## 6 Earth Rotation Parameters Evaluation
### Comparison with IERS 20C04 Products  
In the external accuracy evaluation, we compared the estimated ERP results with reference to the IERS 20C04 products. Figure 12 exhibits the time series of PM differences with reference to IERS 20C04 products for 3-day arc BDS-3 B1I/B3I solutions, B1C /B2a solutions, and GPS solutions. From Figure 12, it is evident that the RMS of the B1C /B2a solution is 80 \(\upmu\)as for X PM and 51 \(\upmu\)as for Y PM. These values are 37% and 20% smaller than the B1I/B3I-based solutions for X and Y PM. In comparison, the RMS values of PM for GPS-based solutions are approximately 30 \(\upmu\)as. Figure 13 illustrates the time series for LOD differences with reference to IERS 20C04 products from 3-day arc BDS-3 B1I/B3I solutions, B1C/B2a solutions, and GPS solutions. The results demonstrate that the RMS of the LOD series for the B1C/B2a solution is 22.3 \(\upmu\)s/d, which is 1% smaller than the B1I/B3I solution. In Figure 14, the time series of the PM rate differences with reference to IERS 20C04 products for the 3-day arc BDS-3 B1I/B3I solutions, B1C/B2a solutions, and GPS solutions are presented. The RMS from the BDS-3 B1C/B2a solution is 124 \(\upmu\)as/d for the X PM rate and 101 \(\upmu\)as/d for the Y PM rate. These values are smaller by 7% for the X PM rate and 4% for the Y PM rate compared with the PM rates from the B1I/B3I solutions.  
Figure 11: Time series of formal errors in ERP estimation for 3-day arc solutions from BDS-3 B1I/B3I solutions, B1C/B2a solutions, and GPS solutions.  
Figure 12: Time series of polar motion differences with reference to IERS 20C04 for 3-day arc BDS-3, B1I/B3I solutions, B1C/B2a solutions, and GPS solutions.  
Figure 13: Time series of length of day differences with reference to IERS 20C04 for 3-day arc BDS-3, B1I/B3I solutions, B1C/B2a solutions, and GPS solutions.  
Table 11 presents the mean bias and STD of ERP differences when compared with IERS 20C04 products for the B1I/B3I solutions and B1C/B2a solutions, with GPS solutions included as a reference. The improvements in STD for the 3-day arc results are approximately 35% for pole coordinates, 30% for LOD, 65% for X pole coordinates, and 80% for Y pole coordinates, compared with the 1-day arc ERP from BDS-3. The mean values of the 3-day arc ERP from the BDS-3 BIC/B2a combination, with reference to IERS 20C04, are 48 uas and 19 uas for X and Y PM, 17 uas/d, and 5 uas/d for the X PM rate and the Y PM rate, and 4 uas/d for LOD. The mean values of the residuals for the 3-day arc BDS-3 BIC/B2a solutions show improvements of 56%, 54%, 20%, 39%, and 64% for the X, Y PM, LOD, X, and Y PM rates, respectively, compared with BDS-3 B1I/B3I solutions. The superior mean bias of the B1C/B2a-based ERP can be attributed to the advantage of the B1C/B2a combination in ambiguity fixing. In the aspect of STD, the results of the 3-day arc ERP from the BDS-3 BIC/B2a combination are 63 uas, 47 uas, 123 uas/d, 101 uas/d, and 22.0 uas/d for the X, Y PM, X, and Y PM rates, and LOD, respectively. The B1C/B2a solutions result in standard deviations of the residuals that are about 3%, 2%, 1%, 6%, and 3% better than the B1I/B3I solutions for the X, Y PM, X, and Y PM rates, and LOD, respectively. While the GPS solutions generally exhibit better mean and STD than BDS-3 ERP, it is worth noting that the mean bias of the LOD in the GPS solutions is larger, approximately 1.5 times higher than the BDS-3 result. This discrepancy arises because the orbital period of GPS exhibits a stronger resonance with the Earth's rotation, which is 2:1. While the corresponding resonance for BDS-3 is weaker, approximately at a 17:9 ratio [5; 15; 16].  
Figure 14: Time series of polar motion rate differences with reference to IERS 20C04 for 3-day arc BDS-3 B1I/B3I solutions, B1C/B2a solutions, and GPS solutions.