The BeiDou navigation satellite system (BDS) currently has 41 satellites in orbits and will reach its full constellation following the launch of the last BDS satellite in June 2020 to provide navigation, positioning, and timing (PNT) services for global users. In this contribution, we investigate the characteristics of inter-system bias (ISB) between BDS-2 and BDS-3 and verify whether an additional ISB parameter should be introduced for the BDS-2 and BDS-3 precise point positioning (PPP). The results reveal that because of different clock references applied for BDS-2 and BDS-3 in the International GNSS Service (IGS) precise satellites clock products and the inconsistent code hardware delays of BDS-2 and BDS-3 for some receiver types, an ISB parameter needs to be introduced for BDS-2 and BDS-3 PPP. Further, the results show that the ISB can be regarded as a constant within a day, the value of which is closely related to the receiver type. The ISB values of the stations with the same receiver type are similar to each other, but a great difference may be presented for different receiver types, up to several meters. In addition, the impact of ISB on PPP has also been studied, which demonstrates that the performance of kinematic PPP could be improved when ISB is introduced.

Utilizing global positioning system (GPS) to determine the precise kinematic orbits for the twin satellites of the Gravity Recovery and Climate Experiment (GRACE) plays a very important role in the earth’s gravitational and other scientific fields. However, the orbit quality is highly depended on the geometry of observed GPS satellites. In this study, we propose a kinematic orbit determination method for improving the GRACE orbit quality especially when the geometry of observed GPS satellites is weak, where an appropriate random walk clock constraint between adjacent epochs is recommended according to the stability of on-board GPS receiver clocks. GRACE data over one month were adopted in the experimental validation. Results show that the proposed method could improve the root mean square (RMS) by 20–40% in radial component and 5–20% in along and cross components. For those epochs with position dilution of precision (PDOP) larger than 4, the orbits were improved by 50–70% in radial component and 17–50% in along and cross components. Meanwhile, the Allan deviation of clock estimates in the proposed method was much closer to the reported Allan deviation of GRACE on-board oscillator. All the results confirmed the improvement of the proposed method.

Multi-frequency and multi-GNSS integration is currently becoming an important trend in the development of satellite navigation and positioning technology. In this paper, GPS/Galileo/BeiDou (BDS) precise point positioning (PPP) with ambiguity resolution (AR) are discussed in detail. The mathematical model of triple-system PPP AR and the principle of fractional cycle bias (FCB) estimation are firstly described. With the data of 160 stations in Multi-GNSS Experiment (MGEX) from day of year (DOY) 321-350, 2018, the FCBs of the three systems are estimated and the experimental results show that the range of most GPS wide-lane (WL) FCB is within 0.1 cycles during one month, while that of Galileo WL FCB is 0.05 cycles. For BDS FCB, the classification estimation method is used to estimate the BDS FCB and divide it into GEO and non-GEO (IGSO and MEO) FCB. The variation range of BDS GEO WL FCB can reach 0.5 cycles, while BDS non-GEO WL FCB does not exceed 0.1 cycles within a month. However, the accuracies of GPS, Galileo, and BDS non-GEO narrow-lane (NL) FCB are basically the same. In addition, the number of visible satellites and Position Dilution of Precision (PDOP) values of different combined systems are analyzed and evaluated in this paper. It shows that the triple-system combination can significantly increase the number of observable satellites, optimize the spatial distribution structure of satellites, and is significantly superior to the dual-system and single-system. Finally, the positioning characteristics of single-, dual-, and triple-systems are analyzed. The results of the single station positioning experiment show that the accuracy and convergence speed of the fixed solutions for each system are better than those of the corresponding float solutions. The average root mean squares (RMSs) of the float and the fixed solution in the east and north direction for GPS/Galileo/BDS combined system are the smallest, being 0.92 cm, 0.52 cm and 0.50 cm, 0.46 cm respectively, while the accuracy of the GPS in the up direction is the highest, which is 1.44 cm and 1.27 cm, respectively. Therefore, the combined system can accelerate the convergence speed and greatly enhance the stability of the positioning results.

It is difficult to enable traditional precise point positioning (PPP) with ambiguity resolution (AR) due to fractional cycle biases (FCBs), which limit the accuracy and reliability of positioning results. The BeiDou Navigation Satellite System (BDS) has been providing continuous positioning, navigation, and timing (PNT) services in the global region since the end of 2018. The BDS constellation includes geostationary earth orbit (GEO), inclined geostationary orbit (IGSO), and medium earth orbit (MEO) satellites. However, its hybrid constellation structure and the satellite-side multipath effect have hindered the BDS PPP AR for two main reasons: (1) some receivers have half-cycle biases between GEO and non-GEO satellites, which result in the inconsistency of hardware delays for each satellite type; (2) the correction model for elevation-dependent satellite-side multipath effect is only applicable to IGSO and MEO, while in the case of GEO the effect cannot be effectively weakened or eliminated. To rectify these problems, a suitable strategy is proposed for estimating BDS FCBs, whereby the GEO FCBs and non-GEO FCBs are estimated independently. Results show that the FCBs estimated by the new strategy for GEO and non-GEO are more stable compared to the traditional strategy. The GEO wide-lane (WL) FCBs fluctuate less than 0.3 cycle in one month, except for C05, while the variation of non-GEO WL FCBs is about 0.1 cycle. In addition, compared to the traditional strategy, the fractions of GEO WL ambiguities after the removal of FCBs estimated by the new strategy can be improved noticeably from 53.5% to 78.5%, and from 71.8% to 92.3% for <0.15 cycle and <0.25 cycle respectively, which could be comparable with non-GEO. Simultaneously, the improvement of GEO narrow-lane (NL) ambiguities is from 28.9% to 40.2%, and from 40.4% to 53.3% for <0.10 cycle and <0.15 cycle respectively, are less noticeable. This is mainly due to the low precision IGS products for GEO. After PPP AR, the mean convergence time is shorted from 56.0 min to 43.6 min, and from 71.6 min to 62.7 min for static PPP and kinematic PPP, respectively.