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In recent years, the rapid development of moving platforms, especially unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), has promoted their widespread applications in various fields such as precision agriculture and formation flight. In these applications, for accurate real-time kinematic positioning between two moving platforms, receiver autonomous integrity monitoring (RAIM) is necessary to assure the reliability of the obtained relative positioning. However, the existing carrier phase-based RAIM (CRAIM) algorithms are mainly a direct extension of pseudorange-based RAIM (PRAIM), whose availability is also a major challenge in signal-harsh environments. Learning from the integrated system between Global Navigation Satellite System (GNSS) and INS and based on a multiple hypothesis solution separation (MHSS) algorithm, we have developed an improved CRAIM algorithm, which combines Beidou Navigation Satellite System (BDS) and INS to offer integrity information for real-time kinematic relative positioning between two moving platforms in challenging environments. To achieve more robust and efficient fault detection and exclusion (FDE) results, an algorithm of observation-domain outlier detection combined with MHSS (OOD-MHSS) is also proposed. In this algorithm, the kinematic relative positioning method with INS addition is performed first, then, based on double-difference (DD) phase observations with known integer ambiguities and the OOD-MHSS method, the integrity monitoring information can be provided for the kinematic relative positioning between two moving platforms. To assess the performance of the OOD-MHSS and the improved CRAIM algorithm, a series of kinematic experiments between different platforms was analyzed and discussed. The results show that the improved CRAIM algorithm can perform effective FDE and provide reliable integrity information, which offers centimeter-level relative position solutions with decimeter-level protection levels (PLs) (integrity budget: 1×10−5/h). Both observation outlier detection and INS improve the continuity and availability of kinematic relative positioning and the PLs in horizontal and vertical directions. The PL values have been improved by up to 24.3%, and availability has reached 96.67% in harsh urban areas. This is of great significance for applications requiring higher precision and integrity in kinematic relative positioning.

A modified multipath error mitigation method using the multi-point hemispherical grid model (MHGM) is proposed, and the influence of changes in the observation environments of IGS stations on their data quality is evaluated. The multipath error models of different satellite pairs for different observation periods can be established using the integrated multi-GNSS data in the proposed method. The test under deliberate high multipath environment reveals that this method can effectively estimate the GNSS multipath error, detect and present the orientation of the interference sources around the station. The RMS of residuals and the kinematic positioning accuracy on day 237 of 2018 are improved by 68% and 61%, respectively. Compared with the empirical site model (ESM), which can also visualize the effects of the multipath, the RMS of residuals when applying the MHGM is improved by 20%. The test with IGS historical observations shows that MHGM can effectively reflect the influence of changing multipath interference around stations on carrier phase observations, with an average improvement of 25% in the RMS of carrier phase residuals in the extrapolated 9-day validations over the past 18 years. The results of a kinematic positioning experiment in 2019 generally coincide with the RMS statistic results of carrier phase residuals as well. The MHGM demonstrates distinct potential in the influence evaluation of changes for the multipath interference around the stations on their observation quality.

The Chinese Beidou navigation satellite system (BDS) has provided regional and global navigation and positioning services for the users via the BDS-2 and BDS-3 satellites. However, BDS-2 and BDS-3 send navigation signals on different frequencies; three of those are identical to assure system compatibility and interoperability. To comparatively analyze these navigation signals, we carried out three zero-baseline experiments with five brands of receivers, including Trimble, Septentrio, NovAtel, ComNav and Unicore. BDS-2 and BDS-3 multi-frequency data were collected during these experiments. The data were processed to evaluate the code and carrier phase measurement noises and investigate the inter-system biases (ISBs) on the three identical frequencies. The effects of the ISB on ambiguity resolution (AR) and position estimation (PE) were also demonstrated using the zero-baseline data with one Trimble receiver and one Septentrio receiver. The results show some new findings: (1) the code and phase noises in BDS-3 are smaller than those in BDS-2 on the same frequencies, and the three new signals B1C, B2b and B2a have comparable noises to the present signals. Besides, millimeter-level code noises are achieved on B3I and B2a signals in NovAtel receivers; (2) the code ISBs on B1I, B2I/B2b and B3I between BDS-2 and BDS-3 were found and distinguished, while no phase ISB could be found. The code ISB seems to be receiver-related and can be as large as 1 m in heterogeneous receivers. It is stable during a whole day but may also vary due to a restart of the receiver. No code and phase ISB on all three frequencies is observed for homogeneous receivers; (3) the code ISB will hamper the reliable AR and precise PE. The HMW (Hatch–Melbourne–Wübbena) combination on B1I and B3I is severely biased by about 0.6 cycles when double differencing between BDS-2 and BDS-3. After ISB calibration, the ratio value of wide-lane (WL) AR has a slight increase, and the accuracy of DD B1I code positioning has improved more than 10%, but few improvements can be seen in the fixed solution. It should be noted that although the inter-system code bias (ISCB) between BDS-2 and BDS-3 is detected in the baseline data, this bias should be considered in the absolute positioning as well.

NaGlobal vigation Satellite System (GNSS) positioning technology is widely used for its high precision, global, and all-weather service. However, in complex environments such as urban canyons, GNSS performance is often degraded due to signal occlusion and even fails to achieve positioning due to the insufficient visible satellites. Because of the characteristics of large bandwidth, low latency, and high Base Station (BS) density, the fifth-Generation mobile communication (5G) technology has gradually become a trend for positioning in cities while offering traditional communication service. To supply the communication demands of the User Equipment (UE), only one BS is usually considered to establish a connection with the UE during the BS construction. However, the positioning accuracy with a single BS in urban canyons will be significantly reduced. To further improve the positioning accuracy in such extreme scenarios, this paper proposes a simplified 5G/GNSS fusion positioning system architecture using observations from only a 5G BS and a GNSS satellite. In this system, the GNSS receiver is mounted on the 5G BS, and the measurements provided by the receiver are used to form the differential code and complete the position estimation. The positioning mathematical models of the system based on the original code and differential code are derived. Then, the impacts of the measurements noise and the time synchronization error on the positioning accuracy are analyzed theoretically. Finally, the positioning performance is investigated by a set of simulation experiments. Numerical results show that under the existing 5G measurement noise and 2 m's code measurement noise, the improvement of the differential code based fusion positioning compared with the 5G-only positioning is more than 32%, which is also about 6% higher than the original code based fusion positioning. Besides, this improvement is not affected by the time synchronization error between the BS and the GNSS satellite.

The BeiDou Navigation Satellite System (BDS) has developed rapidly, and the combination of BDS Phase II (BDS-2) and BDS Phase III (BDS-3) has attracted wide attention. It is found that there are code ISBs between BDS-2 and BDS-3, which may have a certain impact on the BDS-2 and BDS-3 combined positioning. This paper focuses on the performance of BDS-2/BDS-3 combined B1I single-frequency pseudorange positioning and investigates the positioning performance with and without code ISBs correction for different types of receivers, include geodetic GNSS receivers and low-cost receivers. The results show the following: (1) For geodetic GNSS receivers, the code ISBs of each receiver is about −0.3 m to −0.8 m, and the position deviation is reduced by 7% after correcting code ISBs. The code ISBs in the baseline with homogeneous receivers has a little influence on the positioning result, which can be ignored. The code ISBs in the baseline with heterogeneous receivers is about −0.5 m, and the position deviation is reduced by 4% after correcting code ISBs. (2) The code ISBs in the low-cost receivers are significantly larger than those in the geodetic GNSS receivers, and the impact on the positioning performance of the low-cost receivers is significantly greater than that on the geodetic GNSS receivers. After correcting the code ISBs, the position deviation of low-cost receivers can be reduced by around 12% for both undifferenced and differenced modes. (3) For low-cost receivers, correcting the code ISBs can increase the number of epochs successfully solved, which effectively improves the low-cost navigation and positioning performance. (4) The carrier-phase-smoothing method can effectively reduce the distribution dispersion of code ISBs and make the estimation of ISBs more accurate. The STD values of estimated code ISBs in geodetic GNSS receivers are reduced by about 40% after carrier-phase smoothing, while the corresponding values are reduced by about 7% in low-cost receivers due to their poor carrier-phase observation quality.

For kinematic relative positioning users between two moving platforms, limited communication bandwidth and computation ability usually cannot support real-time transmission of high-rate (≥10 Hz) BeiDou Navigation Satellite System (BDS) data. The performance of Ambiguity Resolution (AR) is also a major challenge in signal blocked and loss of lock environments. Based on BDS and Inertial Navigation System (INS) data, we develop a novel mode of INS-aided BDS kinematic relative positioning between two moving platforms, aiming to realize real-time, high-rate and precise positioning with low-cost communication modules in challenge environments. To achieve this goal, the INS-aided high-rate relative kinematic positioning and INS-aided BDS AR re-initialization methods are proposed. In this mode, the baseline bias caused by the different position datum is first defined and resolved. Then, high-rate INS data are assisted to obtain kinematic relative position when real-time kinematic positioning results are unavailable within 1 second. Once the BDS data are available, the predicted relative position is used as additional constraint to facilitate AR re-initialization and improve the kinematic positioning performance. The performance of these methods is discussed in a set of experiments with 1 Hz BDS data and 100 Hz INS data, and compared with the conventional method by sending raw BDS/INS measurements. The results show that the proposed methods can achieve an accuracy of about 5 cm for the INS-aided 100 Hz relative positioning in baseline components and lengths, which is equal to the conventional method, but the transmitted data have been sharply reduced by an average of nearly 80%. With the assistance of INS-predicted baseline constraint, the relative positioning performance has been further improved. The accuracy of baseline length errors is less than 4 cm, and the AR fixing rates keep larger than 95% during the experiment, while the wrongly fixed rates are reduced to less than 0.5%.

The rapid development of unmanned aerial vehicles (UAVs) in recent years has promoted their application in various fields, such as precise agriculture, formation flight, etc. In these applications, the accurate and reliable real-time position and attitude determination between each moving device in the same platform system are the key issue for safe and effective cooperative works. In traditional ways, static reference stations should be set up near the platform to keep the stable position datum of the platform system. In this paper, we abandoned the static stations and expected to achieve stable position datums with the platform system itself. To achieve this goal, we proposed an improved method based on both the Global Positioning System (GPS)/Beidou Navigation Satellite System (BDS) data and the inertial navigation system (INS) data to obtain precise positions of the moving devices. The time-differenced carrier phase (TDCP) was used to get the position variations and update the positions over time, and then, the INS data was integrated to further improve the accuracy and reliability of the updated positions; thus, this method is denoted as the TDCP/INS method. To evaluate the performance of this method and compare it with the traditional single-point positioning (SPP) method and the Kalman filtered SPP (KFSPP) method, a field vehicle experiment was conducted, and the position results achieved from these three methods were compared with those from the tightly combined real-time kinematic positioning (RTK)/INS method, where centimeter-level accuracy was obtained and regarded as the reference. The quantitative analysis where the position variations were evaluated and the qualitative analysis where the vehicle trajectories in three typical urban driving scenarios were discussed were both made for the three methods. The numerical results showed that the accuracy of the position variations from the SPP, KSPP, and TDCP methods was at the meter level, while that from the TDCP/INS method improved to the centimeter level, and the accuracies were 1.9 cm, 2.9 cm, and 3.1 cm in the east, north, and upward directions. The trajectory results also demonstrated a perfect consistency of the driving positions between the TDCP/INS method and the reference. As a contrast, the trajectories from the SPP and KFSPP methods had frequent jumps or sways when the vehicle drove along a large, curved road, turned at a crossroad, and passed under an urban viaduct.

The multipath error is considered to be the most limiting factor for high precision positioning applications. The sidereal filtering (SF) method can be used to mitigate the multipath error in the observation domain, and it has been successfully applied in the multipath mitigation in global positioning systems (GPS) and regional BeiDou navigation satellite systems (BDS2). However, there are few reports on the SF method in other systems. The performance of the SF method relies on the explicit orbit repeat periods of satellites in diverse systems or even different types of constellations. It is therefore inconvenient to utilize the SF method for multi-GNSS multipath error mitigation. Alternatively, a space domain multipath error reduction method, which establishes the multi-point hemispherical grid model (MHGM) using the residuals of the double-differenced carrier phase observations in the ambiguity-fixed period, has been modified. It is an integrated model for multi-GNSS, without considering the diversity of different systems and constellations. To compare the performance of MHGM and SF from a multi-GNSS point of view, the determination method of orbit repeat periods via the broadcast ephemerides is summarized, and the SF method is extended to the global BeiDou navigation satellite system (BDS3) and Galileo navigation satellite system. Further test results show that the performance of MHGM and SF are comparable from the perspective of root mean squares (RMS) and the power spectrum analysis of double-differenced residuals, as well as the static positioning results. This implies that the space domain MHGM can obtain similar correction effects as the SF method in the observation domain, but the former is more flexible for modeling with various systems’ data. In addition, the established MHGM using the data of multi orbit periods demonstrates a better performance compared with that of only one orbit period, and an average improvement of 13.1% in the RMS of the double-differenced residuals can be achieved.

The multipath effect is a crucial error source caused by the environment around the station and cannot be eliminated or mitigated by differential algorithms. Theoretically, the maximum value for the carrier phase is a quarter the wavelength, i.e., about 4.8 cm for the GPS L1 signal. Considering the increasing demands of high-precision applications, the multipath error has become a major factor affecting the accuracy and reliability of GPS millimeter-level data processing. This paper proposes a multi-point hemispherical grid model (MHGM) to mitigate the multipath effect. In this method, the hemisphere centered on each station is divided into a grid, and the multipath error at the station is estimated based on the parameterization of the grid points. The double-differenced (DD) observed-minus-calculated (OMC) values on some previous days are treated as the observation values to model the present multipath error. Contrary to the present methods which rely much on the platform of data collection and processing, MHGM can be potentially applied to GPS data processing with the existing hardware and software. Experiments in high-multipath and low-multipath environments are designed by mounting a baffle or not. The experimental results show that MHGM is effective in mitigating the multipath effect. When using data from the previous day, an average improvement of about 63.3% in the RMS of DD OMC can be made compared with that without correction, and this is basically consistent with the sidereal filtering (SF) method which is 63.0%. Furthermore, the effectiveness of the above two methods is better than that of the empirical site model (ESM). The kinematic positioning results are also basically consistent with the statistical results of the RMS values of DD OMC. Historical data from more than one day can more explicitly and effectively model the MHGM. Furthermore, compared with the SF method, the MHGM can be used not only to mitigate the multipath error, but also to orientate the sources of the multipath error around the station, and give guidance in the physical elimination of these sources.

The loose combination (LC) and the tight combination (TC) are two different models in the combined processing of four global navigation satellite systems (GNSSs). The former is easy to implement but may be unusable with few satellites, while the latter should cope with the inter-system bias (ISB) and is applicable for few tracked satellites. Furthermore, in both models, the inter-frequency bias (IFB) in the GLObal NAvigation Satellite System (GLONASS) system should also be removed. In this study, we aimed to investigate the performance difference of ambiguity resolution and position estimation between these two models simultaneously using the single-frequency data of all four systems (GPS + GLONASS + Galileo + BeiDou Navigation Satellite System (BDS)) in three different environments, i.e., in an open area, with surrounding high buildings, and under a block of high buildings. For this purpose, we first provide the definition of ISB and IFB from the perspective of the hardware delays, and then propose practical algorithms to estimate the IFB rate and ISB. Thereafter, a comprehensive performance comparison was made between the TC and LC models. Experiments were conducted to simulate the above three observation environments: the typical situation and situations suffering from signal obstruction with high elevation angles and limited azimuths, respectively. The results show that in a typical situation, the TC and LC models achieve a similar performance. However, when the satellite signals are severely obstructed and few satellites are tracked, the float solution and ambiguity fixing rates in the LC model are dramatically decreased, while in the TC model, there are only minor declines and the difference in the ambiguity fixing rates can be as large as 30%. The correctly fixed ambiguity rates in the TC model also had an improvement of around 10%. Once the ambiguity was fixed, both models achieved a similar positioning accuracy.