## 1 Introduction
Similarly, the tight combination had the improved position accuracies and successful ambiguity-fixing rates in comparison with the loose combination (differencing the observations within a single satellite system). To identify the estimability of ISB between GPS and Galileo, and GPS and BDS-2, [PERSON] et al. [5] employed the between-receiver single-differenced (SD) multi-GNSS observation equations to formulate the ionospheric-float, ionospheric-fixed, and ionospheric-weighted models. Based on this SD method, the ISB could be estimated for both overlapping and nonoverlapping frequencies in the RTK processing. Attributed to the reasonable ISB calibration, the multi-GNSS RTK accuracy of the intersystem differencing could be improved by 20-35%, as compared to that of the classical differencing. Actually, more studies contributed to the estimation and analysis of ISB in PPP. [PERSON] et al. [6] investigated the effects of receiver types, antenna types, and receiver software versions as well as the sources of precise satellite products (namely analysis centers) on the stability of ISB estimates from GPS/BDS-2 combined PPP solutions. [PERSON] et al. [7] adopted the four-system combined PPP to investigate the ISB between GPS and one of GLONASS, Galileo, and BDS-2. The ISB estimates showed systematic deviations (which were nearly identical for different stations) when using the precise products from different analysis centers. [PERSON] et al. [8] analyzed the long-term characteristics of ISB among GNSSs based on uncombined PPP. The standard deviations (STDs) of the relatively stable epochwise ISB over a day for GPS with respect to GLONASS, Galileo, or BDS-2 were less than 0.6 ns, while the variations of the single-day ISB solutions (average value of the epochwise ISB over a day) could be up to 60 ns, which might be attributed to the satellite reference clock of different systems. [PERSON] et al. [9] comprehensively evaluated the influence of ISB stochastic modeling (constant, random walk process, and white noise process) on the performance of undifferenced and uncombined multisystem (GPS/GLONASS/Galileo/BDS-2/QZSS) integrated PPP with the precise products from different analysis centers. The results indicated that both the positioning accuracy and convergence time were comparable regardless of which ISB strategy was employed when using the precise products from CODE, CNES, and WHU, while the position solutions with constant ISBs showed worse performance among the three ISB strategies when using GFZ products. With the availability of BDS-3 data, several researchers focused on its compatibility with BDS-2. [PERSON] et al. [10] analyzed the ISB estimates between BDS-3 and BDS-2 derived from BDS-3/BDS-2 integrated PPP solutions. No significant day-boundary discontinuities could be found for the ISB estimates, but a difference of several nanoseconds was noted among the stations with the receivers from the same brand. The phase ambiguity estimates, ionospheric delay estimates, and code residuals were obviously affected when ignoring the ISB between BDS-3 and BDS-2, while it was not the case for the positioning accuracies and phase residuals. [PERSON] et al. [11] also demonstrated that an additional ISB parameter should be introduced into the BDS-2/BDS-3 integrated PPP processing due to the different clock references for the precise satellite clock products and the inconsistent code hardware delays between them. Similar to the precise relative positioning, several researchers investigated the contribution of a priori ISB estimates to PPP solutions. [PERSON] et al. [12] focused on the short-term modeling and prediction of piecewise ISB estimates (every 30 min) from GPS/BDS-2 combined PPP. The modeling accuracy was about 0.7 ns, and the prediction accuracy was 0.57-1.21 ns with the 1-day period. When taking the derived ISBs as a priori constraints, the convergence time of PPP could be reduced by 2.4-19.6%.