The Chinese BeiDou Navigation Satellite System (BDS) transited from regional (Asia-Pacific) to global on December 28, 2018. In this study, the performance of PPP-RTK based on BDS-3/BDS-2/GPS observations is analyzed by utilizing the observations in Europe during a calm ionospheric disturbance period with Kp-index ranging from 0o to 2-. Satellite clock offsets are first estimated and then fixed to determine the uncalibrated phase delays (UPDs) and the ionospheric/tropospheric information from the reference network. Real-time PPP and PPP AR based on raw observations are conducted at the user, in which atmospheric constraints are imported as virtual observations if available. Analysis results based on three days of observations reveal that centimeter-level positioning accuracy can be achieved based on GPS, BDS or GPS+BDS observations, and the performance can be further improved by realizing PPP AR. The satellite-differenced ionospheric and tropospheric information can be predicted for the users with an accuracy of 24.6 mm This is the Pre-Published Version.
To provide competitive global positioning and timing services under the condition that monitoring stations are confined to Chinese territory, inter-satellite link (ISL) technology is used by the third-generation BeiDou Navigation Satellite System (BDS-3). The ISL, together with the dual one-way links between satellites and anchor stations, may enable autonomous navigation for BDS-3. In this paper, we propose a general observation model for orbit determination (OD) and time synchronization (TS) directly using non-simultaneous observations, such as raw ISL pseudoranges. With the proposed model, satellite orbits, clocks, and hardware delay biases of ISL equipment can be determined simultaneously by jointly processing inter-satellite one-way pseudorange data and observation data from ground monitoring stations. Moreover, autonomous OD and TS are also achievable with one-way pseudorange data from anchor stations and satellites. Data from eight BDS-3 satellites, two anchor stations, and seven monitoring stations located in China were collected to validate the proposed method. It is shown that by jointly processing data from the ISL and seven monitoring stations, the RMS of overlap orbit differences in radial direction is 0.019 m, the overlap clock difference (95%) is 0.185 ns, and the stability of the estimated hardware delay biases for each satellite is greater than 0.5 ns. Compared with the results obtained with the seven stations, the improvements of orbits in radial direction and clocks are 95.7% and 90.5%, respectively. When the hardware delay biases are fixed to predetermined values, the accuracies of orbits and clocks are further improved. By jointly processing pseudoranges from the satellites and the two anchor stations, the RMS of overlap orbit differences is 0.017 m in the radial direction, and the overlap clock difference (95%) is 0.037 ns. It has also been demonstrated that under the condition of one-way ranging links, the accuracies of orbits and clocks obtained by the above two modes are still significantly better than those obtained by using the data from the monitoring stations alone.
The basic system of the BeiDou global navigation satellite system (BDS-3) with 18 satellites has been deployed since December 2018. As the primary frequency standard, BDS-3 satellites include two clock types with the passive hydrogen maser (PHM) and the rubidium atomic frequency standard (RAFS). Based on the final precise orbit and clock product from Xi’an Research Institute of Surveying and Mapping (XRS), the atomic clock performance of BDS-3 satellites is evaluated, including the frequency accuracy, frequency drift rate, and frequency stability, and compared with GPS block IIF satellites with RAFS, Galileo satellites with PHM, and BDS-2 satellites. A data auto-editing procedure to preprocess clock data and assess the clock performance is developed, where the assessed results are derived at each continuous data arc and the outliers are excluded properly. The stability of XRS product noise is given by using some stations equipped with high-precision active hydrogen masers (AHM). The best stability is 8.93 × 10−15 and 1.85 × 10−15 for the averaging time of 10,000 s and 1 day, which is basically comparable to one-third of the in-orbit PHM frequency stability. The assessed results show the average frequency accuracy and drift rate of BDS-3 with RAFS are slightly worse while the stability is better than BDS-2 medium earth orbit (MEO) satellites. The 10,000 s stability is better but the 1-day stability is worse than GPS, which may be related to the performance of the BDS-3 RAFS clock. As for BDS-3 with PHM, the frequency accuracy is slightly worse than Galileo PHM satellites; the drift rate, when excluding C34 and C35, is basically comparable to Galileo and significantly better than GPS satellites; the stability is comparable to Galileo, where the 10,000 s stability is slightly worse than Galileo and better than GPS. The 1-day stability among BDS-3 PHM, GPS IIF RAFS, and Galileo PHM satellites is basically comparable.
There is increasing concern about the uncombined (UC) observation model in the field of global navigation satellite system (GNSS). Based on the global positioning system (GPS) and the third-generation BeiDou navigation satellite system (BDS-3), this study processed the UC precision orbit determination (POD) for single and dual systems. First, a UC observation model suitable for multi-GNSS POD was derived, and the ionospheric-free (IF) combination observation model was presented. Although the ambiguity parameters of UC and IF strategies were different after reparameterization, the difference could be removed when processing ambiguity resolution, and the equivalence was proved theoretically. To demonstrate the accuracy of BDS-3 orbits fully, the observation data of approximately 1 month were selected for determining the precise orbit for global positioning system (GPS) only, BDS-3 only, and GPS/BDS-3 systems based on the UC and IF models. The orbit precision of BDS-3 satellites was validated by using metrics, including comparison with precision products released by Wuhan University, orbit boundary discontinuity, and satellite laser ranging (SLR) residuals. The results show that the orbit accuracies of the IF and UC models are almost the same, the difference in orbits is approximately several millimeters, and the clock difference is within 0.01 ns. The GPS/BDS-3 combined solution shows better accuracy compared to other solutions. The average accuracies in the R and 3D directions are approximately 4 and 15 cm, and the clock standard deviation is approximately 0.2 ns compared to external orbit product. The root mean square of SLR residuals is approximately 4 cm.
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