## 2 Methodology
### Processing Strategy  
Four POD modes, namely ground-only POD, ISL-only POD, Joint 1 POD, and Joint 2 POD, are utilized to analyze the contribution of BDS-3 ISLs to orbit determination in this research. For ground-only POD, the code and carrier measurements in ionosphere-free combination expressed as Equations (1) and (2) are adopted. For ISL-only POD, only the clock-free pseudoranges described as Equation (11) are used. In particular, only in this mode, two ground anchor stations are added to reduce the constellation rotation resulting from the ISL-only POD [8; 12; 21]. For the Joint 1 POD, only ISL clock-free observations (Equation (11)) along with the IF code and carrier measurements (Equations (1) and (2)) are adopted. The improved joint POD applied in this contribution is expressed as Joint 2 POD, and the IF code and carrier measurements (Equations (1) and (2)) along with ISL geometry-free and clock-free observations (Equations (11) and (12)) are used simultaneously to determine the precise orbit and clock parameters as well as other relevant parameters. Some necessary correction models and settings of L-band and Ka-band observation are summarized in Table 1.  
It is important to emphasize the differences between the observables of L-band and Ka-band. First, the different types of observations have different weight settings. A prior standard deviation for the raw L-band phase, code, and Ka-band measurements are 0.002, 0.2, and 0.5 m, respectively. After that, the final weight of L-band observations needs to be adjusted according to the satellite elevation, while the weight of the Ka-band is independent of the satellite nadir angle. Second, although a pair of one-way ranging is completed at a 3-s interval, the observables are still transformed to the reference time with a sampling interval of 300 s, which is to maintain consistency with the L-band data to facilitate the estimation of the satellite clock offsets. However, due to the accuracy of broadcast ephemeris, the precision of the transformation (Equations (9) and (10)) is limited by the length of the extrapolation time of reference epoch in the broadcast ephemeris, thus only the ISL data in a 120-s time window centered on the reference time are utilized [15]. Moreover, for ISL data, the ionosphere delay is negligible because of the high frequency (23 GHz) of the Ka-band and the low electron density on the signal propagation path. Similarly, there is no need to consider tropospheric correction, if there are no ISL measurements with regard to anchor stations. Besides, the L-band antenna phase center offset (PCO) values are provided by the BDS official website while the Ka-band PCO values are provided by manufacturers. Four groups of precise BDS-3 orbits are processed by revised PANDA software [28], which has an additional function of outlier detection and adjustment for ISL data. The procedure of the Joint 1/2 POD can be divided into three steps. First, the POD using ground code and phase observation is carried out. This step is mainly to eliminate the L-band abnormal data and detect carrier cycle slips. Then, the broadcast orbit is used as a reference for detecting outliers in the ISL data through Equation (11). Once the above two steps are completed, the derived ISL measurements will be added to the