## Appendix C Performance Assessment of Orbit, Clock, and DCB  
In this study, the performances of the orbit, clock, and DCB products recovered from PPP-B2b messages were assessed using the final products provided by the Multi-GNSS Experiment (MGEX) pilot project [77], including the orbit/clock products from the GFZ and DCB products from DLR [84] and CAS [85]. Prior to the comparison between the PPP-B2b and GBM products, several inconsistencies existed between these two sets of products that needed to be fixed. (1) Coordinate and time system: The PPP-B2b orbit products of BDS-3 and GPS use the China Geodetic Coordinate System 2000 (CGCS2000) [86; 87] and World Geodetic System 1984 (WGS84) [88] as their reference systems, respectively; they differ from the coordinate system adopted for the GFZ orbit products, that is, IGb14 [89]. Because these three coordinate systems are aligned to the International Terrestrial Reference Frame (ITRF) [90] and agree with each other at the centimetre level, the coordinate system difference between different orbit products was ignored in this study. For the time system, there is a difference of 14 s between the BDS time (BDT) adopted by PPP-B2b BDS-3 products and the GPS time (GPST) adopted by the GBM final products. This difference needed to be corrected prior to clock evaluation. (2) Satellite orbit evaluation: Because the PPP-B2b satellite orbit and the final orbit from the GBM are referred to APC and the centre-of-mass (CoM), respectively, this reference difference must be corrected using the corresponding phase-centre offset (PCO) values and nominal attitude models using Equation (A6) [91; 92] prior to further satellite orbit analysis. \[\stackrel{{\rightarrow}}{{R}}_{CoM}=\stackrel{{ \rightarrow}}{{R}}_{APC}+A\cdot\mathit{PCO}_{sat}\] (A6)  
In Equation (A6), \(A\) represents the transform matrix from the satellite-fixed coordinate system to the Earth-centered, Earth-fixed (ECEF) coordinate system, \(\stackrel{{\rightarrow}}{{R}}_{APC}\) and \(\stackrel{{\rightarrow}}{{R}}_{CoM}\) denote the satellite position vectors in the ECEF coordinate system that are referred to APC and CoM, respectively. In this study, the PCO values of BDS-3 satellites released by the China Satellite Navigation Office (CSNO) [93] and the PCO values of GPS satellites from the latest IGS antenna information file, that is, isg14.atx, were adopted for this correction. After the PCO correction was made, the RMS of the differences between the PPP-B2b orbit products and the GBM final orbit products could be computed. (3) Clock offset evaluation: For BDS-3, the PPP-B2b clock offsets are referred to as the APC of the B1I signal, while the GBM final clock offsets are referred to as the CoM of the satellite estimated based on the IFLC of B1I/B3I measurements. Therefore, a correction to this difference was essential for clock offset evaluation. As shown in Equation (A5), the PPP-B2b clock offsets contain a specific satellite hardware code bias of signal B3I. As shown in Equation (A7), the GBM final clock offsets contain a satellite hardware code bias for the IFLC of the measurements at the frequencies of \(f_{B1I}\) and \(f_{B3I}\):  
\[\overline{dt}^{C}_{GBM,13}=dt^{C}-\left[\varphi B^{C}_{s,B1I}+(1-\varphi)B^{C} _{s,B3I}\right]\] (A7)  
where \(\varphi=f^{2}_{B1I}/(f^{2}_{B1I}-f^{2}_{B3I})\), \(B^{C}_{s,B1I}\), and \(B^{C}_{s,B3I}\) are the satellite hardware code biases at the frequencies of \(f_{B1I}\) and \(f_{B3I}\), respectively. Therefore, prior to comparing the PPP-B2b clock offsets with the GBM final clock products, the difference in the reference signal caused by the satellite hardware code bias could be calculated using Equation (A8):  
\[\Delta_{DCB}=\left[\varphi B^{C}_{s,B1I}+(1-\varphi)B^{C}_{s,B3I}\right]-B^{C }_{s,B3I}=\frac{f^{2}_{B1I}}{f^{2}_{B1I}-f^{2}_{B3I}}\cdot DCB^{C}_{1,3}\] (A8)  
where \(DCB^{C}_{1,3}=B^{C}_{s,B1I}-B^{C}_{s,B3I}\) is the DCB parameter for the frequency of \(f_{B1I}\) in the PPP-B2b message.