the same level as other GNSS [15]. The ODTS estimation technology has high requirements for GNSS station distribution and quantity. However, since the BDS monitor station are only distributed within China, it is difficult for BDS to realize the above requirements. Under the above circumstances, BDS-3 uses the two-way comparison technology to measure satellite clock offsets [16]. The fundamental principle of the two-way comparison is to subtract two-way measurements to eliminate most of the errors related to spatial information, and obtain their clock offsets. As shown in Figure 1, the BDS-3 time synchronization system owns the Master Control Station (MCS) and Time Synchronization Stations (TSS). All of them are equipped with C-band antennas, allowing BDS-3 to measure their clock offsets by two-way measurements [17]. Moreover, the satellite and BDS-3 ground station are also equipped with L-band two-way antennas and Ka-band phased-array antennas. The above antennas allow BDS-3 to calculate L-band two-way clock offsets and Ka-band two-way inter-satellite clock offsets [18]. According to the tracking status of the ground antenna to the satellite and the link plan of the inter-satellite link (ISL) [19], BDS-3 superimposes the above clock offsets to obtain satellite clock offsets with respect to BDT. This strategy we named the two-way superimposition strategy. Although the two-way superimposition strategy can measure satellite clock offsets, whether overseas or intraregional, it puts forward high requirements for the ability and quantity of ground antenna. More importantly, the final satellite clock offset is only obtained by several superimpositions of the above two-way clock offset.