Global BeiDou Navigation Satellite System Research Articles

Modeling of Solar Radiation Pressure for BDS-3 MEO Satellites with Inter-Satellite Link Measurements

As the largest non-gravitational force, solar radiation pressure (SRP) causes significant errors in precise orbit determination (POD) of the BeiDou global navigation satellite system (BDS-3) medium Earth orbit (MEO) satellite. This is mainly due to the imperfect modeling of the satellite’s cuboid body. Since the BDS-3’s inter-satellite link (ISL) can enhance the orbit estimation of BDS-3 satellites, the aim of this study is to establish an a priori SRP model for the satellite body using 281-day ISL observations to reduce the systematic errors in the final orbits. The adjustable box wind (ABW) model is employed to refine the optical parameters for the satellite buses. The self-shadow effect caused by the search and rescue (SAR) antenna is considered. Satellite laser ranging (SLR), day-boundary discontinuity (DBD), and overlapping Allan deviation (OADEV) are utilized as indicators to assess the performance of the a priori model. With the a priori model developed by both ISL and ground observation, the slopes of SLR residual for the China Academy of Space Technology (CAST) and Shanghai Engineering Center for Microsatellites (SECM) satellites decrease from −0.097 cm/deg and 0.067 cm/deg to −0.004 cm/deg and −0.009 cm/deg, respectively. The standard deviation decreased by 21.8% and 26.6%, respectively. There are slight enhancements in the average values of DBD and OADEV, and a reduced β-dependent variation is observed in the OADEV of the corresponding clock offset. We also found that considering the SAR antenna only slightly improves the orbit accuracy. These results demonstrate that an a priori model established for the BDS-3 MEO satellite body can reduce the systematic errors in orbits, and the parameters estimated using both ISL and ground observation are superior to those estimated using only ground observation.

Precipitable water vapor retrieval for rainfall forecasting using BDS-3 PPP-B2b signal in the coastal region of China

Abstract Currently, rainfall cannot be accurately forecast because of poor network communication at the ocean. The advantage of the BeiDou Global Navigation Satellite System (BDS-3) precise point positioning (PPP-B2b) signal, which does not rely on network communication to receive data, is that it can provide precipitable water vapor (PWV) retrieval application services for the open seas in eastern China, where the communication system presents difficulties. In this study, data from stations in the coastal region of China were used to establish a rainfall forecasting method for monitoring extreme weather on the sea. First, the service performance of PPP-B2b was explored. Then, based on 17 Chinese coastal stations, the PWV accuracy was evaluated. Finally, based on an analysis of the relationship between PWV and actual rainfall, a threshold rainfall forecasting method based on a sliding window was constructed. The experimental results show that the PWV accuracy varies slightly depending on the geographic location, in which the mean absolute error in the North Sea region is the smallest (2.1 mm), that of the South China Sea region is the largest (2.60 mm), and that of the East China Sea region is in the middle (2.48 mm). The optimal predictors of the constructed 12 h sliding-window threshold rainfall prediction method are a PWV maximum of 49 mm, PWV increase of 5 mm, and PWV increase rate of 1.2 mm h−1. The prediction results can reach a critical success index value of more than 45%, indicating high prediction accuracy and applicability to the coastal region of China during the same period.

Temporal Characteristics Based Outlier Detection and Prediction Methods for PPP-B2b Orbit and Clock Corrections

The BeiDou Global Navigation Satellite System (BDS-3) provides real-time precise point positioning (PPP) service via B2b signals, offering real-time decimeter-level positioning for users in China and surrounding areas. However, common interruptions and outliers in PPP-B2b services arise due to factors such as the Geostationary Orbit (GEO) satellite “south wall effect”, Issue of Data (IOD) matching errors, and PPP-B2b signal broadcast priorities, posing challenges to continuous high-precision positioning. This study meticulously examines the completeness, continuity, and jumps in PPP-B2b orbit and clock correction using extensive observational data. Based on this analysis, a two-step method for detecting outliers in PPP-B2b orbit and clock corrections is devised, leveraging epoch differences and median absolute deviation. Subsequently, distinct prediction methods are developed for BDS-3 and GPS orbit and clock corrections. Results from simulated and real-time dynamic positioning experiments indicate that predicted corrections can maintain the same accuracy as normal correction values for up to 10 min and sustain decimeter-level positioning accuracy within 30 min. The adoption of predicted correction values significantly enhances the duration of sustaining real-time PPP during signal interruptions.

Dual-frequency to five-frequency real-time precise point positioning using new BDS-3 PPP-B2b service

BeiDou global navigation satellite system (BDS-3), a developed GNSS by China, has the ability to support five different signals, including B1I, B3I, B1C, B2a, and B2b. Meanwhile, BDS-3 has officially provided the satellite-based precise point positioning (PPP) service through the B2b signal (PPP-B2b) since 2021. It’s necessary to conduct a comprehensive analysis on multi-frequency PPP with PPP-B2b corrections. In this study, a multi-frequency undifferenced and uncombined PPP model (UDUC) using PPP-B2b corrections was employed to investigate dual-frequency to five-frequency real-time PPP performance. The results show that compared with the conventional dual-frequency solutions, multi-frequency solutions can improve both the convergence performances and positioning accuracy of PPP-B2b service, especially during the convergence stage. The quad-frequency and five-frequency solutions can achieve the best positioning performance. The static solutions of multi-frequency PPP models reach the centimeter-level accuracy after convergence. In kinematic mode, the convergence time of the five-frequency PPP results is reduced by 23.5% compared with the dual-frequency results. The root mean square (RMS) errors of the five-frequency PPP in the E, N, and U components are 7.1 cm, 4.8 cm, and 12.4 cm, which are improved by 6.8%, 11.5%, and 5.5%, respectively.Graphical

SLR Validation and Evaluation of BDS-3 MEO Satellite Precise Orbits

Starting from February 2023, the International Laser Ranging Service (ILRS) began releasing satellite laser ranging (SLR) data for all BeiDou global navigation satellite system (BDS-3) medium earth orbit (MEO) satellites. SLR data serve as the best external reference for validating satellite orbits, providing a basis for comprehensive evaluation of the BDS-3 satellite orbit. We utilized the SLR data from February to May 2023 to comprehensively evaluate the orbits of BDS-3 MEO satellites from different analysis centers (ACs). The results show that, whether during the eclipse season or the yaw maneuver season, the accuracy was not significantly decreased in the BDS-3 MEO orbit products released from the Center for Orbit Determination in Europe (CODE), Wuhan University (WHU), and the Deutsches GeoForschungsZentrum (GFZ) ACs, and the STD (Standard Deviation) of SLR residuals of those three ACs are all less than 5 cm. Among these, CODE had the smallest SLR residuals, with 9% and 12% improvement over WHU and GFZ, respectively. Moreover, the WHU precise orbits exhibit the smallest systematic biases, whether during non-eclipse seasons, eclipse seasons, or satellite yaw maneuver seasons. Additionally, we found some BDS-3 satellites (C32, C33, C34, C35, C45, and C46) exhibit orbit errors related to the Sun elongation angle, which indicates that continued effort for the refinement of the non-conservative force model further to improve the orbit accuracy of BDS-3 MEO satellites are in need.

GNSS Reflectometry-Based Ocean Altimetry: State of the Art and Future Trends

For the past 20 years, Global Navigation Satellite System reflectometry (GNSS-R) technology has successfully shown its potential for remote sensing of the Earth’s surface, including ocean and land surfaces. It is a multistatic radar that uses the GNSS signals reflected from the Earth’s surface to extract land and ocean characteristics. Because of its numerous advantages such as low cost, multiple signal sources, and all-day/weather and high-spatiotemporal-resolution observations, this new technology has attracted the attention of many researchers. One of its most promising applications is GNSS-R ocean altimetry, which can complement existing techniques such as tide gauging and radar satellite altimetry. Since this technology for ocean altimetry was first proposed in 1993, increasing progress has been made including diverse methods for processing reflected signals (such as GNSS interferometric reflectometry, conventional GNSS-R, and interferometric GNSS-R), different instruments (such as an RHCP antenna with one geodetic receiver, a linearly polarized antenna, and a system of simultaneously used RHCP and LHCP antennas with a dedicated receiver), and different platform applications (such as ground-based, air-borne, or space-borne). The development of multi-mode and multi-frequency GNSS, especially for constructing the Chinese BeiDou Global Navigation Satellite System (BDS-3), has enabled more free signals to be used to further promote GNSS-R applications. The GNSS has evolved from its initial use of GPS L1 and L2 signals to include other GNSS bands and multi-GNSS signals. Using more advanced, multi-frequency, and multi-mode signals will bring new opportunities to develop GNSS-R technology. In this paper, studies of GNSS-R altimetry are reviewed from four perspectives: (1) classifications according to different data processing methods, (2) different platforms, (3) development of different receivers, and (4) our work. We overview the current status of GNSS-R altimetry and describe its fundamental principles, experiments, recent applications to ocean altimetry, and future directions.

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.

Analysis of BDS inter-satellite link ranging performance

The Ka-band inter-satellite link (ISL) is a key technology of BeiDou Global Navigation Satellite System (BDS-3) that can improve the system performance. Based on 30 days of ISL observations, we analyze the BDS-3 ISL ranging performance and the related influencing factors, such as satellite manufacturer, satellite orbit type and link type. The fitting residuals of the ISL geometry-free observations are used to characterize the measurement noise, and the post-fit ISL residuals from precise orbit determination (POD) and precise clock estimation (PCE) are used to further validate the ranging performance. The fitting residuals follow a normal distribution, and the average root mean square (RMS) value for all 421 links is approximately 2.5 cm. The satellite manufacturers, China Academy of Space Technology (CAST) and Shanghai Engineering Center for Microsatellites (SECM), have an obvious impact on the ISL measurement noise. The RMS of the ISL fitting residuals for the links established by the two CAST satellites is only 1.45 cm, while it can reach 3.34 cm for the links established by the two SECM satellites. This correlation between ISL ranging performance and the satellite manufacturer is also found in the POD and PCE post-fit ISL residuals. The RMS of PCE residuals is about 3.1 cm, while the POD residuals are larger with the RMS of 5.5 cm due to the effect of orbital errors, especially for the Inclined Geosynchronous Orbit (IGSO) and Geostationary Orbit (GEO) satellites. Overall, the ranging accuracy of the BDS-3 ISL is better than 5 cm according to the above analyses. Furthermore, the BDS-3 satellite orbit and clock results are evaluated by internal consistency check and external comparison to analyze the application of ISL observations.

SISRE of BDS-3 MEO: Evolution as well as Comparison between D1 and B-CNAV (B-CNAV1, B-CNAV2) Navigation Messages

The signal-in-space range error (SISRE) has a direct impact on the performance of global navigation satellite systems (GNSSs). It is an important indicator of navigation satellite space server performance. The new B-CNAV navigation messages (B-CNAV1 and B-CNAV2) are broadcast on the satellites of the Beidou Global Navigation Satellite System (BDS-3), and they are different from D1 navigation messages in satellite orbit parameters. The orbit accuracy of B-CNAV navigation messages lacks analyses and comparisons with D1. The accuracy and stability of the new hydrogen and rubidium clocks on BDS-3 satellites need annual analyses of long time series, which will affect the service quality of this system. Based on precise ephemeris products from the Center for Orbit Determination in Europe (COD), the orbit error, clock error, and SISRE of 24 medium Earth orbit (MEO) satellite D1 and B-CNAV navigation messages of BDS-3 were computed, analyzed, and compared. Their annual evolution processes for the entire year of 2022 were studied. Thanks to the use of inter-satellite links (ISLs) adopted by BDS-3 MEO satellites, the ages of the ephemeris are accurate and the percent of ages of data, ephemerides (AODEs), and ages of data and clocks (AODCs) shorter than 12 h were 99.95% and 99.96%, respectively. In addition, the broadcast orbit performance was also improved by ISLs. The root mean square (RMS) values of the BDS-3 MEO broadcast ephemeris orbit error were 0.067 m, 0.273 m, and 0.297 m in the radial, cross, and along directions, respectively. Moreover, the 3D RMS value was 0.450 m. Thanks to the use of new orbit parameters in the B-CNAV navigation messages of BDS-3 MEO, its satellite orbit accuracy was obviously better than that of D1 in the radial direction. Its improved accuracy can reach up to about 1.2 cm, and the percentage of its accuracy improvement was about 19.06%. With respect to clock errors, the timescale differences between the two clock products were eliminated to assess the accuracy of broadcasting ephemeris clock errors. A standard deviation value of 0.256 m shows good performances as a result of the use of the two new types of atomic clocks, although the RMS value was 0.541 m due to a nonzero mean bias. Overall, the accuracy of atomic clocks was good. For the new hydrogen and rubidium atomic clocks, their RMS and standard deviation were 0.563 m and 0.231 m and 0.519 m and 0.281 m, respectively. The stability of the former was better than that of the latter. However, due to the nonzero mean bias the latter was better than the former in accuracy. The RMS value of the SISRE of BDS-3 MEO’s broadcast ephemeris was 0.556 m, and the value was 0.920 m when it had a 95% confidence level. In contrast, after deducting the influence of the clock error, the value of SISRE_ORB was 0.092 m. Since the satellite clock error was substantially larger than the orbit radial error, the SISRE was mainly affected by the clock error, and their annual evolutions were consistent. Because of the improvement to the B-CNAV’s navigation message with respect to orbit radial accuracy, SISRE_ORB has improved in accuracy. Compared to D1, it had a significant effect on improving the accuracy of SISRE_ORB, and the percentage of the accuracy improvement was 8.40%.

Analysis and Assessment of BDS‐3 Five Single‐Frequency Civilian Signals Single Point Positioning Considering Time Group Delay and Intersignal Correction

The BeiDou Global Navigation Satellite System (BDS‐3) has been providing global positioning, navigation, and timing (PNT) services for over 3 years. Single‐frequency single point positioning (SPP) receivers have significant advantages such as low hardware cost and easy implementation, making them widely used in engineering practice. The time group delay (TGD) and intersignal correction (ISC) are the main parameters for single‐frequency SPP and must be corrected. On‐orbit 30 BDS‐3 satellites have upgraded and maintained operation in 2022, while more multi‐GNSS experiment (MGEX) stations can simultaneously receive all five frequency civilian signals of BDS‐3, namely, B1I, B1C, B2a, B2b, and B3I. So now, it is worth assessing the SPP of BDS‐3 five single‐frequency civilian signals considering TGD and ISC corrections, respectively. Then, with 7 days of 73 MGEX stations simultaneously receiving all BDS‐3 five frequencies, GPS L1 and Galileo E1 civilian signals were selected, and the root mean square (RMS) error was used to assess the SPP performance. The BDS‐3 single‐frequency SPP static and kinematic results show that the order of accuracy from high to low is B1C, B1I, B3I, B2b, and B2a. More thorough static results reveal that B1C’s RMS errors in the north, east, and up (NEU) three directions are 1.12, 0.41, and 1.78 m, respectively, and B1C outperforms B2a by 0.85, 0.28, and 1.23 m. More detailed kinematic results reveal that B1C’s NEU RMS errors are 1.47, 0.77, and 2.72 m, respectively, and that B1C outperforms B2a by 1.04, 0.47, and 1.78 m. The single‐frequency SPP has a higher positioning accuracy at mid to high latitudes in the northern hemisphere than at mid to low latitudes in the southern. The single‐frequency SPP of BDS‐3 B1I is competitive with GPS L1 and Galileo E1. BDS‐3’s five single‐frequency signals, GPS L1, and Galileo E1 all perform well in the east direction, while the up direction performs badly in static and kinematic modes.

Investigating the contribution of BDS-3 observations to multi-GNSS single-frequency precise point positioning with different ionospheric models

Due to the advantages of low-cost and high precision, single-frequency precise point positioning (SF-PPP) plays a vital role in the booming market of the SF global navigation satellite system (GNSS) receivers. With the full completion of the BeiDou global navigation satellite system (BDS-3), its contribution to single-GNSS SF-PPP is worthy of comprehensive exploration. In this study, three SF-PPP models including ionosphere-corrected (IC), ionosphere-free (IF), and ionosphere-weighted (IW) strategies are analyzed, and four ionospheric models including the GPS Klobuchar, BDGIM (BeiDou global ionospheric delay correction model), CNES real-time VTEC (vertical total electron content) and GIM (global ionospheric maps) are used for conducting SF-PPP. As to GPS/GLONASS/Galileo-only IC SF-PPP, its 3D positioning accuracy can be improved by 6.9–11.6 % with the adoption of BDS-3 observations. Similarly, for the IF SF-PPP solution, the corresponding positioning accuracy and convergence time can be improved by at least 17.3 and 38.3 %, respectively. In IW SF-PPP, the convergence performance of the CNES-VTEC-constrained SF-PPP is much better than that of both GPS Klobuchar- and BDGIM-constrained solutions. When using the BDGIM constraints, the horizontal/vertical convergence time of GPS/Galileo + BDS-3 solutions can be shortened by at least 16.5/27.9 % in comparison with GPS/Galileo-only solutions. While for GIM-constrained SF-PPP, the convergence improvement is only shown in the vertical component. In summary, the GIM-constrained SF-PPP with quad-system observations has the best performance, compared to IF solution, its convergence time can be shortened by 82.8 % to 5.5 min in horizontal and 29.7 % to 26.0 min in vertical when converging to 0.3 m. Note that the corresponding improvements in the BDGIM-constrained solution are relatively limited with only 5 %. At present, the quad-system IW SF-PPP has the ability to achieve cm-level fast positioning, with an RMS of 0.06 m in horizontal, showing promising applications in engineering and scientific fields.

Performance evaluation of BDS-3 new B1C/B2a and legacy B1I/B3I signals: Observational quality, POD and PPP

In addition to the BeiDou regional navigation satellite system (BDS-2) backward compatible B1I and B3I signals, the BeiDou global navigation satellite system (BDS-3) also broadcast the B1C and B2a signals for compatibility with other Global Navigation Satellite System (GNSS), and providing satellite-based augmentation service for the International Civil Aviation Organization. Considering that the majority of the existing researches on the BDS-3 precise orbit determination (POD) and precise point positioning (PPP) are based on the B1I/B3I signals, the special attention that systematically comparing the data quality, POD accuracy and PPP performance through B1I/B3I and B1C/B2a signals is aroused in this paper. Signal characteristics of different receivers and antennas for the aforesaid four various signals were analyzed in terms of the carrier-to-noise density ratio (C/N0), pseudorange multipath and observation noise. The B1C signal exhibits the minimum C/N0 values, and the B3I and B2a signals have the smaller pseudorange multipath errors. The smallest pseudorange noise can be observed form the B2a signal, while the root mean squares (RMSs) for carrier phase noise show tiny differences among the four signals. The BDS-3 POD results indicate that the orbit overlapping arc error in three-dimensional (3D) direction is 0.069 and 0.076 m for the B1C/B2a and B1I/B3I, and the standard deviation of the satellite laser ranging validation is 0.041 m for both the two schemes. The clock offset products were evaluated with respect to the precise clock products from Deutsches GeoForschungsZentrum (GFZ), and the standard deviations (STDs) are 0.166 and 0.176 ns for the B1C/B2a and B1I/B3I. Finally, there is no apparent difference in the RMSs for B1C/B2a and B1I/B3I static PPP, while the convergence time that shortened by 31.4 % can be achieved for B1C/B2a. For kinematic PPP, the 3D RMS is 0.043 m and the convergence time is 31.1 min for the B1C/B2a, which is reduced by 14.0 % and 35.2 %, respectively, compared to B1I/B3I.

Research on single-epoch ambiguity resolution method based on BDS-3 ionosphere-reduced combinations

In conventional ambiguity resolution method for single-epoch, narrow-lane (NL) observations are often inaccurately fixed due to improper treatment of error sources such as ionospheric and tropospheric delays. Therefore, based on the multi-frequency observation data of the BeiDou Global Navigation Satellite System (BDS-3), this paper adopts a single-epoch resolution method based on the ionosphere-reduced combinations. Firstly, select the appropriate combination observations of extra wide-lane (EWL) and wide-lane (WL) and get its fixed ambiguity. Then the ambiguity of the WL combination with high observation accuracy is obtained by linear combination, which goes to constrain the fixation of NL ambiguity. Secondly, different from the conventional method, the ionosphere-reduced combinations observations were selected as NL, thus significantly weakening the influence of first-order ionospheric delay error on the fixation of narrow-lane ambiguity. The experimental results show that compared with the conventional methods, the method adopted in this paper can significantly improve the fixing success rate of the wide-lane ambiguity. In the NL ambiguity resolution part, using the ionosphere-reduced combinations as NL for solving improved the average fixing success rate from 68.6%/44.4%/35.7%/27.6% to 97.4%/95.4%/95.6%/87.3% compared to the conventional method of using the base frequency as NL for solving. Furthermore, the N/E/U positioning accuracy improved by an average of 63.05%/64.37%/52.27%. To sum up, this method effectively improves the success rate of NL ambiguity fixing and positioning accuracy.

Maintaining real-time precise point positioning during outages of the corrections broadcast by BDS-3 global short-message communication

Real-time precise point positioning (RTPPP) is a popular technique for precision applications, which is based on real-time service (RTS) products. However, one serious problem for RTPPP users is the potential communication break for a period from a few minutes to an hour. A significant decline in positioning accuracy may occur since the receiving of the RTS corrections is discontinuous. In this study, the real-time orbit and clock corrections are converted into the equivalent range corrections and broadcast by BeiDou global navigation satellite system (BDS-3) global short-message communication (GSMC). We focus on maintaining global navigation satellite systems (GNSS) RTPPP during outages of the range corrections. Three prediction methods are presented, including “linear function”, “mean value” and “last value” methods. The predicted corrections will be carried out with only at most 5 latest epochs of the registered corrections. The “last value” method shows the optimal prediction performance and the prediction errors of Galileo are minimal compared to GPS and BDS. Both simulated and vehicle kinematic experiments are conducted to evaluate the performance of RTPPP with the predicted corrections. The results show that the three proposed predicted corrections can maintain centimeter-to decimeter-level accuracy in both static and kinematic mode during outages of the BDS-3 GSMC that may be from a few minutes to an hour. Using the last registered equivalent range correction value is the most recommended choice to maintain multi-GNSS RTPPP.

BDS-3 Triple-Frequency Timing Group Delay/Differential Code Bias and Its Effect on Positioning

BeiDou Global Navigation Satellite System (BDS-3) broadcasts multifrequency signals that offer more choices of frequencies and more signal combinations for positioning. This paper analyzes the effect of timing group delay (TGD) and differential code bias (DCB) of BDS-3 on the corresponding triple-frequency positioning. The triple-frequency observation models of BDS-3 are summarized and the DCB correction models are derived for the four different frequency combinations of triple-frequency ionospheric-free (IF) combination (IF123), two dual-frequency IF combinations (IF1213) and triple-frequency uncombined (UC123) positioning modes. Standard point positioning (SPP) and precise point positioning (PPP) experiments were conducted using 30 days of observations from 25 multi-GNSS experiment (MGEX) stations. The results show that the TGD/DCB correction has a significant impact on the accuracy of SPP. The positioning accuracy using IF123 and IF1213 models improved by about 73~90% after TGD correction, in comparison to a 27~30% improvement achieved using the UC123 model. In addition, the correction effect of DCB is slightly better than TGD. The DCB correction significantly improves accuracy in the initial epoch of the PPP, which helps the convergence of the filtering and reduces the convergence time. The average convergence times of IF123, IF1213 and UC123 are 26.1, 26.9 and 38.3 min, respectively, which are reduced by 6.79, 2.54 and 8.59% with DCB correction. The pseudorange residuals are closer to zero-mean random noise after DCB correction. Furthermore, the DCB affects the evaluation of the inter-frequency bias (IFB), ionospheric delay and floating ambiguity parameters. However, the tropospheric delay is almost unaffected by DCB.

Sensitivity and Consistency Analysis of BDS-3 GEO Satellite Orbit Maneuver Detection

In this study, 22 maneuvering events of C59 and C60 geostationary equatorial orbit (GEO) satellites of the BeiDou global navigation satellite system (BDS-3) in 2021 were detected and analyzed based on a time-differenced carrier phase velocity measurement algorithm combined with a broadcast ephemeris and station data. We set different empirical thresholds to analyze the effect of threshold selection on the maneuvering detection sensitivity. The sensitivity and consistency of this algorithm for GEO satellite maneuvering detection were analyzed by combining BDS-3 with other Global navigation satellite systems (GNSS) and selecting different geographic stations. The results demonstrate that changing the threshold significantly affects the maneuvering detection of C60, with the optimal maneuvering thresholds of C59 and C60 being 0.045 and 0.02, respectively. A combination of BDS-3 and GPS with equal weights was identified to be most suitable for maneuvering detection of GEO satellites. For any specific maneuver, the difference between the maneuvering time detection of C59 by stations at different geographical locations was no more than 1 min. During the maneuvering detection of C60, the start time of maneuvering detected by African stations was 4.26–8.61 min earlier than that detected by the Chinese and Australian stations, and the end time of maneuvering detected by the African stations was consistent with that detected by the Chinese and Australian stations.

Beidou-3 precise point positioning ambiguity resolution with B1I/B3I/B1C/B2a/B2b phase observable-specific signal bias and satellite B1I/B3I legacy clock

In addition to the legacy B1I and B3I signals, the BeiDou global navigation satellite system (Beidou-3) are capable of transmitting B1C/B2a/B2b/B2 several new navigation signals. The multi-frequency signals of Beidou-3 are expected to benefit precise point positioning with ambiguity resolution (PPP AR). Currently, most international GNSS service (IGS) analysis center adopt the Beidou-3 B1I/B3I ionosphere-free (IF) combination to estimate the satellite orbit and clock products, the Beidou-3 B1C/B2a/B2b/B2 phase biases should be aligned with satellite B1I/B3I clocks. Therefore, in this paper, the multi-frequency phase observable-specific phase biases (OSB) estimation method is developed for Beidou-3 system, which is compatible with satellite B1I/B3I legacy clock. Experimenting on the Beidou-3 multi-frequency observations over 30 days from the globally distributed stations, the characteristics of the estimated Beidou-3 multi-frequency phase OSB and the positioning performance of the IF kinematic PPP AR with different frequency combination are assessed. After the OSB are used in the raw observations, the results demonstrate that the wide-lane ambiguities residuals within ± 0.25 cycle are approximately 97%, 94%, 97% and 93% for Beidou-3 B1I/B3I, B1C/B2b, B1C/B3I and B1C/B2a combinations, respectively. When the OSB and satellite B1I/B3I legacy clock are used in different dual-frequency combination PPP AR tests, over 94% of the corresponding narrow-lane ambiguities are within ± 0.25 cycle. In addition, owing to the low noise of the B1C/B2a combination, the positioning performance of B1C/B2a PPP AR outperforms that of the other frequency combinations. More specifically, in case of B1I/B3I PPP AR, almost 22.7 min is required to successfully achieve 10 cm for east, north and up components, while only 18.8 min is needed for B1C/B2a PPP AR. The results show that such phase OSB, along with Beidou-3 satellite B1I/B3I legacy clock, can fully recover the PPP ambiguities based on all available frequency choices and observable combinations.

The benefit of B1C/B2a signals for BDS-3 wide-area decimeter-level and centimeter-level point positioning with observable-specific signal bias

In addition to the legacy of B1I and B3I signals, the BeiDou Global Navigation Satellite System (BDS-3) also broadcasts the new navigation signals B1C and B2a, which brings new challenges and opportunities for multi-frequency precise point positioning (PPP) ambiguity resolution. The observable-specific signal biases (OSBs) provide flexible frequency choice for multi-frequency ambiguity resolution. This work implemented an approach of BDS-3 quad-frequency OSBs estimation, making the generated OSBs suitable for ambiguity resolution using any frequency combinations. Besides, the benefits of B1C and B2a signals for wide-area decimeter-level and centimeter-level point positioning with ambiguity resolution are also investigated in depth. The BDS-3 B1C/B1I/B2a/B3I measurement data of 110 stations over one month were used to estimate the quad-frequency phase OSBs, and 20 different stations were selected for PPP verification. The results indicate that the BDS-3 quad-frequency phase OSBs are relatively stable, with a standard deviation of less than 0.06 cycle. The B1C/B2a/B3I combination achieved the highest positioning accuracy for instantaneous triple-frequency PPP wide-lane ambiguity resolution, with root-mean-square of 0.15 m, 0.17 m and 0.51 m in the east, north and up directions, respectively. Moreover, the use of B1C/B2a instead of the traditional frequency B1I/B3I as the WL combination improved the single-epoch PPP accuracy. Furthermore, after solving the narrow-lane ambiguity, the median convergence time of B1C/B2a for the kinematic and static mode was 26.5 min and 14.5 min, which was shortened by 29.3 % and 27.5 % compared to the results of the B1I/B3I combination, respectively.

Long-Term Performance Evaluation of BeiDou PPP-B2b Products and Its Application in Time Service

Precise Point Positioning (PPP) is an official service of the BeiDou Global Navigation Satellite System (BDS-3) through the PPP-B2b signal. In this paper, we mainly focus on the long-term performance evaluation of BDS-3 PPP-B2b products and their application in time service. Since the PPP-B2b product is only available in and around China area, the arcs of PPP-B2b products are about several hours. We propose to evaluate the time datum stability by using all available satellites. Then, 557 day PPP-B2b products are collected for this experiment. The results show that there are large jumps in the GPS satellite clock time datum series. However, the BDS-3 satellite clock datum stability is almost at the same level with current Space State Representation (SSR) corrections from the International Global navigation satellite system Service (IGS). The difference between PPP-B2b GPS and BDS-3 satellite clock time datum will be absorbed into the Inter System Bias (ISB) parameter. Thus, it should be specially noted that the ISB parameter cannot be estimated as constant values if users use PPP-B2b products. In addition, the accuracy of the BDS-3 satellite clock is significantly better than that of the GPS for both the Root Mean Square Error (RMSE) and standard deviation (STD). The average Signal in Space Range Errors (SISREs) is 0.22 ns and 0.13 ns for GPS and BDS-3, respectively. The one-way timing experiment shows BDS-3 timing stability is 2.9 × 10−14@104 s. In addition, 10 baselines from 13 km to 4494 km are formed for time synchronization evaluation by using PPP-B2b products. The average RMSEs of time synchronization is from 0.46 ns to 1.58 ns and from 0.66 ns to 1.19 ns for GPS and BDS-3, respectively. As for STD, the average values are from 0.27 ns to 0.74 ns and from 0.27 ns to 0.47 ns for GPS and BDS-3, respectively. Overall, the results show that the time datum stability, accuracy, and service performance of BDS-3 PPP-B2b products has been stable over the past two years.

PPP/INS Tight Integration with BDS−3 PPP−B2b Service in the Urban Environment

To provide continuous and reliable real-time precise positioning services in challenging environments and poor internet conditions, the real-time precise corrections of the BeiDou global navigation satellite system (BDS-3) PPP-B2b signal are utilized to correct the satellite orbit errors and clock offsets. In addition to this, using the complementary characteristics of the inertial navigation system (INS) and the global navigation satellite system (GNSS), a PPP-B2b/INS tight integration model is established. With observation data collected in an urban environment, the results show that PPP-B2b/INS tight integration can ensure a decimeter-level positioning accuracy; the positioning accuracies of the E, N, and U components are 0.292, 0.115, and 0.155 m, respectively, which can provide a continuous and secure position during short interruptions in the GNSS. However, there is still a gap of about 1 dm compared with the three-dimensional (3D) positioning accuracy obtained from Deutsche GeoForschungsZentrum (GFZ) real-time products, and a gap of about 2 dm compared with the GFZ post-precise products. Using a tactical inertial measurement unit (IMU), the velocimetry accuracies of the tightly integrated PPP-B2b/INS in the E, N, and U components are all about 0.3 cm/s, and the attitude accuracy of yaw is about 0.1 deg, while the pitch and roll show a superior performance of less than 0.01 deg. The accuracies of the velocity and attitude mainly depend on the performance of the IMU in the tight integration mode, and there is no significant difference between using real-time products and post products. The performance of the microelectromechanical system (MEMS) IMU and tactical IMU is also compared, and the positioning, velocimetry, and attitude determinations with the MEMS IMU are significantly worsened.