Cycle slip detection and repair is a prerequisite for high-precision global navigation satellite system (GNSS)-based positioning. With the modernization and development of GNSS systems, more satellites are available to transmit triple-frequency signals, which allows the introduction of additional linear combinations and provides new opportunities for cycle slip detection and repair. In this paper, we present a new real-time cycle slip detection and repair method under high ionospheric activity for undifferenced Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) triple-frequency observations collected with a single receiver. First, three optimal linearly independent geometry-free pseudorange minus phase combinations are selected to correctly and uniquely determine the cycle slips on the original triple-frequency carrier phase observations. Then, a second-order time-difference algorithm is employed for the pseudorange minus phase combinations to mitigate the impact of between-epoch ionospheric residuals on cycle slip detection, which is especially beneficial under high ionospheric activity. The performance of the approach is verified with static GPS/BDS triple-frequency observations that are collected with a 30 s sampling interval under active ionospheric conditions, and observations are manually inserted with simulated cycle slips. The results show that the method can correctly detect and repair cycle slips at a resolution as small as 1 cycle. Moreover, kinematic data collected from car-driven and airborne experiments are also processed to verify the performance of the method. The experimental results also demonstrate that the method is effective in processing kinematic data.

The BeiDou global navigation satellite system (BDS-3) constellation deployment has been completed on June 23, 2020, with a full constellation comprising 30 satellites. In this study, we present the performance assessment of single-epoch Real-Time Kinematic (RTK) positioning with tightly combined BeiDou regional navigation satellite system (BDS-2) and BDS-3. We first investigate whether code and phase Differential Inter-System Biases (DISBs) exist between the legacy B1I/B3I signals of BDS-3/BDS-2. It is discovered that the DISBs are in fact about zero for the baselines with the same or different receiver types at their endpoints. These results imply that BDS-3 and BDS-2 are fully interoperable and can be regarded as one constellation without additional DISBs when the legacy B1I/B3I signals are used for precise relative positioning. Then we preliminarily evaluate the single-epoch short baseline RTK performance of tightly combined BDS-2 and the newly completed BDS-3. The performance is evaluated through ambiguity resolution success rate, ambiguity dilution of precision, as well as positioning accuracy in kinematic and static modes using the datasets collected in Wuhan. Experimental results demonstrate that the current BDS-3 only solutions can deliver comparable ambiguity resolution performance and much better positioning accuracy with respect to BDS-2 only solutions. Moreover, the RTK performance is much improved with tightly combined BDS-3/BDS-2, particularly in challenging or harsh conditions. The single-frequency single-epoch tightly combined BDS-3/BDS-2 solution could deliver an ambiguity resolution success rate of 96.9% even with an elevation cut-off angle of 40°, indicating that the tightly combined BDS-3/BDS-2 could achieve superior RTK positioning performance in the Asia–Pacific region. Meanwhile, the three-dimensional (East/North/Up) positioning accuracy of BDS-3 only solution (0.52 cm/0.39 cm/2.14 cm) in the kinematic test is significantly better than that of the BDS-2 only solution (0.85 cm/1.02 cm/3.01 cm) due to the better geometry of the current BDS-3 constellation. The tightly combined BDS-3/BDS-2 solution can provide the positioning accuracy of 0.52 cm, 0.22 cm, and 1.80 cm, respectively.

In this contribution, we assess, for the first time, the tightly combined real-time kinematic (RTK) with GPS, Galileo, and BDS-3 operational satellites using observations from their overlapping L1-E1-B1C/L5-E5a-B2a frequencies. First, the characteristics of B1C/B2a signals from BDS-3 operational satellites is evaluated compared to GPS/Galileo L1-E1/L5-E5a signals in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, as well as double-differenced carrier phase and code residuals using data collected with scientific geodetic iGMAS and commercial M300Pro receivers. It’s demonstrated that the observational quality of B1C/B2a signals from BDS-3 operational satellites is comparable to that of GPS/Galileo L1-E1/L5-E5a signals. Then, we investigate the size and stability of phase and code differential inter-system bias (ISB) between BDS-3/GPS/Galileo B1C-L1-E1/B2a-L5-E5a signals using short baseline data collected with both identical and different receiver types. It is verified that the BDS-3/GPS/Galileo ISBs are indeed close to zero when identical type of receivers are used at both ends of a baseline. Moreover, they are generally present and stable in the time domain for baselines with different receiver types, which can be easily calibrated and corrected in advance. Finally, we present initial assessment of single-epoch tightly combined BDS-3/GPS/Galileo RTK with single-frequency and dual-frequency observations using a formal and empirical analysis, consisting of ambiguity dilution of precision (ADOP), ratio values, the empirical ambiguity resolution success rate, and the positioning accuracy. Experimental results demonstrate that the tightly combined model can deliver much lower ADOP and higher ratio values with respect to the classical loosely combined model whether for GPS/BDS-3 or GPS/Galileo/BDS-3 solutions. The positioning accuracy and the empirical ambiguity resolution success rate are remarkably improved as well, which could reach up to approximately 10%∼60% under poor observational conditions.

Global navigation satellite system (GNSS)-based attitude determination has been widely applied in a variety of fields due to its high precision, no error accumulation, low power consumption, and low cost. Recently, the emergence of common-clock receivers and construction of GNSS systems have brought new opportunities for high-precision GNSS-based attitude determination. In this contribution, we focus on evaluating the performance of the BeiDou regional navigation satellite system (BDS-2)/BeiDou global navigation satellite system (BDS-3)/Global Positioning System (GPS)/Galileo navigation satellite system (Galileo) attitude determination based on the single-differenced (SD) model with a common-clock receiver. We first investigate the time-varying characteristics of BDS-2/BDS-3/GPS/Galileo line bias (LB) with two different types of common-clock receivers. The results have confirmed that both the phase and code LBs are relatively stable in the time domain once the receivers have started. However, the phase LB is expected to change to an arbitrary value after each restart of the common-clock receivers. For the first time, it is also found that the phase LBs of overlapping frequencies shared by different GNSS systems are identical. Then, we primarily evaluated the performance of BDS-2/BDS-3/GPS/Galileo precise relative positioning and attitude determination based on the SD model with a common-clock receiver, using a static dataset collected at Wuhan. Experimental results demonstrated that, compared with the double-differenced (DD) model, the SD model can deliver a comparable root–mean–square (RMS) error of yaw but a significantly smaller RMS error of pitch, whether for BDS-2, BDS-3, GPS, or Galileo alone or a combination of them. The improvements of pitch accuracy are approximately 20.8–47.5% and 40.7–57.5% with single- and dual-frequency observations, respectively. Additionally, BDS-3 can deliver relatively superior positioning and attitude accuracy with respect to GPS and Galileo, due to its better geometry. The three-dimensional positioning and attitude (including yaw and pitch) accuracy for both the DD and SD models can be remarkably improved by the BDS-2, BDS-3, GPS, and Galileo combination with respect to a single system alone.

The development of the commercial multi global navigation satellite system (GNSS) dual (multi)-antenna common-clock receiver that uses time-synchronization technology has brought new opportunities for high-precision GNSS-based attitude determination. In this article, for the first time, we present a performance comparison of global positioning system (GPS) L1/Galileo navigation satellite system (Galileo) E1 attitude determination with a common-clock receiver using four different models, i.e., the loosely combined single-differenced (SD-LC) model, the tightly combined single-differenced (SD-TC) model, the loosely combined double-differenced (DD-LC) model, and the tightly combined double-differenced (DD-TC) model. We first introduce the SD-LC, SD-TC, DD-LC, and DD-TC relative positioning models with GPS L1/Galileo E1 observations from a common-clock receiver. Then, we present a performance comparison of the four models in both single-epoch and multi-epoch modes using static data collected with a Trimble BD992 common-clock receiver in terms of the ambiguity dilution of precision (ADOP), the ambiguity resolution (AR) success and failure rates, and the positioning and attitude determination accuracy. In the case of the single-epoch mode, the experimental results revealed that the results of the single-differenced (SD) models were identical to those of double-differenced (DD) models, i.e., the results of SD-LC and SD-TC models were identical to DD-LC and DD-TC models, respectively. Moreover, compared with the loosely combined model (SD-LC/DD-LC), the tightly combined model (SD-TC/DD-TC) delivered a much higher AR success rate and a lower AR failure rate, especially under a high elevation cutoff angle. The AR success rate increased by approximately 35.1% under a 40° elevation cutoff angle, while the AR failure rate decreased by approximately 4.3%. In the case of the multi-epoch mode, the experimental results confirmed the advantages of the tightly combined model over the loosely combined model as well as the SD model over the DD model. Compared with the DD-LC and SD-LC models, the AR success rates of the DD-TC and SD-TC models were improved by approximately 16.7% and 0.6% under a 45° elevation cutoff angle, respectively. The AR failure rates were reduced by approximately 12.4% and 0.3%, respectively. Moreover, compared with the DD-LC and DD-TC models, the AR success rates of the SD-LC and SD-TC models under a 45° elevation cutoff angle were improved by approximately 24.0% and 7.9%, respectively, and the AR failure rates were reduced by approximately 19.9% and 7.8%, respectively. Meanwhile, compared with the DD model, the SD model delivered comparable yaw accuracy and remarkably better pitch accuracy. The pitch accuracy was improved by approximately 65.2–75.0%.

Global Navigation Satellite System (GNSS)-based attitude determination with joint use of the single-differenced (SD) model and common-clock receiver has attracted much attention recently. In this contribution, for the first time we investigate the impact of antenna type and coaxial cables on the GNSS line bias (LB). The experimental results demonstrated that no apparent impact of antenna type is observed on the stability of the LB. The phase LB could, however, vary significantly if large difference exists between the lengths of the involved two cables of the same type and specification. Moreover, we found that large variations in the phase LB may be present during a continuous long-term observation period even if two cables with the same length are used. Then we evaluate the performance of BDS-3 attitude determination with SD and double-differenced (DD) models, using both static and car-driven kinematic data collected with a Trimble BD992 common-clock receiver. Particularly, for the first time the performance of the new B1C/B2a signals are presented and compared with B1I/B3I signals. Experimental results demonstrated that compared with the DD model, the SD model provides improved ambiguity resolution success rate and attitude accuracy. The achievable ambiguity resolution success rate and yaw accuracy are slightly improved whereas the pitch accuracies are remarkably improved by approximately 37.9%-50.0% and 46.0%-53.1% for the two datasets. Moreover, the results of static data have revealed that the BDS-3 B1C solution delivers comparable attitude accuracy with B1I solution whereas the B1C/B2a solution provides lower attitude accuracy than B1I/B3I solution.