BeiDou Navigation Satellite System Research Articles

Multiple integer candidates ambiguity resolution: a unification ambiguity resolution algorithm

Among all the ambiguity resolution techniques, the Full Ambiguity Resolution (FAR), Partial Ambiguity Resolution (PAR) and Best Integer Equivariant (BIE) estimator are widely used. Although the researches have been done on the different classes of ambiguity resolution, we still hope to find the relationships among these specific algorithms. In this work, we unify the PAR and FAR algorithms under a whole framework of BIE by applying multiple integer candidates. A concise estimation formula of the variance of Gaussian BIE estimator based on the variance of float solution and the probability distribution of the candidates is first derived. Then, we propose an algorithm named Multiple Integer Candidates Ambiguity Resolution (MICAR) to discover as many ambiguities in the BIE as possible that can be estimated more precisely by PAR (FAR) algorithm instead of BIE. In the experiments, we utilize the simulated data of GPS (Global Positioning System) + BDS (BeiDou Navigation Satellite System) + Galileo (Galileo navigation satellite system) to contrast the effects of MICAR and single candidate estimator, i.e., FAR. By taking the threshold of 5 cm at 95% confidence level as an example, MICAR accelerates the convergence process by about 3.0 min. When the positioning sequence converges, MICAR reduces the root mean square of the positioning error by 9.8% in horizontal directions and 3.5% in vertical direction, which is attributed to more fixed NL.

Extension of the BDS IGSO and MEO satellite antenna patterns with FengYun-3C and LuTan-1 onboard data

The International Global Navigation Satellite System (GNSS) Service (IGS) has recommended calibrating the extended satellite antenna Phase Center Variation (PCV) model for all navigation satellites to support low-Earth-Orbit (LEO) satellite applications. Owing to the absence of ground-calibrated PCVs for the BeiDou Navigation Satellite System (BDS), tracking data from global ground stations were used for in-orbit estimations. However, limited by the observed maximum nadir angle, PCVs based on ground data cannot cover the entire range of nadir angles observed using by LEO satellites. In this study, the FengYun-3C and LuTan-1 missions were used to extend the PCVs of the BDS Inclined GeoSynchronous orbit (IGSO) and medium-Earth-orbit (MEO) satellites. The PCVs corresponding to the ionosphere-free linear combinations of B1I/B2I, B1I/B3I, and B1C/B2a were calibrated in-orbit by extending the maximum nadir angle from 9° to 10° for the IGSO and from 13° to 15° for the MEO. There was good consistency among the estimated PCVs of satellites of the same type. In addition, these estimated PCVs were close to the corresponding satellite block-specific values estimated based on ground tracking data. The impact of the extended PCVs of the BDS satellite antenna was investigated by comparing them with the unextended PCVs model in the receiver antenna PCVs pattern estimation and precise orbit determination of the FengYun-3C and LuTan-1 satellites. The results showed that the extended BDS satellite PCVs effectively reduced the unmodeled error of the unextended BDS satellite PCVs in the low-elevation region of the LEO receiver antenna PCV patterns. In addition, compared with the introduction of phase center offset alone, the introduction of ground-based PCVs can improve the overlapping orbit differences (OODs) of LEO satellites, and the extended BDS satellite PCVs can further improve the OODs. Taking B1C/B2a as an example, the improvement ratio of OODs in the 3D direction of Lutan-1A increased from 5.2 % to 8.0 %, and that of Lutan-1B can rise from 1.7 % to 4.2 %.

High-precision services of BeiDou navigation satellite system (BDS): current state, achievements, and future directions

With the rapid development of technologies such as autonomous driving and robotic navigation, the demand for accurate and reliable positioning results with BDS has increased. The current status and future development of BDS high precision services are reviewed. The operational PPP-B2b of BDS-3 achieves positioning accuracy at decimeter-level within 14 min and has the drawbacks in regional coverage and long convergence time compared with the international counterparts, such as CLAS of QZSS and HAS of Galileo. A development frame for multi-layer BDS high-precision services is proposed by considering its construction cost, compatibility of user terminal, operating maintenance burden, and service level. The global high-precision service with the improved orbit and clock accuracy enhanced with the inter-satellite link is taken as the most fundamental layer. By incorporating inter-satellite link observations, the orbit errors URE and clock errors are significantly reduced to approximately 0.05 m and 0.16 ns, respectively, which will expand PPP service to global. Based on this, the regional PPP-AR and PPP-RTK services with improved convergence performance are taken as the second layer. With PPP-AR, the convergence time drops to 10 min. With PPP-RTK, the convergence time would be further shortened to less than 3 min. The LEO enhanced PPP service is taken as the third layer which overcomes both drawbacks of the long convergence time of the inter-satellite link enhanced service (the first layer) and the regional coverage of the PPP-AR/PPP-RTK services (the second layer). The simulation results show that by introducing a LEO constellation of 288 satellites, the LEO enhanced PPP can achieve positioning accuracy better than 5 cm within approximately 1 min. In addition, the integration of LEO constellation and PPP-RTK is further proposed to enable instantaneous convergence. The implementation challenges are also presented.

Satellite orientation modelling with quaternions and its impact on BDS-3 PPP-AR

Satellite orientation is a fundamental component of processing high-precision data from the Global Navigation Satellite System (GNSS). However, insufficient handling of satellite orientation may substantially affect the quality of the precise point positioning (PPP) solutions. This research investigates the influence of satellite orientation using satellite attitude quaternions on the third-generation BeiDou Navigation Satellite System (BDS-3) PPP. To illustrate the impact of satellite attitude, both float and PPP with integer ambiguity resolution (PPP-AR) were undertaken using observations from a multi-GNSS Experiment (MGEX) network. To fully evaluate the effect of the quaternions on PPP, a comprehensive comparison between BDS-3 and Galileo constellations was conducted using nominal attitude and quaternions. The findings indicate a significant performance difference between BDS-3 and Galileo satellites in phase observations after resolving integer ambiguities, with Galileo consistently demonstrating superior phase residuals across various receivers. When it comes to positioning accuracy, the utilisation of quaternions improves coordinate precision across both constellations. Furthermore, the quaternions enhance the stability of time series for the positioning biases and observational residuals.

Elevating performance in BDS-3 Precise Point Positioning Ambiguity Resolution through LEO augmented constellations

With the help of constellations combined BDS-3 (BeiDou Navigation Satellite System) and LEO (Low Earth Orbit), we aim to improve the performances of PPP (Precise Point Positioning) and PPP Ambiguity Resolution (PPP-AR). First, LEO constellations with 66, 96, 156, 192, 270, and 288 satellites are designed to establish six LEO augmented constellations. Based on four challenge scenarios, PPP of six LEO augmented constellations are performed. Even in the strip-shaped obstruction area losing more than 60% of observations, the positioning accuracies of static PPP are improved by (1.0%, 5.7%, 0.2%) for BDS+66LEO, and (14.9%, 33.7%, 7.5%) for BDS+288LEO in the east, north, and up components. The positioning accuracy and convergence time improve quickly as the number of LEO satellites increased from 66 to 156, and slowdown from 192 to 288. Two constellations, BDS+156LEO and BDS+192LEO, are considered to strike the balance of acceptable PPP performance and constellation load. Then, the performance of PPP-AR is realized with the estimated UPD (Uncalibrated Phase Delay). The correlations among geodetic parameters and ambiguities deriving from the post-fit variance–covariance matrix are analyzed to illustrate the enhancement of LEO augmented constellations. Under the condition of 20°elevation angle occlusion with azimuth ranging from 0 to 360°, BDS+156LEO can achieve an ambiguity fix rate of up to 98.37% with a faster mean TTFF (Time To First Fix) of 12.76 min, and the positioning accuracies in the east, north, and up components are improved by 28.2%, 21.4%, and 15.1% respectively, compared with BDS-3. BDS+192LEO realized an 98.42% ambiguity fixing rate, and improved BDS-3 by 31.4%, 26.7% and 11.5% with its TTFF been 12.25 min.

Statistical study of BDS-2/BDS-3 satellite signal quality and positioning accuracy during weak and moderate geomagnetic storms

We statistically study 10 weak to moderate geomagnetic storms that occurred since the 25th solar activity cycle to evaluate the quality of satellite signal and positioning accuracy of Beidou Navigation Satellite System (BDS). The results show that the PAS (Percentage of Affected Satellites) index, which integrates three scenarios: satellite signal loss, satellite signal loss of lock, and carrier phase signal anomaly, appears significant anomaly changes during weak and moderate geomagnetic storms, and its changing trend is closely related to the geomagnetic storm Kp index and Dst index, the correlation coefficient is greater than 0.75. Based on the results of PAS signal quality evaluation, the effect of PAS on the positioning error of Precision Point Positioning (PPP) of BDS-2/BDS-3 systems is analyzed and verified in conjunction with PAS. The results show that there is a strong agreement between the time of PAS anomaly and the time of PPP positioning accuracy anomaly. The positioning error of PPP increases by 9 to 44 times compared to the quiet period. The statistical results indicate that the PAS index is useful for the signal quality evaluation of the Beidou Navigation Satellite System under different space weather conditions.

Initial Study of Adaptive Threshold Cycle Slip Detection on BDS/GPS Kinematic Precise Point Positioning during Geomagnetic Storms

Global navigation satellite system (GNSS) provides users with all-weather, continuous, high-precision positioning, navigation, and timing (PNT) services. In the operation and use of GNSS, the influence of the space environment is a factor that must be considered. For example, during geomagnetic storms, a series of changes in the Earth’s magnetosphere, ionosphere, and upper atmosphere affect GNSS’s positioning performance. To investigate the positioning performance of global satellite navigation systems during geomagnetic storms, this study selected three geomagnetic storm events that occurred from September to December 2023. Utilizing the global positioning system (GPS)/Beidou navigation satellite system (BDS) dual-system, kinematic precise point positioning (PPP) experiments were conducted, and the raw observational data from 100 stations worldwide was analyzed. The experimental results show that the positioning accuracy of some stations in high-latitude areas decreases significantly when using the conventional Geometry Free (GF) cycle-slip detection threshold during geomagnetic storms, which means that the GF is no longer applicable to high-precision positioning services. Meanwhile, there is no significant change in the satellite signal strengths received at the stations during the period of the decrease in positioning accuracy. Analyzing the cycle-slip rates for stations where abnormal accuracy occurred, it was observed that stations experiencing a significant decline in positioning accuracy exhibited serious cycle-slip misjudgments. To improve the kinematic PPP accuracy during magnetic storms, this paper proposes an adaptive threshold for cycle-slip detection and designs five experimental strategies. After using the GF adaptive threshold, the station positioning accuracy improved significantly. It achieved the accuracy level of the quiet period, while the cycle-slip incidence reached the average level. During magnetic storms, the ionosphere changes rapidly, and the use of the traditional GF constant threshold will cause serious cycle-slip misjudgments, which makes the dynamic accuracy in high latitude areas and some mid-latitude areas uncommon, while the use of the GF adaptive threshold can alleviate this phenomenon and improve the positioning accuracy in the high-latitude regions and some of the affected mid-latitude areas during the magnetic storms.

Influence of Inter-System Biases on Combined Single-Frequency BDS-2 and BDS-3 Pseudorange Positioning of Different Types of Receivers

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.

Real-Time Estimation of BDS-3 Satellite Clock Offset with Ambiguity Resolution Using B1C/B2a Signals

The third generation of the BeiDou navigation satellite system (BDS-3) can transmit five-frequency signals. The real-time satellite clock offset of BDS-3 is typically generated utilizing the B1I/B3I combination with the ambiguity-float solutions. By conducting the ambiguity resolution (AR), the reliability of the satellite clock offset can be improved. However, the performance of BDS-3 ambiguity-fixed real-time satellite clock offset with B1C/B2a signals remains unknown and unrevealed. In this contribution, the performance of the BDS-3 ambiguity-fixed satellite clock offset with the new B1C/B2a signals is investigated. One week of observation data from 85 stations was used to perform ambiguity-fixed satellite clock offset estimation. For B1I/B3I and B1C/B2a signals, the wide-lane (WL) uncalibrated phase delay (UPD) on the satellite end is fairly stable for one day, while the narrow-lane (NL) UPD standard deviation (STD) amounts to 0.122 and 0.081 cycles, respectively. The mean ambiguity fixing rate is 80.7% and 78.0% for these two signal combinations, and the time to first fix (TTFF) for the B1C/B2a signals is remarkably shorter than that of the B1I/B3I signals. The STDs of the ambiguity-float and -fixed satellite clock offsets are 0.033 and 0.026 ns, respectively, for the B1I/B3I combination, and it is reduced to 0.024 and 0.023 ns for B1C/B2a signals, respectively. Using the estimated UPD and clock offset products, the positioning performance of the kinematic Precise Point Positioning (PPP)-AR results amounts to 1.56, 1.23, and 4.46 cm in the east, north, and up directions for B1I/B3I signals, respectively. It is improved to 1.36, 1.16, and 4.25 cm using the products estimated with the B1C/B2a signals, with improvements of 12.8%, 5.7%, and 4.7% in three directions, respectively. The experiments showed that the performances of the ambiguity-fixed satellite clock offsets and the PPP-AR results using B1C/B2a signals are better than those of B1I/B3I.

Orbit Determination of High Orbit Spacecraft based on BDS-3 using Extended Kalman Filter

The positioning of highly elliptical orbit (HEO) spacecraft is very important in deep space exploration and other missions. The Beidou Navigation Satellite System (BDS-3), which was completed in 2020, has put forward new ideas for using GNSS technology to make up for the lack of earth-based TT&C systems. At the same time, the selection of the gravity field order and the perturbation forces must be considered when using dynamical methods for HEO spacecraft positioning. In this paper, simulation experiments are carried out based on the Two-Line Orbital Element (TLE) data of BDS. Two HEO satellites with different semimajor-axis (67509.6 km, 212857.3 km) are selected as the target spacecraft orbits. The single point positioning (SPP) method and Extended Kalman Filter (EKF) method are used for HEO spacecrafts positioning respectively. The experiments show that a 20×20 order gravity field model can be chosen for the orbital integral of HEO spacecraft orbits, and the integration error caused by solar gravity and lunar gravity should be taken into account with the change of orbital altitude. Adding Geostationary Orbit (GEO) and Inclined GeoSynchronous Orbit (IGSO) navigation satellites improved the visibility of these two orbits by 19.45% and 16.64%, respectively, and improved the GDOP value by 14.1% and 3.8%, respectively, compared to observing MEO satellites only. The use of the EKF method can effectively improve the positioning accuracy of the HEO spacecraft compared to the SPP method. For the spacecraft in HEO-1, the RMS value of the positioning errors of the EKF method was 67.82 m, and the accuracy of each direction was improved by 44.28%, 38.85%, and 38.62%, respectively. For the spacecraft in HEO-2, the positioning errors in the x direction of EKF method was within 12 km and within 2 km in the y and z directions. The accuracy of these three directions was improved by 84.91%, 79.24%, and 58.64%, respectively.

A novel method for cycle slip detection and restoration of BDS carrier phase

The chief purpose of this present study is to develop a new approach to cycle slip detection and restoration of the BeiDou Navigation Satellite System (BDS) carrier phase. Based on the RAIM algorithm in the application of aviation safety, we extend the application to ensure the precision of the carrier phase. To stand-alone receivers of a low-cost single frequency, carrier phase data is made different between adjacent epochs. Then least-square residuals were to design a RAIM scheme with differential carrier phase data to find out the epoch with cycle slip, and finally repair cycle slip by Chebyshev polynomial. Results indicate that the approach can detect cycle slip effectively and both big cycle slip and small cycle slip could be repaired.

Evaluation methods of BDS-3 ground-segment defensive capability oriented to satellite navigation countermeasures

Owing to intentional interference and destructions during satellite navigation countermeasures, the security application of global navigation satellite systems (GNSS) faces immense challenges. To ensure the safe application of the GNSS in complex electromagnetic environment, the system-level defensive capability need be assessed, which can make for maintaining GNSS normal service during countering and further realizing the optimal decision. Therefore, this study used the ground control segment in the GNSS as the evaluation object, the bottom indices related to the criterion layers including service performance and station function as the key evaluation indices, and the technical requirement of each index under a secure situation as the standard, to propose the evaluation system including index system and evaluation methods for the ground-segment defensive capability. As BeiDou navigation satellite system III (BDS-3) is a global navigation satellite system independently built and operated by China, it was taken as a case for method verification. Then, BDS-3 two-way observation data between the satellite and the ground and between stations, which was collected from Beijing flight Control Center, from March 5 to 12 (2022) were selected during tests, and the results were compared with the existing standards contained in BDS open service performance standard to evaluate the system-level defensive capability. Evaluation Results of positioning accuracy and error correction ability for the BDS-3's ground stations determined through seven damage experiments with different interference strength show that: Corresponding horizontal and vertical positioning accuracy of stations under test did not exceed 1 m in the statistical period and their convergence time did not exceed the limit (30 min); thus, the ground segment of the BDS-3 has a good defensive capability. Compared to comprehensive evaluation results of the BDS-3, based on the theoretical threshold (the ground-segment threshold ≤48.40 % and the space-segment threshold ≤51.60 %), we know that its ground-segment defense (14.06 %) was worse than GPS ground-segment defense (14.43 %), whereas the ground-segment defense of the BDS/GPS integrated system (15.29 %) was best and its capability evaluation grade was strong. They indicate system's future improvements should focus more on enhancing the development scale and service efficiency of the BDS-3's ground stations in the Western Hemisphere, and reasonably promote system compatibility and interoperability while considering facility cost and operating efficiency.

Construction of a meteorological application system based on BDS ground-based augmentation network and water vapor products validation

The national Beidou Navigation Satellite System (BDS) ground-based augmentation network (BGAN) of China is constructed with the existing GNSS observation resources of industrial sectors and local governments, based on the concept of joint building and sharing with sustainable development. This study provides a detailed introduction to the design, construction and operation of a meteorological application system based on BGAN, and validation of its water vapor products. BDS and GPS real-time observation of atmospheric water vapor is achieved nationwide in China and multi-GNSS applications. Through the application of multi-GNSS data and validation of the water vapor products from 2018 to 2020, the accuracy of precipitable water vapor (PWV) derived from BDS only is equivalent to that from GPS only. The root mean square error (RMSE) between them is about 2 mm with high correlation coefficient. Based on radiosonde data, the validation is conducted with the products of BDS-PWV, GPS-PWV, and Combined-PWV derived with multi-GNSS of BDS and GPS. The error characteristics of the three products show a consistent trend over the months. The bias is relatively small. The RMSE of the three products is in the range of 2.18–2.73 mm. The BDS-PWV has the largest RMSE, followed by GPS-PWV, and Combined-PWV has the smallest RMSE.

A novel mode of INS-aided BDS real-time high-rate and precise kinematic relative positioning between two moving platforms

ABSTRACT 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%.

Wheat height and phenology retrieval using GPS/BDS interferometric reflectometry technology

Monitoring vegetation growth utilizing the Global Navigation Satellite System-interferometric reflectometry (GNSS-IR) technology has obtained widespread attention in recent years. GNSS-IR based approaches demonstrate the advantageous characteristics of high temporal resolution while maintaining cost-effectiveness. Most existing studies generally utilize reflected signals to retrieve the plant height and vegetation water content, while few studies focus on vegetation phenology and yield. In this study, both phenology metric dates and plant height of wheat were extracted using reflected signals data from GPS and BeiDou Navigation Satellite System (BDS) in a wheat farmland, located at northeast of Henan, China. The results showed that there was reasonable consistency between the retrieval heights and in-situ measurements, with the correlation coefficient of 0.836 for GPS and 0.868 for BDS. The damping coefficient calculated by signal-to-noise ratio (SNR) presented obvious characteristics during different wheat growth stages and the trends of the damping coefficient were basically consistent with that of the normalized difference vegetation index (NDVI). When taking a lag between the leaf area index (LAI) and the damping coefficient into consideration, the correlation was greatly increased. Moreover, the phenology metrics dates extracted by the damping coefficient were close to those estimated by NDVI with errors less than 8 days. Hence, this research preliminarily proves the feasibility of obtaining the wheat phenological period by using GNSS-IR technology.

Earth Rotation Parameters Derived from BDS-3 New Signals B1C/B2a Dual-Frequency Combination Observations

The Earth rotation parameters (ERP) play a crucial role in defining the global reference frame and the Global Navigation Satellite System (GNSS) is one of the important tools used to obtain ERP, including polar motion (PM), its rates, and length of day (LOD). The latest IGS Repro3 ERP products, which provided the IGS contribution to the latest ITRF2020, were generated without consideration of the Beidou Navigation Satellite System (BDS) observations. The global BDS, namely the BDS-3 constellation, has been completely constructed from July 2020 and the observing stations are evenly distributed globally now. Two couple dual-frequency combinations, including the B1I/B3I and B1C/B2a combinations, are commonly used for BDS-3 ionosphere-free combination usage. With the goal of identifying the optimal dual-frequency combination for BDS-3 ERP estimates for the future ITRF definition with a consideration of BDS-3, this research evaluated the performance of ERP estimation using B1I/B3I and B1C/B2a combinations. Firstly, we conducted a comparison of the ambiguity resolutions. The mean percentage of successfully resolved ambiguities for the BDS-3 B1C/B2a combination is 86.5%, surpassing that of B1I/B3I. The GNSS satellite orbits and ERP were estimated simultaneously, thus the accuracy of orbits could also reflect the performance of the ERP estimates. Subsequently, we validated the orbits of 22 BDS-3 Medium Earth Orbit (MEO) satellites using Satellite Laser Ranging (SLR), and the root mean square error (RMS) of the SLR residuals for the 3-day arc orbit with B1C/B2a signals was 5.72 cm, indicating superior accuracy compared with the B1I/B3I combination. Finally, we compared the performance of ERP estimation, considering both internal and external accuracy. For the internal accuracy, B1C/B2a-based solutions demonstrated a reduction in mean formal errors of approximately 17% for PM, 22% for LOD, and 21% for PM rates compared with B1I/B3I-based solutions. In terms of external accuracy, we compared BDS-3-derived ERP estimates with the IERS 20C04 products. The B1C/B2a combination exhibited a slightly better standard deviation performance and a significant reduction in mean bias by 56%, 54%, 39%, 64%, and 23% for X, Y polar motion, X, Y polar motion rates, and LOD, respectively, compared with B1I/B3I solutions. In conclusion, the results highlight the excellent signal quality for BDS-3 B1C/B2a and its superiority in ERP estimation when compared with the B1I/B3I combination.

Orbit and clock products for quad-system satellites with undifferenced ambiguity fixing approach

Integer Ambiguity Resolution (IAR) can significantly improve the accuracy of GNSS Precise Orbit Determination (POD). Traditionally, the IAR in POD is achieved at the Double Differenced (DD) level. In this contribution, we develop an Un-Differenced (UD) IAR method for Global Positioning System (GPS)+ BeiDou Navigation Satellite System (BDS) + Galileo navigation satellite system (Galileo)+ Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) quad-system POD by calibrating UD ambiguities in the raw carrier phase and generating the so-called carrier range. Based on this method, we generate the UD ambiguity-fixed orbit and clock products for the Wuhan Innovation Application Center (IAC) of the International GNSS Monitoring and Assessment System (iGMAS). One-year observations in 2020 from 150 stations are employed to investigate performance of orbit and clock products. Notably, the UD Ambiguity Resolution (AR) yields more resolved integer ambiguities than the traditional DD AR, scaling up to 9%, attributable to its avoidance of station baseline formation. Benefiting from the removal of ambiguity parameters, the computational efficiency of parameter estimation undergoes a substantial 70% improvement. Compared with the float solution, the orbit consistencies of UD AR solution achieve the accuracy of 1.9, 5.2, 2.8, 2.1, and 2.7 cm for GPS, BeiDou-2 Navigation Satellite System (BDS-2), BeiDou-3 Navigation Satellite System (BDS-3), Galileo, and GLONASS satellites respectively, reflecting enhancements of 40%, 24%, 54%, 34%, and 42%. Moreover, the standard deviations of Satellite Laser Ranging (SLR) residuals are spanning 2.5–3.5 cm, underscoring a comparable accuracy to the DD AR solution, with discrepancies below 5%. A notable advantage of UD AR lies in its capability to produce the Integer Recovered Clock (IRC), facilitating Precise Point Positioning (PPP) AR without requiring additional Uncalibrated Phase Delay (UPD) products. To assess the performance of quad-system kinematic PPP based on IRC, a network comprising 120 stations is utilized. In comparison to the float solution, the IRC-based PPP AR accelerates convergence time by 31% and enhance positioning accuracy in the east component by 54%.

The communication and measurement architecture of BDS-3 global operations and services

This study introduces the third-generation BeiDou Navigation Satellite System (BDS-3) system’s creative global operation and service architecture based on regional stations and Ka-band inter-satellite links (ISLs). The architecture’s contributions to BDS-3 include not only combined orbit determination and time synchronization but also autonomous orbit determination and time synchronization, global operations and services. The BDS-3 on-orbit operation results are being presented in the paper to verify the designed capabilities. Compared with BDS-2, the orbit determination accuracy is improving from 0.6 m to 0.15 m, and the time synchronization accuracy is improving from 6.67 ns to 1.16 ns. Under autonomous orbit determination and time synchronization, the 30-day orbit maintenance accuracy reaches 16 m, and the time synchronization accuracy reaches 3.74 ns. The success rate of data transmission reaches 99%, and the delay is better than 12.9 s. In the future, laser ISLs will be used to enhance the system structure and further improve global operation and service capabilities.

Orbit determination of Earth-Moon libration point navigation constellation based on Inter-satellite links

Earth-Moon libration point navigation constellation has a merit of fully covering the cislunar space and providing navigation services with merely a small number of satellites. Furthermore, this type of constellation itself can achieve orbit determination by using only its Inter-satellite links (ISL) owing to the well-known gravitational asymmetry near the libration points. This paper adopts a representative four-satellite navigation constellation including three satellites located near the libration point L3, L4, L5, and an extra one in Distant Retrograde Orbit (DRO), and studies the orbit determination accuracy of the constellation under two conditions: establishing ISLs within itself (called Solely libration point satellites) and establishing additional ISLs with BeiDou Navigation Satellite System (BDS) (called Libration + BeiDou satellites). The simulation results indicate that, for the Solely libration point satellites scenario with the 1 m range error and solar radiation pressure (SRP) error with the level of 10% deviation between ball model and macro model, the final orbit accuracies for L3, L4, L5, and DRO satellites can respectively achieve 11.3 m, 12.7 m, 12.6 m, and 7.3 m. Reducing the link interval can significantly shorten the arc length to achieve final accuracy, whileas it has less impact on the final orbital accuracy. When the link interval is set as 240, 60, 10, and 2 min, the arc lengths at the final accuracy of better than 15 m are about 35, 29, 23, and 20 days, respectively. To balance the communication burden and the orbit determination arc length, the recommended ISL building interval is 10 min. Errors coming from range measurement model and dynamic model, in addition, are key factors in orbit determination, which can result in meters to tens of meters of orbital accuracy. For the Libration + BeiDou satellites scenario, the augmented ISLs to BDS can substantially improve constellation orbital accuracy and shorten the orbit determination arc length. When the DRO satellite attached to the Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) satellites of BDS respectively, the improved accuracy are 37.1%, 61.2%, and 42.2%, while the shortened arc length are 20.1%, 28.3%, and 28.1%, respectively. The research findings presented in this paper can serve as a reference for the construction and assessment of navigation constellations in the Earth-Moon system.

Performance comparison of orbit and clock augmentation corrections from PPP-B2b, HAS and CLAS

Precise Point Positioning (PPP) augmentation corrections can enhance the accuracy of Global Navigation Satellite System (GNSS) positioning. Three prominent PPP augmentation services: the third generation of BeiDou Navigation Satellite System (BDS-3) PPP-B2b, Europe's Galileo High Accuracy Service (HAS) and Quasi-Zenith Satellite System (QZSS) Centimeter Level Augmentation Service (CLAS), are evaluated and compared, contributing to the optimal utilization of these services. Based on a 25-day dataset in March 2023, all the three services have made significant improvements in GPS orbit accuracy compared to the broadcast ephemeris. Galileo HAS achieved the highest three-dimension (3D) orbit accuracy for both GPS and Galileo (10.5 and 10.4 cm), followed by CLAS (48.1 and 16.3 cm) and PPP-B2b (GPS: 73.0 cm, BDS-3: 44.6 cm). This distinct performance of PPP-B2b orbits is found for the first time to be related to the large constellation rotation errors, which accounts for roughly half of the orbit errors of along and cross components. Regarding clock errors, PPP-B2b and HAS enhanced GPS clock accuracy to 0.20 ns (70 %) and 0.17 ns (74 %), respectively, over the broadcast clock (0.66 ns), while CLAS shows a much smaller improvement. Moderate correlations of 0.3–0.8 between orbit and clock errors are observed for the three augmentation corrections. For signal in space ranging error (SISRE), HAS (GPS:5.5 cm, Galileo:4.9 cm) outperforms PPP-B2b (GPS:14.3 cm, BDS-3:8.9 cm) and CLAS (GPS:23.6 cm, Galileo:13.7 cm). The 2-hourly kinematic positioning results with an accuracy of better than 20 cm (95th percentile) for the horizontal and vertical component, could be achieved for both PPP-B2b and HAS within 20 min within their service area. It is not recommended rely solely on the orbit/clock/code bias of CLAS for precise positioning, as the positioning accuracy is influenced by the SISRE. PPP-RTK of CLAS achieves horizontal 10 cm (95th percentile) and rapid convergence of mostly less than a minute by incorporating phase bias and atmospheric corrections.