Inter-system bias (ISB) will affect accuracy and processing time in integrated precise point positioning (PPP), and ISB stochastic models will largely determine the quality of ISB estimation. Thus, the impacts of four different stochastic models of ISB processing will be assessed and studied in detail to further reveal the influence of ISB in positioning. They are ISB-PW considering ISB as a piece-wise constant, ISB-RW considering ISB as random walk, ISB-AD considering ISB as an arc-dependent constant, and ISB-WN considering ISB as white noise. Together with the model without introducing ISB called ISB-OFF, i.e., five different schemes, ISB-OFF, ISB-PW, ISB-RW, ISB-AD, and ISB-WN, will be designed and tested in this study. From the results of pseudorange residuals, it can be noticed that when considering ISB, the Root-Mean-Square (RMS) of ionosphere-free combined pseudorange residuals are much smaller than without ISB (ISB-OFF). The results of convergence time and positioning accuracy analysis show that PPP performance with ISB-AD is even worse than ISB-OFF, when using the precise products from the German Research Centre for Geosciences (GFZ) named as GBM products here; while the strategies of ISB-RW, and ISB-WN achieve the best results. For the products from Wuhan University called WUM products, a completely different result is achieved. PPP with the stochastic models of ISB-PW and ISB-AD perform best. The most likely reason is the ISB stochastic models applied by the analysis centers are consistent with those used in the PPP on the user side. So, ISB-RW, or ISB-WN is recommended when GBM products are used, and for the WUM products, ISB-PW, or ISB-AD is chosen. From the statistics of PPP precision during the convergence period, it can be concluded that considering ISB also has a great improvement on combined PPP accuracy during the initialization phase.
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