Many applications, such as marine navigation, land vehicles location, etc., require real time precise positioning under medium or long baseline conditions. In this contribution, we develop a model of real-time kinematic decimeter-level positioning with BeiDou Navigation Satellite System (BDS) triple-frequency signals over medium distances. The ambiguities of two extra-wide-lane (EWL) combinations are fixed first, and then a wide lane (WL) combination is reformed based on the two EWL combinations for positioning. Theoretical analysis and empirical analysis is given of the ambiguity fixing rate and the positioning accuracy of the presented method. The results indicate that the ambiguity fixing rate can be up to more than 98% when using BDS medium baseline observations, which is much higher than that of dual-frequency Hatch-Melbourne-Wübbena (HMW) method. As for positioning accuracy, decimeter level accuracy can be achieved with this method, which is comparable to that of carrier-smoothed code differential positioning method. Signal interruption simulation experiment indicates that the proposed method can realize fast high-precision positioning whereas the carrier-smoothed code differential positioning method needs several hundreds of seconds for obtaining high precision results. We can conclude that a relatively high accuracy and high fixing rate can be achieved for triple-frequency WL method with single-epoch observations, displaying significant advantage comparing to traditional carrier-smoothed code differential positioning method.

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.