Performance of ionospheric-free PPP time transfer models with BDS-3 quad-frequency observations

[Display omitted] •BDS-3 (B1I/B3I), (B1I/B2a), (B1C/B2a) and (B1C/B3I) ionospheric-free PPP time transfer model are proposed.•The assessment of the PPP time transfer with four BDS-3 PPP model.•Comparison of the BDS-2 B1I/B2I and B1I/B3I combined PPP performances are presented.•BDS-2, BDS-3 and BDS-2 + BDS-3 PPP time transfers were evaluated and investigated. The BeiDou Navigation Satellite System (BDS) has as achieved the status of a global navigation satellite system. Compared to BDS-2 satellites, BDS-3 satellites transmit B1C, B2a, and B2b signals but not B1I and B3I signals. In this study, for the four open-services of BDS-3 satellites, four ionospheric-free combinations, namely (B1I/B3I), (B1I/B2a), (B1C/B2a) and (B1C/B3I) were first proposed. Then, the performance of the BDS-3 carrier-phase time transfer was assessed and investigated. For comparison and evaluation purposes, precise point positioning (PPP) time transfer with BDS-2, GPS, and Galileo was also assessed. Analogous to the BDS-3 signal structure, the performance of BDS-2 based on the B1I/B2I- and B1I/B3I- combined PPP solutions was first validated. Then, with respect to the GPS and Galileo PPP time transfer, the BDS-3 B1I/B3I, B1I/B2a, B1C/B2a, and B1C/B3I; BDS-2 B1I/B2I; and BDS-2 + BDS-3 B1I/B3I PPP time transfers were assessed and analysed. The experimental results demonstrated that the BDS-3 B1I/B3I performance was slightly better than the BDS-3 B1I/B2a, B1C/B3I and B1C/B2a performances due to the differential code bias (DCB) accuracy. Furthermore, the BDS-2 B1I/B3I PPP was worse than the other PPP solutions, while BDS-2 + BDS-3 B1I/B3I PPP outperformed the other PPP solutions. Compared with the BDS-2 B1I/B3I PPP, the mean reductions in the standard deviation (STD) values were approximately (77.2, 21.3, 1.8, 1.3, 13.1) % from (0.241, 0.687, 0.547, 0.218, 0.585) ns to (0.136, 0.566, 0.537, 0.215, 0.517) ns calculated from BDS-3 and (97.5, 23.5, 4.9, 4.8, 16.7)% from (0.241, 0.687, 0.547, 0.218, 0.585) ns to (0.122, 0.556, 0.521, 0.208, 0.501) ns calculated and BDS-2 + BDS-3, respectively. For the frequency stability, BDS-3 demonstrated better results, while BDS-2 + BDS-3 presented significant improvements with respect to BDS-2. The maximum improvement in BDS-2 + BDS-3 reached up to 56.1% from 3.3973E-14 to 1.49E-14. Additionally, the modified Allan deviation (MDEV) of BDS-2 + BDS-3 was analogous to that of GPS and Galileo.