# High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Using Multi-Source Observations
## 3 Results  
In the new strategy, only using redundant ISL two-way observations and first least square estimation processing, the variations of inter-satellite clock offsets between other satellites can be real-time estimated. The two-way inter-satellite clock offsets are independent of L-band two-way measurements. Taking the clock offsets between the MEO-1 and MEO-2 as the example, the differences in the 1-day quadratic fitting residual between the two-way inter-satellite estimated clock offsets and the ODTS inter-satellite clock offsets from the German research center for geosciences Beidou multi-GNSS (GBM) [33] are plotted in Figure 9. Wherein, the blue curves of Figure 9a are the two-way estimated clock offsets between the MEO-1 and MEO-2. The green curves of Figure 9a are their ODTS clock offsets. Both of them are deducted with the same trends, and their differences are plotted in Figure 9b. Although the STD of their differences is less than 0.1 ns in the timescale of 1 day, due to the day-boundary discontinuities in the ODTS clock offsets [34], their differences exist in the obvious \"hop\" at the boundary between two days, which are given in Figure 10.  
In order to suppress the influence of day-boundary discontinuities in the ODTS clock offsets, we deducted the same trends per day in the following comparisons between the ODTS clock offsets and the two-way clock offsets. Referring to BDS-3 M1, Tab1 lists 9-day averaging statistical results of their 1-day quadratic fitting residual and the STD of their differences for all BDS-3 satellites. Except for BDS-3 C61, the statistical results show that the averaged STD of the differences between the two-way estimated clock offsets and GBM clock offsets is 0.19 ns. Among them, the averaged STD for BDS-3 MEOs is 0.14 ns and 0.40 ns, 0.36 ns for IGSOs and GEOs, respectively. Figure 8: The procedure of the estimation and elimination of the bias of the two-way estimated clock offsets. As shown in Table 1, In most cases, the large differences between the two kinds of clock offset with the larger fitting residuals in the GBM ODTS clock offsets. Epically for the GEOs and IGSOs. Taking the two kinds of clock offset between the IGSO-1 and MEO-1 as an example, their comparisons are given in Figure 11. Both of them are deducted the same trends per day. From Figure 10, It can be clearly found that their larger differences  
Figure 10: 9-day Satellite clock offset differences between the Ka-band inter-satellite estimated clock offsets and GBM products. Wherein, (**a**) describes the two kinds of clock offsets after deducting the same trend. (**b**) describes their differences. The reason why “hop” exist in the bottom figure is that the day-boundary discontinuities exist in the ODTS clock offsets (since 19 May 2022). Figure 9: 1-day Satellite clock offset differences between the Ka-band inter-satellite estimated clock offsets and GBM products (since 19 May 2022). Wherein, (**a**) describes the two kinds of clock offsets after deducting the same trend. (**b**) describes their differences. are caused by the large fluctuation in GBM ODTS clock offsets. We believe that the IGSOs and GEOs clock offsets with large fluctuations are that there exist larger orbit errors in GEOs and IGSOs. Some results suggest it is probably due to the not accurate enough solar radiation pressure model adopted in ODTS processing [33; 35]. Taking the high-accuracy inter-satellite clock offsets and L-band two-way clock offsets of GEOs as inputs, the clock offsets of all satellites can be further traced to the BDT so as to estimate the final clock offsets, whose accuracy should be better than the clock offsets calculated by two-way superimposition strategy, which can be shown in Figure 9. The top panel of Figure 9 describes the GEO clock offsets. The middle panel of Figure 9 describes the typical IGSO clock offsets, and the bottom panel of Figure 12 describes the typical MEO clock offsets curves are the two-way estimated clock offsets.