With the official announcement of open service since the end of 2018, the BeiDou navigation satellite system (BDS) has started to provide global positioning, navigation and timing (PNT) services. Thus, it is worth assessing the positioning service of new BDS satellites and signals. In this paper, we comprehensively assess the system status and the global positioning performance of BDS regarding single point positioning (SPP) and real-time kinematic (RTK) performance. Results show that the signal in space range error (SISRE) of BDS-3 satellites is superior to that of BDS-2 satellites, showing an overall accuracy of 0.71 m versus 0.97 m, which is competitive with GPS and Galileo. With the contribution of BDS-3, the number of global average visible satellites has increased from 5.1 to 10.7, which provides a mean global position dilution of precision (PDOP) value better than 6 at 99.88% and the mean availability of basic PNT performance is also improved from 35.25% to 98.84%. One week of statistical results from 54 globally distributed international GNSS service (IGS) stations show that the root mean square (RMS) of SPP accuracy is 1.1 m in horizontal and 2.2 m in vertical, which is at the same level of GPS. The new B1c and B2a signals show a smaller observation noise than B1I, and SPP performance of B1c is similar to that of B1I. However, the positioning precision is slightly worse at the B2a frequency, which may be due to the inaccurate BDS ionosphere correction. As for short baseline RTK, baseline accuracy is also improved due to the increased number of new BDS satellites.

With the completion of the BeiDou Global Navigation Satellite System (BDS-3), the multi-system precise point positioning ambiguity resolution (PPP-AR) has been realized. The satellite phase fractional cycle bias (FCB) is a key to the PPP-AR. Compared to the combined ionosphere-free (IF) model, the undifferenced and uncombined (UDUC) model retains all the information from the observations and can be easily extended to arbitrary frequencies. However, the FCB is difficult to apply directly to the UDUC model. An observable-specific signal bias (OSB) can interact directly with the original observations, providing complete flexibility for PPP-AR for multi-frequency multi-GNSS. In this study, the OSB product generation for the GPS (G), Galileo (E), and BDS-3 (C) systems is performed using 117 globally distributed multi-GNSS experiment (MGEX) stations, and their performances are evaluated. Then, the PPP-AR comparison and analysis of the two positioning models of the UDUC and IF are conducted. The results show that the stability of OSB products of the three systems is better than 0.05 ns. For the precise point positioning (PPP) ambiguity fixed solution, with comparable positioning accuracy and convergence time to the products of both the Wuhan University (WUM) and the Centre National d’Etudes Spatials (CNES) institutions, an average fixed-ambiguity rate is over 90%. Compared to the PPP float solution, the PPP-AR has the most significant improvement in positioning accuracy in the E-direction. The average improvements in the positioning accuracy under the IF and UDUC models in the static and kinematic modes are higher than 45% and 40%, respectively. The convergence times of the IF and UDUC models are improved on average by 48% and 60% in the static mode and by 40% and 55% in the kinematic mode, respectively. Among the IF and UDUC positioning models, the former has slightly better positioning accuracy and convergence time than the latter for the PPP float solution. However, both models have comparable positioning accuracy and convergence time after the PPP-AR. The GCE multi-system combination is superior to other system combinations. The average convergence time for the static PPP fixed solution is 8.5 min, and the average convergence time for the kinematic PPP fixed solution is 16.4 min.

The accuracy of the timing group delay (TGD) transmitted in the broadcast ephemeris is an important factor that affects the service performance of a GNSS system. In this contribution, an apparent bias is found by comparing the orbit and clock difference using half-year data of the BeiDou navigation satellite system (BDS) broadcast ephemeris and precise post-processed products. The bias differs at each satellite on each frequency and shows a general systematic difference between BDS-2 and BDS-3. We attribute this to the satellite-dependent TGD bias of the BDS broadcast ephemeris, which is subsequently calibrated. Moreover, to calibrate the bias independently, a network solution strategy is proposed based on 87 globally distributed multi-GNSS experiment (MGEX) stations spanning 25 weeks. The estimated bias shows good agreement with the values observed from the orbit and clock comparison. For the validation of the bias, we compared the signal-in-space range error (SISRE) performance with and without the TGD bias correction. The results show that the SISRE of the BDS improved from 0.71, 0.81, and 1.40 m to 0.64, 0.66, and 0.64 m in the B1I, B3I, and B1I/B3I frequencies. For BDS-3, the SISRE is well within 0.50 m after the bias correction. To further validate the bias, a week’s data were collected at 97 globally distributed MGEX stations. When the TGD bias is corrected, the root mean square (RMS) of single point positioning (SPP) can be improved by 5.6, 8.4, and 21.6% in the B1I, B3I, and B1I/B3I frequencies. Meanwhile, the SISRE and SPP assessment results also indicate that the TGD bias should be corrected by each satellite rather than only corrected between BDS-2 and BDS-3.

The multi-global navigation satellite system (GNSS) undifferenced and uncombined precise point positioning (UU-PPP), as a high-precision ionospheric observables extraction technology superior to the traditional carrier-to-code leveling (CCL) method, has received increasing attention. In previous research, only dual-frequency (DF) or multi-frequency (MF) observations are used to extract slant ionospheric delay with the UU-PPP. To reduce the cost of ionospheric modeling, the feasibility of extracting ionospheric observables from the multi-GNSS single-frequency (SF) UU-PPP was investigated in this study. Meanwhile, the between-satellite single-differenced (SD) method was applied to remove the effects of the receiver differential code bias (DCB) with short-term time-varying characteristics in regional ionospheric modeling. In the assessment of the regional real-time (RT) between-satellite SD ionospheric model, the internal accord accuracy of the SD ionospheric delay can be better than 0.5 TECU, and its external accord accuracy within 1.0 TECU is significantly superior to three global RT ionospheric models. With the introduction of the proposed SD ionospheric model into the multi-GNSS kinematic RT SF-PPP, the initialization speed of vertical positioning errors can be improved by 21.3% in comparison with the GRAPHIC (GRoup And PHase Ionospheric Correction) SF-PPP model. After reinitialization, both horizontal and vertical positioning errors of the SD ionospheric constrained (IC) SF-PPP can be maintained within 0.2 m. This proves that the proposed SDIC SF-PPP model can enhance the continuity and stability of kinematic positioning in the case of some GNSS signals missing or blocked. Compared with the GRAPHIC SF-PPP, the horizontal positioning accuracy of the SDIC SF-PPP in kinematic mode can be improved by 37.9%, but its vertical positioning accuracy may be decreased. Overall, the 3D positioning accuracy of the SD ionospheric-constrained RT SF-PPP can be better than 0.3 m.

Rapid and accurate ambiguity resolution is the core of high-precision precise point positioning (PPP) data processing. However, the ambiguity parameters in PPP observation models are easily affected by atmospheric residual and gross errors, which lead to the probability of successfully fixing decreases and computational burden increases in full ambiguity resolution. Therefore, an increasing number of partial ambiguity resolution (PAR) strategies have been proposed. The selection of the optimal subset of PAR is crucial in this method. The traditional optimal subset selection method of PAR commonly leads to a single judgment criterion and weakened geometric configuration strength because the satellites with low elevation angles are often easily eliminated during the optimal subset selection. In this paper, a multi-factor constrained optimal subset selection method for PAR was proposed, which incorporates the ambiguity variance, the ambiguity dilution of precision (ADOP), satellite position dilution of precision (PDOP) and ratio test values. In order to verify the feasibility of the proposed optimal subset selection method, PAR tests under two schemes were performed for GPS/Galileo based on the static observation data of 15 Multi-GNSS Experiment (MGEX) tracking stations. The results show that, compared with the ambiguity variance sorting method, the proposed subset selection method can further improve the accuracy of the coordinate solution and the strength of geometric figure positioning. The average root mean square of the coordinate residuals is found to decrease by about 12.90%, 6.83% and 9.39% in the eastern, northern and vertical directions, respectively. The increase in the fixed epoch rate ranged from 0.87% to 33.33%, with an average of about 8.71%.

High-precision DCBs are essential for effective multi-frequency and multi-constellation GNSS integration, especially in processing compatible signal observations. This study utilizes data from MGEX, iGMAS, and CORS stations to estimate and analyze long time series of BDS/GNSS DCBs, focusing on stability and influencing factors. Results indicate that DCBs for the same signal, but different channels exhibit similar ranges and trends. Among BDS DCBs, those from satellites with rubidium atomic clocks are more stable than those with hydrogen atomic clocks. An upgrade and maintenance of BDS in late 2022, reported by NABU, likely contributed to DCB jumps. BDS-compatible signal DCBs show weaker stability compared to GPS and Galileo. Variations in GNSS signal processing and receiver algorithms also impact DCB stability. Converting DCBs to OSBs and performing RMS statistics revealed that smaller differences between signals increase the susceptibility of observation equations to observation quality.