BDS-3 geostationary orbit (GEO) satellites broadcast PPP-B2b real-time precise products to support real-time precise point positioning (RT-PPP) without dependence on the ground network communication. Since all BDS-3 satellites can provide multi-frequency signals, we investigate the effect of different multi-frequency integrations and the refinement of multi-frequency stochastic model for PPP-B2b RT-PPP. Given that the retrieval of PPP-B2b real-time precise corrections relies on the B1C and B2b frequencies, this study first investigates the kinematic uncombined (UC) RT-PPP performance of the B1C/B2b integration with a comparison to the conventional B1I/B3I integration. The results indicate that the convergence time (with a convergence threshold of 20 cm) of the RT-PPP with the B1C/B2b integration is shortened by 16 %, 15 %, and 12 % over the B1I/B3I integration in the east, north, and up directions, respectively. Further, this study compares the kinematic UC RT-PPP performance of the B1C/B2b dual-frequency integration, B1C/B2b/B3I triple-frequency integration, and B1C/B2b/B3I/B1I/B2a five-frequency integration. Compared with the dual-frequency integration, the positioning performance of the triple-frequency integration is slightly improved. By contrast, the performance improvement of the five-frequency integration is more significant, which can reach 6 %, 32 %, and 9 % for the convergence time, and 11 %, 9 %, and 6 % for the positioning accuracy in three directions, respectively. To further enhance the multi-frequency PPP performance, a refined stochastic model for the BDS-3 five-frequency integrated PPP-B2b RT-PPP is proposed by taking the inconsistency of signal quality among multi-frequency signals into account. After applying the refined stochastic model, the convergence time of the five-frequency kinematic RT-PPP is shortened by 10 %, 14 %, and 9 % to 32, 7, and 19 min in east, north, and up directions, respectively. The positioning accuracy (the root mean square of all the positioning errors excluding the first two hours) of the five-frequency RT-PPP with the refined stochastic model can reach the optimal level, which is 9.9, 6.5, and 14.0 cm in three directions, respectively.
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