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The integrated navigation of single-frequency global navigation satellite system (GNSS) and inertial navigation system (INS) has broad application prospects with the development of multi-constellation GNSS. However, GNSS signals are susceptible to interference from a complex environment, which results in low-quality observations. The combination of frequencies cannot be applied for a single-frequency signal, so it is difficult to fix the ambiguity and process cycle slip. Therefore, the method of ambiguity resolution and cycle slip processing with INS aiding is proposed in this paper. When full ambiguities cannot be completely fixed, a subset of ambiguity is determined based on the elevation angle and posteriori residuals. The satellite is firstly eliminated one by one if the absolute value of posteriori residual is over the set threshold. And if the ambiguities still cannot be fixed, the satellite with the minimum elevation angle is eliminated each one. The short-term and high-accuracy position predicted by the INS was used as the constraint equation of the cycle slip detection. The unit weight mean square error of the cycle slip detection equation was used to identify the epoch where the cycle slip occurs, and the residual calculated by robust estimation was used to detect and repair the cycle slip. A set of data collected by a vehicle was used to analyze the proposed method. The experimental results showed that the proposed partial ambiguity resolution can obtain the optimal ambiguity fixing rate and positioning performance compared with the full ambiguity resolution and partial ambiguity resolution based on the elevation angle. The proposed algorithm can effectively detect and accurately repair the cycle slip for the simulated small and large cycle slips, and the cycle slips can still be detected when the global positioning system (GPS), global navigation satellite system of Russia (GLONASS), and BeiDou navigation satellite system (BDS) were outage for 10 s, 5 s, and 10 s without sufficient visible satellites.

A compact dual-band Wilkinson power divider (WPD) using the via-free dual-composite right/left-handed (D-CRLH) resonators is presented for application in the Beidou navigation satellite system in this paper. First, by establishing an equivalent circuit model and using Bloch theory, a dual-band resonator is further analyzed to gain insight into its working mechanism, which can exhibit -90∘ phase shift at lower frequencies and + 90∘ phase shift at upper frequencies, respectively. Then, to facilitate the design, ignoring parasitic parameters, a simplified circuit model retaining the physical meaning is presented, and the closed-form formulas for determining lumped element values of a dual-band characteristic are derived. Next, there is a significant rejection performance between two operating frequencies due to the inherent band-stop filtering effect of the D-CRLH resonator. Following that, the WPD is verified through experiments, showing excellent performance. Finally, based on this property, a dual-band feeding network (FN) is constructed by the combination of a WPD and a phase shifter with the proposed resonator. The simulated and measured results are found in good agreement with each other, which further demonstrated our proposed design conception.

The BeiDou Navigation Satellite System with global coverage (BDS-3) was officially launched on July 31, 2020. In addition to the legacy B1I and B3I signals from the regional system (BDS-2), BDS-3 provides several new signals, i.e., B1C, B2a, B2b and B2a + b, with advanced technologies and global availability, which brings new opportunities for ground-based BDS multipath reflectometry (BDS-MR) altimetry. Previous studies focused on the MR altimetry performance of the legacy signals using signal-to-noise ratio (SNR) observations, but the new BDS signals have not been investigated. In this contribution, all types of BDS-3 SNR data collected from seven International GNSS Service (IGS) stations are analyzed signal by signal in terms of SNR quality and altimetry performance, while the legacy BDS B2I and Global Positioning System (GPS) L2C signals are also selected for comparison. Seven globally distributed IGS stations are first investigated for the quality of SNR observations, and then two optimally selected land stations are used to assess BDS-MR based altimetry performance, while a coastal station is used to assess BDS-MR for sea level retrieval performance. It is found that the quality of SNR observations varied site by site due to the differences in environment and equipment, but in general, the new signals except B1C show a higher level of SNR. Then, no detectable biases among each signal are found for land altimetry, while new signals could yield higher amplitude when performing spectral analysis. In coastal sea level altimetry, only two new signals B1C and B2a are available at the selected IGS station, and it is observed that the retrieval performance of BDS B2a is comparable to that of B2I, B3I and GPS L2C with root-mean-square errors (RMSEs) of about 21 cm, while that for B1I and B1C is slightly poorer with RMSEs of 29.68 cm and 26.66 cm respectively.

As the significant error sources influencing the Global navigation satellite system (GNSS) positioning, navigation and timing (PNT) services, ionospheric delay and satellite hardware delay should be properly calibrated. Particularly, the pseudorange observable-specific signal bias (OSB) is convenient and can be directly corrected in the raw pseudorange measurement. In this work, we present a novel single-frequency ionospheric-free-half PPP (SFPPP2) approach for ionospheric studies, in which the ionospheric VTEC and satellite OSB are isolated from the slant ionospheric observables by means of the ionospheric multi-layer mapping function (MF). The computation and parameterization methods of the ionospheric vertical total electron content (VTEC) and satellite pseudorange OSB are present. To validate the effectiveness and reliability of the novel method, we investigate and compare the performance of the single-frequency ionospheric-float PPP (SFPPP1), SFPPP2 and dual-frequency ionospheric-float PPP (DFPPP1) solutions for ionosphere sensing. The analytical results indicate that the novel approach can extract the slant ionospheric observables with the accuracy of sub-meters. The accuracy of the estimated ionospheric VTEC by the single-frequency PPP approaches is in sub-meter level, which exhibits the slightly worse accuracy than that from the dual-frequency PPP solution. The estimated ionospheric VTEC accuracy is improved with the multi-layer MF compared with the single-layer MF. The estimated BeiDou Navigation Satellite System (BDS) pseudorange OSB with the proposed SFPPP2 approach is stable, reliable and of the high accuracy, and the RMS with respect to Chinese Academy of Sciences (CAS) product for C2I and C6I signals with single-layer and multi-layer MFs are 0.40, 0.41, 0.60 and 0.63 ns, respectively. The proposed PPP approach can retrieve the VTEC and satellite pseudorange OSB by mass-market receivers for the GNSS users.

With the deployment of the global BeiDou navigation satellite system (BDS-3) constellation completed, the positioning service performance is significantly improved relative to the regional system (BDS-2). As one of the key prerequisite products for precise point positioning (PPP), the combined BDS-2/BDS-3 real-time satellite clock estimation method is investigated in this study. Since the code hardware delays of BDS-2/BDS-3 satellites might be inconsistent for some receiver types, the inter-system bias (ISB) is considered in the combination although the overlapping B1I/B3I signal is employed. The combination processing is comprehensively evaluated in terms of satellite tracking coverage, clock precision, and convergence time. The experiment results indicate that the standard deviation (STD) precision of the estimated clocks for BDS-2 medium Earth orbit (MEO) satellites is improved by 52.0% from 0.150 ns to 0.072 ns due to the improvement of satellite tracking coverage. Introducing the ISB parameter as piece-wise constants improves the STD of all clocks from 0.076 ns to 0.067 ns and BDS-3 clocks achieve a significant improvement from 0.065 ns to 0.053 ns. The real-time clock estimation is demonstrated to be robust for the clock datum transformation, and it converges after one hour to a stable precision but needs a long time to achieve the best performance. The BDS real-time clocks are estimated with the proposed strategy to support real-time PPP based on the predicted satellite orbits. Results show that the clock STD is about 0.1 ns for most BDS satellites and the positioning accuracy of about 10 cm is achieved after the convergence time of about half an hour. The clock precision for BDS-2 geostationary Earth orbit (GEO) satellites is degraded to 0.303 ns due to the impact of poor orbit prediction errors. The exclusion of GEO satellites improves the positioning accuracy by about 15% and reduces the convergence time by 22–34%.

BeiDou high-precision power line inspection can improve the efficiency and automation level of inspection operations, reduce labor intensity, and save inspection costs. However, although the satellite-based augmentation technology can solve the problem of large-scale positioning, it will introduce too many parameters into the positioning system through the method of parameter estimation. As a result, the behavior of the equation deteriorates, which makes it difficult to separate some parameters, and the convergence time of ambiguity parameters is too long. Under normal circumstances, the satellite-based augmentation standard positioning service needs at least about 30 min to converge to the centimeter level, and the ground-based augmentation system can provide an accurate model. This paper proposes a fast positioning method for satellite-based augmentation assisted by the BeiDou ground-based augmentation station. The receiver adopts the least square method, combined with the extended Kalman filter positioning, to achieve the improvement of the regional positioning effect of the satellite-based augmentation system. Positioning accuracy error does not exceed 1.6 meters. The error in the three directions of X, Y, and Z can be converged to the centimeter level in about 8 min. It can significantly improve the convergence time of satellite-based augmentation, and maintain continuous, stable and high-precision positioning of unmanned aerial vehicle in power line inspection.

Inter-satellite link (ISL) scheduling is required by the BeiDou Navigation Satellite System (BDS) to guarantee the system ranging and communication performance. In the BDS, a great number of ISL scheduling instances must be addressed every day, which will certainly spend a lot of time via normal metaheuristics and hardly meet the quick-response requirements that often occur in real-world applications. To address the dual requirements of normal and quick-response ISL schedulings, a data-driven heuristic assisted memetic algorithm (DHMA) is proposed in this paper, which includes a high-performance memetic algorithm (MA) and a data-driven heuristic. In normal situations, the high-performance MA that hybridizes parallelism, competition, and evolution strategies is performed for high-quality ISL scheduling solutions over time. When in quick-response situations, the data-driven heuristic is performed to quickly schedule high-probability ISLs according to a prediction model, which is trained from the high-quality MA solutions. The main idea of the DHMA is to address normal and quick-response schedulings separately, while high-quality normal scheduling data are trained for quick-response use. In addition, this paper also presents an easy-to-understand ISL scheduling model and its NP-completeness. A seven-day experimental study with 10 080 one-minute ISL scheduling instances shows the efficient performance of the DHMA in addressing the ISL scheduling in normal (in 84 hours) and quick-response (in 0.62 hour) situations, which can well meet the dual scheduling requirements in real-world BDS applications.

China’s BeiDou Navigation Satellite System (BDS) can provide real-time precise point positioning (PPP) service for users in China and surrounding areas with PPP-B2b signal. In this paper, real-time PPP is assessed and studied based on 8 days of PPP-B2b and BDS/GPS broadcast messages. Real-time precise ephemerides are compared against Multi-GNSS Experiment (MGEX) final products and the positioning performance of real-time PPP is evaluated with MGEX/iGMAS stations. Results show that the real-time orbit accuracy is about 0.0725, 0.2479 and 0.2587 m in directions of radial (R), along (A) and cross (C) for BDS-3 satellites, and 0.0729, 0.3098 and 0.2193 m for GPS satellites. The standard deviation values of the clock offset errors are about 0.05–0.18 ns for BDS-3 satellites, and 0.05–0.15 ns for GPS satellites. In addition, the differential code bias (DCB) parameters of PPP-B2b agree well with parameters of MGEX DCB and time group delay (TGD), with the differences less than 2 and 0.15 ns, respectively. Furthermore, for the positioning experiments, the average positioning accuracies of BDS and GPS integrated real-time PPP are about 1.07, 2.69 and 2.25 cm in north (N), east (E), and up (U) directions for static mode; and about 3.6, 5.9 and 9.4 cm for kinematic mode. Moreover, the convergence times for an accuracy level of 20 cm in N, E and U components are about 8–22 min, and 10–8 min, for static mode and kinematic mode, respectively.

Low-cost global navigation satellite system (GNSS) receiver terminals are widely used in the field of navigation and location-based services due to their small size, low weight and low power consumption. For users equipped with low-cost receivers on the mass market, it is important to improve the performance of single point positioning (SPP) with single-frequency pseudorange measurement. In this study, we constructed a low-cost receiver using a single-frequency receiver module named u-blox M8T, and a compact core board named COM-IMX6UL. The receiver is capable of receiving the B1 signal of the BeiDou Navigation Satellite System (BDS) and L1 signal of the Global Positioning System (GPS). With the view of verifying the performance of single-frequency GPS/BDS single point positioning (SPP) in practice, we carried out static and vehicle-mounted kinematic experiments using the low-cost receiver and evaluated its capability based on observations and positioning results. It is demonstrated that the GPS/BDS SPP can achieve competitive satellite tracking and positioning performance compared to the GPS-only and BDS-only SPP, especially when the receiver was in a restricted environment. In the case of static experiment, the BDS/GPS SPP positioning accuracy is better than 1.5 m and 3.0 m in the horizontal and vertical directions within the cut-off angle range of 10° to 35°, which is a 10 ~ 30% improvement over the BDS-only SPP and a 10 ~ 60% improvement over the GPS-only SPP. In the case of the vehicle-mounted kinematic experiment, the horizontal positioning accuracy of GPS/BDS SPP is better than 1 m on urban general roads and expressways, which is approximately 50% improvement than that of GPS-only SPP.

In order to probe into the characteristics of positioning deviation between Beidou Navigation Satellite System (Beidou) and global positioning system (GPS), and investigate possible contribution of Beidou data to refinement of global coordinate system, refined calculation is made on observation data of 240 national reference stations that are distributed uniformly across China on the whole in this study. These stations support satellite signals of four global navigation satellite systems, including Beidou, GPS, GLONASS and Galileo, and a 5-year time span from 2016 to 2020 is adopted. In this study, PPP is calculated based on GPS data and Beidou single system data in no-difference resolution network mode, and accurate coordinates of national reference stations in two processing modes are obtained. Analysis of difference between the calculations based on Beidou data and on GPS data shows that the consistency between Beidou and GPS positioning results reaches about 5 mm in the east and in the north, and about 1.3 cm in the height direction.

BeiDou navigation satellite system transmits triple-frequency signals. This paper reviews the disadvantages of the traditional least-squares ambiguity decorrelation adjustment algorithm in the ambiguity resolution and exploits the advantages of triple-frequency BDS. A new ambiguity resolution method that is based on adaptive ionosphere estimation constraints for medium-length baselines (from 50 to 100 km) is proposed. We realize the method in two steps. First, double-differencing uncombined observables (B1/B2/B3 observables) are used to obtain float solutions with atmospheric delay estimated as a random walk parameter by using the extended Kalman filter. Second, two ambiguity search equations are constructed between any two uncombined ambiguities. The adaptively estimated ionospheric delay shown in step one is also used to constrain ambiguity search equations. Finally, traversal search of integer ambiguity is performed. The method is decreasingly affected by the cycle slips and reference satellite switching, which can effectively avoid the unstable positioning accuracy of the carrier in the RTK positioning of medium-length baselines. In this study, BDS triple-frequency data collected from two baselines of 53 km and 103 km, respectively, are used to validate the proposed method. Experiments show that the medium-length baseline ambiguity can be rapidly fixed within one single epoch. Although the baseline is over 100 km, the accuracy of coordinate component under dynamic conditions can reach the centimeter level.

The service areas of the BeiDou Navigation Satellite System (BDS) are China, the Asia–Pacific, and the world via three stages of development. The BDS constellation is designed to maintain a geostationary Earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO). These orbital maneuvers yield certain difficulties for data processing, especially for the BeiDou satellites, such as a decrease in the real-time service performance, which causes a missing precise orbit product from the maneuvered satellites. The frequencies of the orbital maneuvers for the GEO and IGSO satellites are higher than those for the MEO satellites. The maneuvering time and strategy cannot be obtained by common users due to secrecy, which can yield a decline in the service performance of the BDS. Thus, in this study, we analyzed the variation in the orbital semimajor axis for the satellites. The long-term variation in the orbital semimajor axis changes linearly. The short-term variation in the orbital semimajor axis also has periodicity, which can be described by the sum of sine functions. According to the long-term variation in the orbital semimajor axis for the satellites, we propose a detection method for in-plane orbital maneuvering of the GEO, IGSO, and MEO satellites. We then propose a detection method for out-of-plane maneuvering of the GEO satellites. BDS and Global Positioning System (GPS) data from the broadcast ephemeris were analyzed to verify the proposed methods. The experimental results from 2013 to 2019 show that the frequency of orbital maneuvering is approximately once a month for the GEO satellites, once every six months for the IGSO satellites, and once every 1.4 years for the MEO satellites.

The ionospheric error affects the accuracy of the Global Navigation Satellite Systems observation and precise orbit determination. Usually, only the first order ionospheric error is considered, which can be eliminated by the ionospheric-free linear combination observation. But the remaining higher order ionospheric error will affect the accuracy of observations and their applications. In this paper, the influence of the higher order ionospheric error have been studied by using the International Geomagnetic Reference Field 13 and the Global Ionosphere Maps model produced by the Center for Orbit Determination in Europe. Focus on ionospheric error, the experiment of paper at doy 302 in 2019, which show that the second order ionospheric error impacting BeiDou Navigation Satellite System (BDS) B1I and B3I observation is 6.3569 mm and 11.8484 mm, respectively. Whereas, the third order ionospheric error impacting BDS B1I and B3I observation is 0.1734 mm and 0.3977 mm, respectively. Due to the current measurement accuracy of BDS carrier-phase observation can reach 2 mm, the influence of high order ionospheric error on observation should be considered. For BDS precise orbit determination, the orbit overlapping results are indicated that its orbit accuracy can be improved approximately 5 mm with the higher order ionospheric error correction, which is also in agreement with the results of Satellite Laser Ranging in this work.

In the design of a BeiDou navigation satellite system(BDS) receiver, the carrier loop is largely influenced by the loop filter, and the selection of loop filter parameters is crucial to the performance of the carrier loop. In this paper, by analyzing the relationship between the parameters of the loop filter transfer function of the BDS receiver’s fourth-order carrier loop system and the time-domain index of the system, the loop filter transfer function parameters of the fourth-order system are obtained when the dynamic performance is best optimized under the condition that the maximum steady-state error is limited. The relationship between the phase margin, magnitude margin of the system and the parameters of the system transfer function is obtained through simulation experiment and theoretical derivation. The simultaneous equations of deriving the loop system transfer function parameters are given under the following conditions: the optimal phase margin and magnitude margin of the system are settled. These research results have important reference significance for the design of a high-performance BDS receiver.

Detecting and characterizing Total Electron Content (TEC) depletion is important for studying the ionospheric threat due to the Equatorial Plasma Bubble (EPB) when applying the Ground-Based Augmentation System (GBAS) at low latitudes. This paper develops a robust method to automatically identify TEC depletion and derive its parameters. The rolling barrel algorithm is used to automatically identify the TEC depletion candidate and its parameters. Then, the depletion candidates are screened by several improved techniques to distinguish actual depletions from other phenomena such as Traveling Ionospheric Disturbance (TID) or abnormal data. Next, based on the depletion signals from three triangular receivers, the method derives EPB parameters such as velocity, width and gradient. The time lag and front velocity are calculated based on cross-correlation using TEC depletions and the geometrical distribution of three triangular receivers. The width and gradient of slope are then determined by using TEC depletion from a single receiver. By comparison, both the station-pair method and proposed method depend on the assumption that the EPB morphology is frozen during the short time when the plasma bubble moves between the receivers. However, our method relaxes the restriction that the baseline length should be shorter than the width of slope required by the station-pair. This relaxation is favorable for studying small-scale slope of depletions using stations of a longer baseline. In addition, the accuracy of the width and gradient is free of impact from hardware biases and small-scale disturbance, as it is based only on the relative TEC variation. The method is demonstrated by processing Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) data on 15 August, 2018, in a solar minimum cycle.

Le systeme de navigation par satellites BeiDou a ete developpe par la Chine de facon autonome afin de remplir des missions tant au plan national qu’international. Si les politiques chinoises deployees aussi bien nationalement que localement concernant le GNSS ont ouvert la voie a l’edification de BeiDou et au developpement de ses applications, la promotion de ce systeme dans le monde entier rencontre de nombreux defis legaux parmi lesquels la demande concernant une gestion saine, un regime de responsabilite a l’egard des tiers, les moyens de proteger la vie privee des utilisateurs etc… La Chine doit regler ces problemes legaux si elle veut que BeiDou parvienne aux buts qui lui ont ete assignes.

BeiDou Navigation Satellite System (BDS) is composed of satellites in geostationary Earth orbit (GEO), medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO). However, the orbit determination of geostationary Earth orbits and of geosynchronous orbits (GSO) with small inclination angle and small eccentricity is a challenging task that is addressed in this paper using Extended Kalman Filter (EKF). The satellite positions were predicted in Earth-centred inertial (ECI) reference frame when propagated through Keplerian model and perturbation force model for different values of right ascension of ascending node (RAAN). Root mean square (RMS) errors of 9.61 cm, 6.73 cm and 11.46 cm were observed in ECI X, Y and Z satellite position coordinates of GSO respectively, whereas, the RMS errors for GEO satellite were 8.89 cm, 7.92 cm, and 0.93 cm respectively in ECI X, Y and Z coordinates; for perturbation force model with maximum value of RAAN when compared with dynamic orbit determination model. Kolmogorov-Smirnov test for EKF reported a p-value > 0.05, indicating a good fit of perturbation force model for orbit propagation. Orbit determination using EKF with perturbation force model were compared with that using EKF with Kepler's model. Wilcoxon Rank Sum test was used to compare the residuals from EKF algorithm through Kepler's model and perturbation force model. EKF with Perturbation force model showed improvement in predicting the satellite positions as compared to Kepler's model. EKF with Perturbation force model was further applied to International GNSS Service (IGS) station data and kilometre level accuracy was achieved. RMS errors of 0.75 km, 2.53 km and 1.91 km were observed in ECI X, Y and Z satellite position coordinates of GSO, respectively, whereas, the RMS errors for GEO satellite were 3.89 km, 4.20 km and 6.66 km respectively in ECI X, Y and Z coordinates for perturbation force model.

This letter is dedicated to evaluating the potential use of reflected signals from the BeiDou Navigation Satellite System for retrieving the thickness of sea ice. Accurate phase altimetry results over sea ice would be helpful for detecting the sea ice thickness. Here, a new phase processing approach is proposed to estimate the adaptable phase altimetry result. During the data processing, fake wrap points in the residual interferometric phase are replaced by fit values; moreover, the phase altimetry result is shown to reach centimeter accuracy. A coastal experiment was performed from January 22 to February 19, 2016, in Dashentang, Tianjin, China. The sea ice thicknesses calculated from the phase altimetry results and Archimedes’ principle range from 5 to 25 cm, which are consistent with the thicknesses of samples collected during the experimental period in Bohai Bay near Dashentang.

Short Message Communication (SMC) is a featured service of BeiDou Navigation Satellite System (BDS). After its successful deployment in 2003, Regional Short Message Communication (RSMC) service has been continuously serving China and its neighboring countries and regions, especially in life safety scenarios. In this paper, the architecture of the Global Short Message Communication (GSMC) system is proposed based on the medium earth orbit (MEO) constellation and the crosslinks of the global BeiDou navigation system (BDS-3). Three subtypes of GSMC service, i.e. positioning report, emergency search and rescue (SAR) and regular SMC are designed in accordance with the technical characteristic of integration of navigation and communication in BDS-3, which supports future wide applications of GSMC. The performance of the designed GSMC system is analyzed by numerical calculations. As BDS-3 was officially announced completion on July 31, 2020, GSMC has been providing initial service. First test results of the in orbit GSMC payloads are also presented in the paper to verify the designed capabilities. Preliminary results also show that the requirements of Global Maritime Distress and Safety System (GMDSS) can also be fulfilled.

In dense urban environment, Multipath (MP) and Non-line-of-sight (NLOS) signals will degrade the performance of BeiDou Navigation Satellite System (BDS) Position, Velocity and Timing (PVT). In order to mitigate this negative impact, a Constrained Robust Unscented Kalman Filter (CRUKF) is implemented based on pseudorange/Doppler shift measurements. An equivalent weight function based on the innovation vector is constructed, which can overcome the problem of performance degrading of traditional robust methods caused by the inaccurate initial state vector. Then, the motion information, navigation direction and elevation, is included to further constrain the Robust UKF (RUKF) solution. The performance of CRUKF is analyzed using two real car tests in a dense building area, Tokyo. It is shown that there is a clear correlation between MP/NLOS errors and Position Dilution of Precision (PDOP), which seriously lows the positioning accuracy. Regarding the horizontal position, the Root Mean Square Error (RMSE) of CRUKF is 5.6 m, while those of Robust Iterative Least Square (RILS) and RUKF are 15.3 m and 6.4 m, respectively. Similar improvements are presented in vertical position and velocity and hence show the superior positioning performance of CRUKF. In addition, without sensor aiding or coupling, CRUKF can be suitable for real-time application of low-cost receiver.

To realize the smooth transition from regional BeiDou Navigation Satellite System (BDS-2) to the global one (BDS-3), the integration of BDS-2 and BDS-3 is important for providing continuous, stable and reliable positioning, navigation and timing (PNT) services for global users. This work used 154 globally distributed multi-GNSS (Global Navigation Satellite System) experiment stations spanning 30 days to analyze the satellite availability and positioning performance of uncombined precise point positioning (UC-PPP) under current BDS-2 and BDS-3 constellations. We focused on three issues: the influence of BDS-3 receiver tracking abilities, the positioning performance among different areas, and the benefit of multi-frequency observations. The results show that the elliptical zone caused by poor BDS-2 satellite visibility is disappeared when the evenly distributed BDS-3 medium earth orbit satellites are introduced. When BDS-3 are integrated with BDS-2, the area with the Position Dilution of Precision (PDOP) less than 2 can be expanded to 75° S-75° N and 30° E-150° W. The positioning performance of BDS-3 and BDS-2/BDS-3 UC-PPP are seriously affected by the receiver tracking abilities of BDS-3 signals. When the maximum pseudo-random noise sequences (PRNs) of BDS-3 satellites tracked by stations are within 30 or 37, the positioning accuracy of static UC-PPP can be improved by 22.94% or 8.27% due to the integration of BDS-2 and BDS-3. Besides, the most improvement of BDS-2 and BDS-3 integration is achieved in Asia-Pacific regions, especially for the kinematic UC-PPP or the poor receiver tracking abilities of BDS-3. Similar to the multi-frequency BDS-2 UC-PPP, the benefit of multi-frequency signals for BDS-3 or BDS-2/BDS-3 UC-PPP is also non-vital. The three-dimensional positioning accuracy of BDS-2/BDS-3 multi-frequency UC-PPP in static mode and kinematic mode are 2.24 cm and 5.39 cm, while the corresponding convergence time are 49.62 min and 73.80 min, respectively. Compared with BDS-2, both the positioning accuracy and the convergence time of BDS-2/BDS-3 joint UC-PPP are improved by approximately over 50%, which indicates that BDS-3 has a great potential to provide high-quality PNT services as other global navigation satellite systems.

Vehicular dynamic positioning based on tightly coupled (TC) Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS) integration in urban areas is due to either low accuracy of pseudorange or poor continuity of carrier phase, resulting in insufficient positioning performance. To enhance the stability while ensuring positioning accuracy, this paper proposed a tightly coupled Beidou Navigation Satellite System (BDS)/INS integration scheme by improving measurement modelling with triple-frequency observations: first, a stepwise single-epoch ambiguity resolution of extra-wide-lane (EWL)/wide-lane (WL) combined observations and then modelling the measurement equation with fixed WL observation instead of conventional pseudorange or carrier phase. Experiments were carried out for verification with data collected in real traffic by a measurement vehicle. The proposed method achieved single-epoch output with an RMS statistical accuracy of decimetre level of 0.152 m horizontally and 0.196 m vertically. The signal outage experiment verified that the proposed algorithm is restoring high-accuracy positioning output in single-epoch once the signal is recaptured. The proposed method obtained a positioning accuracy improvement of 43.6% horizontally and 6.2% vertically in signal outage sections compared to the conventional method. This avoids the multiepoch ambiguity searching to fix with conventional carrier-phase processing, thereby improving the positioning stability.

The full deployment of China’s BeiDou navigation satellite system (BDS) was finalized in June 2020. To support safety-critical applications, the system must provide assured signal-in-space (SIS) performance. As one of the key steps forward for BDS, this paper characterizes the SIS range errors (SISREs) for both the regional (BDS-2) and the global (BDS-3) systems from the integrity perspective. Following the safety standards in aviation, a data-driven SISRE evaluation scheme is presented in this work. This scheme evaluates the overbounding user range accuracy (URA) and the prior fault probability to respectively capture the nominal and anomalous SIS behaviors. By processing the 4.5-year ephemerides starting from 2016 for BDS-2 and the recent 1.5-year data from2019 for BDS-3, we preliminarily provide an overall picture of the BDS SIS characteristics and reveal the significant performance variation among different satellites.

Much attention has been paid to the subsidence monitoring of large-scale man-made linear features, which are usually characterized by long-distance, large-scale, and nonuniform distribution. The multitemporal interferometric synthetic aperture radar (InSAR) technique can provide ground deformation maps for a large area with high spatial resolution and millimeter precision at low costs. The technique overcomes the limitations of ground-based survey instruments. However, the variable atmospheric turbulent component in flat areas has impacts on InSAR detection capability, especially over low-amplitude quasi-stable deformation areas. We propose an imagewise stacking method, which can improve the InSAR time-series analysis by reducing residual noise while retaining the ground deformation signal. We integrate persistent scatterer and distributed scatterer in our processing strategy and conduct a tentative test on the roadbed subsidence monitoring of the Lianyan high-speed railway using 47 medium-resolution Sentinel-1 images. Comparing the InSAR displacement time series and the results with a continuous BeiDou navigation satellite system network, the standard deviation of 3.3 mm and the mean absolute error of 2.2 mm are obtained. The proposed method reduced the above two error measures by 66.3% and 65.6%, respectively, compared with the spatiotemporal filtering. Moreover, the analysis of the spatiotemporal characteristics of the railway deformations also tells that the railway under study is stable.

The BeiDou Navigation Satellite System (BDS) is China's space‐based navigation system, designed to be compatible and interoperable with other global navigation satellite systems (GNSSs). Unlike other GNSSs, it was a two‐way active positioning system designed to provide regional radio determination satellite services (RDSS) service, including two‐dimensional position, timing, and short message communication. This chapter provides a comprehensive and in‐depth introduction to BDS. It outlines the evolution of BDS. The chapter introduces the geodesy and time systems employed by BDS. It describes BDS I and BDS II, respectively. BDS is rapidly expanding from a regional system to a global system. In the late 1970s, China continued to search for a suitable solution to provide regional or global services for China. The chapter presents the latest progress of the emerging BDS III. Finally, it offers a brief summary of BDS.

In this study, a Dual Smoothing Ionospheric Gradient Monitor Algorithm (DSIGMA) was developed for Code-Carrier Divergence (CCD) faults of dual-frequency Ground-Based Augmentation Systems (GBAS) based on the BeiDou Navigation Satellite System (BDS). Divergence-Free (DF) combinations of the signals were used to form test statistics for a dual-frequency DSIGMA. First, the single-frequency DSIGMA was reviewed, which supports the GBAS approach service type D (GAST-D) for protection against the effect of large ionospheric gradients. The single-frequency DSIGMA was used to create a novel input scheme for the dual-frequency DSIGMA by introducing DF combinations. The steady states of the test statistics were also analysed. The monitors were characterized using BDS measurement data, whereby standard deviations of 0.0432 and 0.0639 m for the proposed two test statistics were used to calculate the monitor threshold. An extensive simulation was designed to assess the monitor performance by comparing the Probability of Missed Detection (PMD) according to the differential error with the range domain PMD limits under different fault modes. The results showed that the proposed algorithm has a higher integrity performance than the single-frequency monitor. The minimum detectable divergence with the same missed probability is less than 50% that of GAST-D.

The third phase BeiDou Navigation Satellite System (BDS-3) provides a BeiDou Global broadcast Ionospheric delay correction Model (BDGIM) for single-frequency navigation and positioning applications. According to the BDS Interface Control Document (ICD) Signal B1C (Version 1.0), the BDGIM contains nine parameters and was broadcast in December 2018. The BDGIM will gradually replace the BDS-2 ionospheric 8-parameter Klobuchar model (BDSKlob). A preliminary evaluation of the BDGIM was conducted using data collected at multiple stations across the international GNSS Monitoring and Assessment System (iGMAS) global tracking network. The high-precision global grid ionospheric delay sequences obtained from the Center of Orbit Determination in Europe (CODE) were selected as references to evaluate the BDGIM performance worldwide. The synthetic analysis and comparison results show that the BDGIM provides the best global description of the ionosphere and improves the nocturnal performance of the Klobuchar model and its sharp increase in the Polar Regions. The VTEC (Vertical Total Electron Content) calculated by the BDGIM exhibited the smallest RMS (Root Mean Square) values, the highest precision, and better performance for most northern hemisphere latitudes. BDGIM RMS values for most world regions were generally less than 5 TECU (Total Electron Content Unit), and its ionospheric delay correction rate reached nearly 80%.

The radio determination satellite service (RDSS) is an advantageous and unique aspect of the BeiDou Navigation Satellite System (BDS) because other satellite navigation systems do not incorporate the RDSS. Due to the ageing of RDSS equipment, there is a long-term drift in various types of RDSS equipment time delays. There are some differences in the RDSS positioning accuracy with the change in the out-station beams, which seriously affects the positioning accuracy and service capability of the RDSS system. At present, the time delay calibration method involves sending the device to the equipment verification field to remeasure the time delay, which is cumbersome and time-consuming. The service performance and availability of the RDSS system have become greatly degraded. Therefore, a simple and efficient RDSS time delay calibration method has become an important topic for the global BeiDou system. In this study, the time delays of all channels, in-station beams, and out-station beams were obtained by the O-C method (O is the measured value and C is the theoretical value). The experiments were performed using BeiDou RDSS data in continuous 8-day tests involving five RDSS users. The results showed that the time delay accuracies of the RDSS channels, in-station beams, and out-station beams were 2.37 ns, 1.63 ns, and 2.39 ns, respectively. The positioning tests were performed based on the original and adjusted delays. The mean horizontal positioning accuracy of the five RDSS users improved from 19.71 to 4.14 m, with an average increase of 77%. The positioning accuracy achieved in this paper is much better than that of 20 m in the Beijing calibration area at present.

The single initial Global Positioning System (GPS) has been expanded into multiple global and regional navigation satellite systems (multi-GNSS/RNSS) as the Global Navigation Satellite System (GLONASS) is restored and the BeiDou Navigation Satellite System (BDS), Galileo Satellite Navigation System (Galileo) and Quasi-Zenith Satellite System (QZSS) evolve. Using the differences among these five systems, the paper constructs a consolidated multi-GNSS/RNSS precise point positioning (PPP) observation model. A large number of datasets from Multi-GNSS Experiment (MGEX) stations are employed to evaluate the PPP performance of multi-GNSS/RNSS. The paper draws three main conclusions based on the experimental results. (1) The combined GPS/GLONASS/Galileo/BDS/QZSS presents the PPP with the shortest mean convergence time of 11·5 min, followed by that of GPS/GLONASS/Galileo/BDS (12·4 min). (2) The combined GPS/GLONASS/BDS/Galileo/QZSS shows the optimal PPP performance when the cut-off elevation angle is basically the same because of the rich observation data due to a large number of satellites. To be specific, for combined GPS/GLONASS/BDS/Galileo/QZSS, the PPP convergence percentage is 80·9% higher relative to other combined systems under 35° cut-off elevation angle, and the percentages of the root mean square values of PPP within 0–5 cm are enhanced by 80·5%, 81·5% and 87·3% in the North, East and Up directions relative to GPS alone at 35° cut-off elevation angle. (3) GPS alone fails to conduct continuous positioning due to the insufficiency of visible satellites at 40° cut-off elevation angle, while the kinematic PPP of multi-GNSS/RNSS remains capable of obtaining positioning solutions with relatively high accuracy, especially in the horizontal direction.

The construction of the third generation of the Chinese BeiDou navigation satellite system (BDS), which provides global positioning, navigation, and timing (PNT) services, will be completed in 2020. As BDS satellites contain the geostationary orbit (GEO), inclined geosynchronous (IGSO), and medium earth orbit (MEO), orbital manoeuvres occur more frequently. Thus, orbit manoeuvre detection is important for continuous and reliable PNT services. A BDS orbit manoeuvre detection method based on the combination of global positioning system (GPS) and BDS observations is proposed in this study. The standard deviations of the observation residuals of the epoch-differenced velocity estimation of the single BDS system and combined GPS + BDS system were compared to determine the beginning and end of the orbit manoeuvre. The results show that the orbital manoeuvre leads to a position, velocity, and receiver clock error bias of approximately tens to hundreds of metres, several centimetres per second, and tens to hundreds of metres, respectively. Based on the proposed method, the start and end times can be detected in real time and the usable observation time can be extended by >157 min.

Navigation augmentation based on Low Earth Orbit (LEO) satellites has become a hot topic in recent years. The orbital design of LEO augmentation constellations and the analysis of their performance are essential issues for the development of LEO augmentation systems. In this paper, LEO constellations for navigation are designed with the constraint that they augment the BeiDou Navigation Satellite System (BDS) in independent and combined modes. First, the calculation of the dilution of precision (DOP) values in different augmentation work modes is derived. Second, some numerical simulations of LEO constellations with different altitudes and inclinations are carried out. Based on the designed constellations, the coverage performance in typical regions and the global DOP values are analyzed, the suitable constellations with the orbital altitude of 500 km, 1000 km, 1500 km and 2000 km are derived. Finally, the suitable LEO constellations combined with the BDS in a time synchronized scenario and a non-synchronized scenario are demonstrated. The results show that 320/16/1:500 km, 80°, 144/12/1:1000 km, 70°, 100/10/1:1500 km, 70° and 80/8/1:2000 km, 60° are the suitable constellations, and the average GDOP values of these constellations are all below 5. In the combined work mode, the amplitude and stability of the DOP are improved significantly in the time-synchronized scenario of LEO navigation system and the BDS compared with only applying the BDS. The GDOP and TDOP values are improved by up to 22.46–44.41% and 29.06–60.62% respectively. When the non-synchronized scenario is considered, i.e. the LEO navigation system and the BDS are independent systems, the improvement of the DOP value is relatively limited because a new LEO clock error parameter has to be introduced in the positioning estimation. In that case, the improvement of the GDOP values is only 3.11–22.28%, and the TDOP values become worse at medium and low latitudes.

The hardware delay difference for different navigation signals in satellite or receiver channels is called Differential Code Bias (DCB). DCB is a major error of global navigation satellite system (GNSS), which may lead to tens of Total Electron Content unit (TECu) ionospheric delay errors or several-meter ranging errors. The basic system of BeiDou Navigation Satellite System has opened services and three new navigation signals, namely B1C, B2a at the end of 2018, and B2b at the end of 2019. As the BeiDou satellite broadcast clock difference is based on the phase center of the B3I signal antenna, it is necessary to estimated the DCB values of the new navigation signals relative to B3I. Considering that BDS broadcasts the BeiDou global ionospheric delay correction model (BDGIM) parameters with the highest precision, the method of solving satellite or receiver DCB based on the BDS-3 BDGIM parameter constraint is proposed and verified. Theoretical analysis shows that the mean square error of daily solution is about 0.63–1.96 ns. The measured data of 25 iGMAS stations from January 1 to 30, 2019, are used for verification. The results show that the solution precision of satellite DCB is better than 1.0 ns and that of receiver DCB is slightly worse. This method does not need the support of external ionospheric products and provides a possibility for online real-time estimating of the satellite and receiver DCB.

In this study, the authors mainly explore the relationship between the data quality of smartphones equipped with global navigation satellite system (GNSS) modules and the accuracy and reliability of single-frequency real-time kinematic (RTK) positioning. Specifically, the visible satellite number, code minus carrier and the signal-to-noise ratio of the GNSS raw observations were evaluated through static experiments and dynamic experiments, and the performance difference between single-frequency global positioning system (GPS) RTK and single-frequency BeiDou Navigation Satellite System (BDS) RTK positioning was compared and analysed. In the static experiment, the average values of visible satellites of BDS and GPS in Xiaomi Mi 8 smartphone are 7.4 and 8.4, respectively. The average code minus carrier error of GPS is 5.234 m, the BDS is 5.518 m, and the average signal-to-noise ratio of GPS is ~29.092 dB Hz and the BDS is ~28.718 dB Hz. The data quality of the dynamic experiment is similar to the static experimental result. The positioning accuracy obtained by the static experiment from the single-frequency GPS RTK and single-frequency BDS RTK in the east/north/up (E/N/U) directions is 0.146/0.555/0.464 m and 0.843/0.287/0.317 m, respectively. The instability of BDS-locked satellite in dynamic experiment results the positioning accuracy of BDS RTK is lower than that of GPS.

The next-generation satellite-based augmentation system (SBAS) will follow the dual-frequency multi-constellation (DFMC) protocol and broadcast satellite clock-ephemeris corrections and integrity information via GPS L5-like signals to improve the accuracy and integrity for GNSS dual-frequency users. BeiDou Navigation Satellite System (BDS)-3 B1C/B2a dual-frequency users will obtain a higher positioning accuracy using DFMC clock-ephemeris corrections. This paper focuses on an approach for the generation of DFMC SBAS corrections and its preliminary results. Analyzing the signal-in-space ranging error characteristics of BDS-3 satellites reveals that it is impossible to obtain orbits that are more accurate than the broadcast orbits using regionally distributed SBAS monitoring stations. Therefore, a novel DFMC SBAS correction generation approach for BDS-3 satellites is proposed in which only clock offset corrections are calculated. The effectiveness of the proposed approach is validated using measurements from mainland China. By using clock corrections only, B1C/B2a dual-frequency users can obtain the best accuracy. The results of the BDS-3 B1C/B2a dual-frequency positioning experiment show that the user equivalent ranging error is reduced from 0.59 m to 0.37 m with clock corrections but is reduced to only 0.43 m with the addition of clock-ephemeris corrections. With clock corrections only, the 95% positioning errors are reduced from 3.57 m to 1.53 m and from 3.79 m to 2.24 m in the horizontal and vertical directions, respectively, indicating a 48% reduction in positioning errors compared to users without SBAS corrections; however, the error reduction is only 40% with clock-ephemeris corrections.

The Autonomous Navigation (AutoNav) mode of a Global Navigation Satellite System (GNSS) utilizes Inter-Satellite Links (ISLs) to maintain satellite operations without the service from the ground control segment. The newly launched Beidou satellites are capable of conducting ISLs for orbit determination to improve their autonomy, integrity, reliability, and robustness. However, the satellite orbit errors can increase over time due to various force model errors, particularly that of Solar Radiation Pressure (SRP). Accelerometers aboard satellites can measure non-conservative forces directly and have been successfully used in satellite missions for gravity recovery and atmosphere study (i.e., GRACE, CHAMP, and GOCE). This study investigates the feasibility to use accelerometers aboard Beidou satellites to improve AutoNav accuracy and service span. The results show that in a simulated 180-day AutoNav period, the orbit accuracy with the aid of accelerometers is two times better than that of using ISL data only.

Using the FengYun-3C (FY-3C) onboard BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS) data from 2013 to 2017, this study investigates the performance and contribution of BDS to precise orbit determination (POD) for a low-Earth orbit (LEO). The overlap comparison result indicates that code bias correction of BDS can improve the POD accuracy by 12.4%. The multi-year averaged one-dimensional (1D) root mean square (RMS) of the overlapping orbit differences (OODs) for the GPS-only solution is 2.0, 1.7, and 1.5 cm, respectively, during the 2013, 2015, and 2017 periods. The 1D RMS for the BDS-only solution is 150.9, 115.0, and 47.4 cm, respectively, during the 2013, 2015, and 2017 periods, which is much worse than the GPS-only solution due to the regional system of BDS and the few BDS channels of the FY-3C receiver. For the BDS and GPS combined solution (also known as the GC combined solution), the averaged 1D RMS is 2.5, 2.3, and 1.6 cm, respectively, in 2013, 2015, and 2017, while the GC combined POD presents a significant accuracy improvement after the exclusion of geostationary Earth orbit (GEO) satellites. The main reason for the improvement seen after this exclusion is the unfavorable satellite tracking geometry and poor orbit accuracy of GEO satellites. The accuracy of BDS-only and GC combined solutions have gradually improved from 2013 to 2017, thanks to improvements in the accuracy of International GNSS Service (IGS) orbit and clock products in recent years, especially the availability of a high-frequency satellite clock product (30 s sampling interval) since 2015. Moreover, the GC POD (without GEO) was able to achieve slightly better accuracy than the GPS-only POD in 2017, indicating that the fusion of BDS and GPS observations can improve the accuracy of LEO POD. GC combined POD can significantly improve the reliability of LEO POD, simply due to system redundancy. An increased contribution of BDS to LEO POD can be expected with the launch of more BDS satellites and with further improvements in the accuracy of BDS satellite products in the near future.

In the BeiDou Navigation Satellite System (BDS) B1 band, a single-sideband complex binary offset carrier (SCBOC) modulation is employed to combine the legacy and the modernized B1 signals into an asymmetric-wideband composite signal for the backward compatibility. However, SCBOC modulation has only been regarded as a means to achieve the co-existance between B1I and B1C signals, whose high-precision ranging potential is not fully understood or exploited. In this paper, a new pathway for BDS B1 receivers to further enhance their ranging precision is established for the first time, by proposing an unambiguous cross-assisted tracking (CAT) loop, which fully exploits the ranging performance of the SCBOC subcarrier and the inherent coherence between components in the composite signal. Simulation and experiment using live BDS-3 signals show that compared to the traditional tracking processing for independent components, the CAT loop can significantly improve ranging performance precision, thus providing a high-precision processing mode for the BDS B1 composite signal.

On account of the different parameters of delay-locked loop, multipath effect and code bandwidth, the Global Navigation Satellite System (GNSS) pseudorange noise of each frequency is different. An unequal-weighted three-carrier ambiguity resolution (TCAR) algorithm for long-baseline static triple-frequency ambiguity resolution is proposed. The algorithm is conducted in cascaded steps. When calculating the coefficients of the extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL) combinations, the difference of pseudorange noise is considered. Real triple-frequency BeiDou Navigation Satellite System and Global Positioning System observations from four International GNSS Service stations from 13 January to 19 January 2019 are analysed to evaluate the performance of the proposed algorithm. Results show that compared to the classical equal-weighted algorithm, the proposed algorithm shows a comparable performance for the EWL and WL ambiguity resolution and much better performance for the NL ambiguity resolution.

Timing group delay (TGD) is an important parameter that affects the positioning performance of global navigation satellite systems (GNSS). The BeiDou navigation satellite system (BDS) broadcasts TGD corrections from B3I frequency to B1I and B2I frequencies, namely TGD1 and TGD2. On July 21, 2017, BDS updated TGD values with a maximum change of more than 4 ns. In this contribution, we explain the motivation for the BDS TGD update, which is due to the systematic bias between narrowly correlated and widely correlated pseudo-ranges in BDS monitoring receivers. To investigate the impact of the updated TGD, BDS signal-in-space range error (SISRE) and user positioning performance regarding single point positioning (SPP) and precise point positioning (PPP) are analyzed. Results show that after the update of TGD, the difference between the new TGD and multi-GNSS experiment (MGEX) differential code bias (DCB) decreases from 1.38 ns to 0.29 ns on TGD1 and from 0.40 ns to 0.25 ns on TGD2. With the contribution of more accurate TGD, the systematic bias of BDS radial SISRE no longer exists, and the overall BDS SISRE also reduces from 1.33 m to 0.87 m on B1I/B2I frequency, from 1.05 m to 0.89 m on B1I frequency, from 0.92 m to 0.91 m on B2I frequency, respectively, which proves the similar precision of BDS TGD and MGEX DCB. One week of statistical results from 28 globally distributed MGEX stations shows that the SPP performance improves on non-B3I frequencies after the TGD update, with a maximum improvement of more than 22% for the B1I/B2I or B1I/B3I combination. The new TGD mainly reduces SPP positioning bias in the East component. The updated TGD also slightly improves the PPP convergence performance for the B1I/B3I combination, but mostly contributes to a more accurate estimation of the receiver clock and ambiguities.

Diversity reception of multipath Global Navigation Satellte System (GNSS) signals offers a new insight into carrier phase-based high-precision positioning. The focus of this paper is to demonstrate the fading independence between space and frequency diversity GNSS signals. In harsh urban environments, multipath components arrive to the mobile receiver antenna with different phases and Doppler shifts, therefore giving rise to the discontinuity of code and Doppler observations and large tracking errors. In this paper, an empirical model of fading GNSS signals is constructed, including power fluctuations and spread metrics. Based on this model, real BeiDou Navigation Satellite System (BDS) signals from two GNSS dual-frequency antennas are characterized, at both information and signal level. The block processing algorithm is utilized for signal investigation. Results show that: (1) a high proportion of asynchronous loss-of-lock (around 16%) is experienced by observations of diversity signals; and (2) power fluctuations of fading signals are uncorrelated in frequency separated branches unconditionally, yet for space diversity signals the independency exists in dynamic fading channels only. The results above corroborate the significant potential gain of diversity reception, and could be further implemented in researches of diversity combined GNSS parameter estimation in dense fading conditions.

BDS (BeiDou Navigation Satellite System) ground tracking stations are equipped with high accuracy atomic clocks, and they are synchronized with the BDS time scale (BDT) via the Precise Orbit Determination (POD) processing. During the periods of satellite maneuver and post-maneuver, station clocks are kept fixed as known values in the POD processing. To improve the real-time POD capability, station clocks need to be predicted. In this paper, the performance of three clock prediction models is evaluated, including quadratic polynomial model (QP), periodical term model (PM), and grey model (GM). The precision of clock fitting and prediction, as well as the performance of the prediction models in POD are compared. Data of six stations are used for test, and the results show that: the mean fitting accuracy of quadratic polynomial model, periodical term model, and grey model is 0.14 ns, 0.05 ns, 0.27 ns, respectively; the 1 h and 2 h prediction precision of the three models is 1.17 ns, 0.88 ns, 1.28 ns, and 2.72 ns, 2.09 ns, 2.53 ns, respectively. Applying the 1 h and 2 h predicted station clocks in the POD, the 3D orbit accuracy reaches the best using the periodical term model, while the radial accuracy of satellite orbit is rather close for the three models with the difference within 3 cm.

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Expanded Abstract Attached: Global navigation satellite system (GNSS) positioning has recently gained attention in the autonomous driving, machine control, and construction industries. With the development of low-cost multi-GNSS receivers and the advent of new types of GNSS, such as China's BeiDou Navigation Satellite System and the EU's Galileo, the potential of GNSS positioning has increased. In particular, the advent of a new type of GNSS directly increases the number of line-of-sight (LOS) signals under multipath conditions, such as urban canyons, and improves the positioning accuracy. Unfortunately, GNSS receivers can observe not only LOS signals, but also non-line-of-sight (NLOS) signals and LOS+reflected signals under multipath conditions. The multipath condition generally has a greater effect on the pseudorange than the carrier phase; however, the use of LOS and other signals causes large pseudorange positioning errors. Furthermore, the accuracy of the estimated receiver clock error is directly related to the accuracy of the real-time kinematic GNSS (RTK-GNSS) using GLONASS. In this research, we propose a method for detecting the NLOS and LOS+reflected signals to improve the accuracy of pseudorange positioning and RTK-GNSS using GLONASS.

The Ka-band dual one-way measurements from Inter-Satellite Link (ISL) devices equipped on the third-generation Beidou Navigation Satellite System (BDS3) follow a time division multiple access (TDMA) structure and can calculate inter-satellite and satellite-ground clock offsets. L-band two-way satellite time and frequency transfer (TWSTFT) is also applied for time synchronization between satellites and ground master. We focus on a full-ISL clock offset estimation and prediction algorithm that estimates all satellite clock parameters simultaneously utilizing ISL clock observations and also synchronizes the constellation to the system time in Beidou Time (BDT) using Ka-band satellite-ground clock observations. We discuss the applications of this algorithm by assessing the clock performance of all BDS3 satellites equipped with a passive hydrogen maser (PHM) or rubidium atomic clock. After investigating the proper prediction model for each satellite, we use the full-ISL algorithm for 24-h clock predictions. The constant hardware delays in the ISL measurements are calibrated by comparing the derived clock parameters with TWSTFT measurements; the full-ISL clock products show high accuracy and continuity. The BDS3 PHMs and rubidium clocks both have a small clock rate drift of 10–20 s/s2. The frequency stability of the BDS3 PHMs and some rubidium clocks is approximately 6–9 × 10–15 at 1-day intervals. A linear model is suitable for these small-drift clocks, while a quadratic model is essential for the other rubidium clocks. Applying the full-ISL clock prediction method improves the RMS of the 24 h prediction error from 0.88 to 0.75 ns for PHMs and from 2.62 to 1.64 ns for rubidium clocks. The estimated ISL hardware delay STDs are less than 0.2 ns, and the prediction errors evaluated with TWSTFT clock observations are similar to those evaluated with Ka-band clock observations.

Global Navigation Satellite System Real-Time Kinematic (GNSS-RTK) technology is widely used in vehicle navigation, but in complex environments such as urban high-rise street, wooded street, overpass, and tunnel, satellite signals are prone to attenuation or even unavailability. It brings great challenges to the continuous high-precision navigation. For this reason, a tightly coupled (TC) integration algorithm for GPS (Global Positioning System)/BDS (BeiDou Navigation Satellite System)/MEMS-INS (Micro-Electro-Mechanical System-Inertial Navigation System)/Odometer (GCIO) is proposed for vehicle navigation in complex urban environments. The accuracy improvement and ambiguity resolution (AR) performance are analysed in this research. First of all, the INS positioning error is constrained by fusion GPS/BDS (GC) and odometer; then, the predicted position information is used to aid GPS/BDS ambiguity resolution. In GNSS-denied environments, the odometer/INS integration is still carried out for continuous navigation. Real-time experiments are carried out in urban degraded and denied environments to validate the performance of the integrated system. In high-rise streets, the ambiguity fixing success rate of GCIO mode is 13.57% higher than that of GC mode. In the wooded street environment, the success rate has increased particularly significantly, by about 55 percent. The positioning accuracy analysis for open environment, high-rise street, wooded street, overpass, and tunnel is conducted. The experimental results show that in the above environment, the order of 0.1 m positioning accuracy can be achieved in the case of satellite outage for 1 minute, which can meet the positioning needs in most scenarios.

The BeiDou navigation satellite system (BDS) signal-in-space anomaly is an important factor affecting the signal-in-space quality assessment. Detecting and excluding signal-in-space anomalies is not only a method for constructing a BDS signal-in-space fault model but can also help ensure the BDS navigation and positioning integrity. Traditional methods, based on post precision ephemeris and broadcast ephemeris, maintain some disadvantages, such as a large delay and a low sampling rate. In this paper, a carrier-phase smoothing pseudorange algorithm based on Kalman filtering is proposed, and a real-time estimation method of a BDS signal-in-space user range error is established to detect and eliminate signal-in-space anomalies in real time, based on the statistical characteristics of signal-in-space user range error. The experimental results, based on 1 Hz data of the international GNSS service (IGS) ground observation network, show that the proposed method has an estimation accuracy of 1.15 m for a BDS signal-in-space user range error, which can effectively identify signal-in-space anomalies caused by satellite orbit and clock faults.

With the improvement in the service accuracy and expansion of the application scope of satellite navigation systems, users now have high demands for system integrity that are directly related to navigation safety. As a crucial index to measure the reliability of satellite navigation systems, integrity is the ability of the system to send an alarm when an abnormity occurs. The new-generation Beidou Navigation Satellite System (BDS-3) prioritized the upgrading of system integrity as an important objective in system construction. Because the system provides both basic navigation and satellite-based augmentation system (SBAS) services by the operational control system, BDS-3 adopts an integrated integrity monitoring and processing strategy that applies satellite autonomous integrity monitoring and ground-based integrity monitoring for both the basic navigation service and SBAS navigation service. BDS-3 also uses an improved and refined integrity parameter system to provide slow, fast and real-time integrity parameters for basic navigation, and provide SBAS-provided integrity information messages in accordance with Radio Technical Commission for Aeronautics (RTCA) specification and dual frequency, multi-constellation (DFMC) specification to support the SBAS signal frequency, single constellation operation and DFMC operation respectively. The performance of BDS-3 system integrity monitoring is preliminarily verified during on-orbit testing in different states, including normal operation, satellite clock failure and satellite ephemeris failure. The results show that satellite autonomous integrity monitoring, ground-based integrity monitoring and satellite-based augmentation all correctly work within the system. Satellite autonomous integrity monitoring can detect satellite clock failure but not satellite orbit failure. However, ground-based integrity monitoring can detect both. Moreover, the satellite-based augmentation integrity system monitors the differential range error after satellite ephemeris and clock error corrections based on user requirements. Compared to the near minute-level time-to-alert capability of ground-based integrity monitoring, satellite autonomous integrity monitoring reduces the system alert time to less than 4 s. With a combined satellite-ground monitoring strategy and the implementation of different monitoring technologies, the BDS-3 integrity of service has been considerably improved.

Ionospheric total electron content (TEC) is an important parameter in ionospheric researches and applications. However, the determination of the absolute value of TEC can be greatly influenced by the differential code biases (DCBs) estimation. Nowadays, there are more and more Global Navigation Satellite System (GNSS) signals available all over the world, which allow us to solve TEC and DCBs with the hypothesis of local spherical symmetry (LSS) imposed on the dual-frequency observations from only one individual station. For comparison, the results based on the global ionospheric map (GIM) act as a reference in this article. On the one hand, different combinations of Global Positioning System (GPS), GLONASS, and BeiDou Navigation Satellite System (BDS) are considered to illustrate the significance of multi-GNSS observations, with the mixed GPS, GLONASS, and BDS combination performing best when compared to the referenced results. On the other hand, different parameters in LSS condition are taken into account to investigate the suitable geometric constraint of LSS, with the differential longitude, latitude, and epoch suggested to be 3.0°, 0.6°, and 4 min, respectively. Moreover, a group of detailed comparisons from several different stations also show that the combined DCBs and ionospheric TEC derived from our method are compatible with those from the GIM-aided method, especially in the low-latitude area. In summary, with the advantage of the multi-GNSS signals from an individual station, our method can estimate the ionospheric TEC and DCBs independently, which could provide a potential tool in the future real-time applications.

Ground-based augmentation systems (GBASs) are widely used augmentation systems using satellite navigation. GBAS can improve the performance of BeiDou navigation satellite system (BDS) in civil aviation application. Evaluation is necessary before using a GBAS. On the basis of the flight trials conducted at the Dongying airport, evaluation results show that based on both the global positioning system (GPS) L1 signal and BDS B1I signal, ground accuracy designators (GADs) of four reference receivers are consistent with GAD-C levels. The improvement in accuracy obtained with GBAS differential process is ∼60%, and the differential position error based on the BDS B1I signal is 40% greater than that of the GPS L1 signal, because currently incomplete BDS satellites distribution is worse than that of GPS. Airborne protection levels assessments show that the approach trials based on the BDS B1I signal exhibit several false alarm events. Further analysis indicates that BDS vertical protection levels were larger because of larger pseudoinverse S result from low elevation angle and unsatisfactory geometric distribution of BDS satellites. Besides, monitors show that BDS B1I signal is more affected by ionospheric delay than GPS L1 signal, which can also contribute to false alarm events.