Being the first mixed-constellation global navigation system, the global BeiDou navigation system (BDS-3) designs new signals, the service performance of which has attracted extensive attention. In the present study, the Signal-in-space range error (SISRE) computation method for different types of navigation satellites was presented. And the differential code bias (DCB) correction method for BDS-3 new signals was deduced. Based on these, analysis and evaluation were done by adopting the actual measured data after the official launching of BDS-3. The results showed that BDS-3 performed better than the regional navigation satellite system (BDS-2) in terms of SISRE. Specifically, the SISRE of the BDS-3 medium earth orbit (MEO) satellites reached 0.52 m, slightly inferior compared to 0.4 m from Galileo, marginally better than 0.57 m from GPS, and significantly better than 2.33 m from GLONASS. And the BDS-3 inclined geostationary orbit (IGSO) satellites achieved the SISRE of 0.90 m, on par with that of the QZSS IGSO satellites. However, the average SISRE of BDS-3 geostationary earth orbit (GEO) satellites was 1.15 m, which was marginally inferior to that of the QZSS GEO satellite (0.91m). In terms of positioning accuracy, the overall three-dimensional single-frequency standard point positioning (SPP) accuracy of BDS-3 B1C, B2a, B1I, and B3I gained an accuracy level better than 5 m. Moreover, the B1I signal exhibited the best positioning accuracy in the Asian-Pacific region, while the B1C signal set forth the best positioning accuracy in the other regions. Owing to the advantage in signal frequency, the dual-frequency SPP accuracy of B1C+B2a surpassed that of the transitional signal of B1I+B3I. Since there are more visible satellites in Asia-Pacific, the positioning accuracy of BDS-3 was moderately superior to that of GPS. The precise point positioning (PPP) accuracy of BDS-3 B1C+B2a or B1I+B3I converged to the order of centimeters, marginally inferior to that of the GPS L1+L2. However, these three combinations had a similar convergence time of approximately 30 minutes.
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