BDS-3 Satellites Research Articles

A Modified Single-Frequency PPP Method for the Positioning and Time Transfer with BDS-3.

In this paper, time-frequency transfer and positioning experiments with signal coexistence in the BDS system were conducted using the four types of open service signals of the BDS-3 satellite (B1I, B1C, B2a, and B3I), as well as the B2I signals broadcast by the BDS-2 satellites. The experiments used the single-frequency PPP (precise point positioning) method. The experiment validated a modified version of the group and phase ionospheric correction (GRAPHIC) technique. The results demonstrate that, with a single frequency, 18 selected stations may provide positioning results accurate to within a few decimeters. The positioning accuracy of five frequencies signals is improved by 40.4%, 32.2%, 80.3%, 12.4%, and 10.3% when compared to the positioning accuracy of the same signals when using the general observation approach. Currently, the frequency stability may be as precise as dual frequencies with BDS.

Theory and Experiment Analysis on the Influence of Floods on a GNSS Pseudo-Range Multipath and CNR Signal Based on Two Cases Study in China

The surrounding environment of a GNSS observation station is changed during a flood, and this results in a more serious multipath than in a normal environment. Considering that the multipath error is largely related to the pseudo-range multipath and CNR (Carrier-to-noise ratio) of the GNSS signal, the influence of floods on a pseudo-range multipath and CNR is analyzed in theory and through experiment. To ensure the accuracy of the analysis results, the ground track repeat period of GPS, GLONASS, and BDS satellites is investigated from the perspective of theory and skyplots. Two real cases study collected in Zhengzhou and Xinxiang, China, in 2021, are used to demonstrate the influence of floods on a pseudo-range multipath and CNR in detail. Experimental results show that the pseudo-range multipath of a GPS satellite performs more seriously during a flood. The maximum RMS increase rate is approximately 17.85%, and the average of all other satellites with a whole arc is approximately 6.55%. In addition, the CNR of three GNSS systems performs a decrease during a flood. For GPS and GLONASS satellites, the decrease performs more seriously at a high elevation angle than that at a low elevation angle. The maximum decrease is approximately 5 dB-Hz for the GPS satellite and approximately 7 dB-Hz for the GLONASS satellite. In terms of the BDS system, the CNR of all three orbital type satellites decreases during a flood. The average decrease is approximately 2 dB-Hz for BDS MEO and GEO satellites, and about 1 dB-Hz for the BDS IGSO satellite.

Orbit determination of BeiDou navigation satellite system maneuvered satellites based on instantaneous velocity pulses parameters

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver.

The Initial Performance Evaluation of Mixed Multi-Frequency Undifferenced and Uncombined BDS-2/3 Precise Point Positioning under Urban Environmental Conditions

With the full operation of the global BeiDou navigation satellite system (BDS-3), positioning performance can be further enhanced by BDS-3 combined with the regional BeiDou navigation satellite system (BDS-2). However, due to satellite signals being out of lock and the limited visibility of satellites, the traditional multi-frequency BDS-2/3 precise point positioning (PPP) model is unable to maintain great positioning performance under urban environmental conditions. In this study, a mixed multi-frequency undifferenced and uncombined (UDUC) BDS-2/3 PPP model is presented to improve the positioning performance under urban environmental conditions by making full use of B1I, B1C, B2I, B2a, and B3I signals from all visible BDS satellites. In this model, BDS satellites with single-, dual-, triple- and quad-frequency observations all can participate in PPP. The static and kinematic experiments were carried out using the mixed multi-frequency UDUC BDS-2/3 PPP model to fully assess the positioning performance under urban environmental conditions with comparisons to the multi-frequency model. The static experiments indicated that the mixed multi-frequency UDUC BDS-2/3 PPP could continuously achieve decimeter-level positioning accuracy at a cut-off elevation angle of 40°, but part of the BDS-3 PPP would lose resolution due to limited visible satellites. Furthermore, the initial kinematic vehicle experiment showed that mixed multi-frequency UDUC BDS-2/3 PPP had better satellite geometry and more observation redundancy than the traditional multi-frequency model. Compared with the traditional multi-frequency BDS-2/3 model, the positioning accuracy of the mixed multi-frequency model was improved by 51.6, 35.5, and 39.1%, respectively, in east, north, and up directions. The convergence time was shortened by 40%.

Comprehensive Analysis of PPP-B2b Service and Its Impact on BDS-3/GPS Real-Time PPP Time Transfer

2020 saw the official completion of the BDS-3 and the start of the PPP-B2b signal-based real-time precise point positioning (PPP) service to users in China and the neighboring areas. In this work, the quality of PPP-B2b products is first evaluated and compared with real-time products from the CNES and the differential code bias (DCB) from the Chinese Academy of Science (CAS). Then, a detailed performance evaluation of the PPP time transfer based on the PPP-B2b service (B2b-RTPPP) is conducted. Three solutions, namely, GPS-only (G), BDS-3-only (C), and GPS + BDS-3 (GC) B2b-RTPPP solutions, are compared and assessed. The results suggest that for the PPP-B2b products, BDS-3 satellites have better orbit and clock offset quality than GPS satellites, while the opposite is true for CNES products. The quality of the PPP-B2b orbit and clock offset is poorer than those of the CNES. The PPP-B2b DCB shows excellent agreement with the CAS DCB. The accuracy of the B2b-RTPPP solutions is sub-nanosecond level. The accuracy of B2b-RTPPP time transfer with DCB correction is approximately improved by 64% compared with that without DCB correction. The GC B2b-RTPPP solution has the greatest frequency stability, while G B2b-RTPPP solution has the poorest. Considering that the receiver may be blocked, the B2b-RTPPP time transfer performance is also evaluated at different cut-off elevation angles. As the angle increases, the B2b-RTPPP time transfer performance decreases. Additionally, the short-term frequency stability remains constant at different cut-off elevation angles, but deteriorates in the long term, especially when the angle is 40°.

Improved method for BDS-3 satellite clock parameterization in the broadcast ephemeris, real-time service (RTS) and IGS final products

We find that a quadratic polynomial plus a harmonic function of order 8 is better than 7th order polynomial and reaches a mean accuracy of 0.060 ns in DBS-3 satellite clock modeling. The parameterization product, which provides the coefficients of a combined quadratic polynomial plus a harmonic function of order 8 instead of interval-based series, can simplify delivery and save memory space. The 1-h arc satellite clock correction series is optimal to fit the extrapolation parameters, and the harmonics-based function has the best performances in 1 and 2 min extrapolations. The improved real-time service of the BDS-3 satellite clock correction broadcasts the coefficients of a combined quadratic polynomial plus a harmonic function of order 4 at 2 min intervals and its update interval at least 20 times is longer than that of current method. The improved broadcast ephemeris method, whose age is prolonged at least 2 h, is set up.

Evaluation of Real-time Precise Point Positioning with Ambiguity Resolution Based on Multi-GNSS OSB Products from CNES

Ambiguity resolution (AR) is a core technology that helps to speed up convergence time and increase positioning accuracy for precise point positioning (PPP), and the performance of PPP-AR is based on the quality of ambiguity resolution products. Real-time PPP-AR becomes a reality as users can now obtain publicly accessible real-time observable-specific signal bias (OSB) products from the Centre National d’Etudes Spatiales (CNES). Therefore, an analysis of the quality of OSB products and an evaluation of the performance of PPP-AR are required to promote the application of real-time positioning. For a total of 31 days between day of year (DOY) 121 and 151 in 2021, observation data were collected from 90 stations, and the OSB products were used to assess the experiments. As for the quality of the OSB products, the data availability (DA) of the GPS and Galileo satellites was greater than 97%, whereas that of BDS was less than 60%; the maximum fluctuation value (MAX) and standard deviation (STD) of the GPS, Galileo, and BDS satellites were 0.045 and 0.012; 0.081 and 0.028; and 0.292 and 0.085 cycles, respectively. In terms of ambiguity residuals using the OSB products, the wide-lane (WL) residual percentages within ±0.25 cycles for the GPS, Galileo, BDS-2, and BDS-3 systems were more than 92%, and the narrow-lane (NL) residual percentages within ±0.25 cycles for the four systems were 92%, 89%, 79%, and 60%, respectively. With regard to the performance of PPP-AR, the GPS+Galileo solution showed the best performance in the kinematic positioning mode, in which the mean root mean square (RMS) of positioning accuracy was 1.06, 1.27, and 2.85 cm for the east (E), north (N), and up (U) components, respectively, and the mean convergence time reached 9.6 min. In the static positioning mode, the mean convergence times of the GPS-only and GPS+Galileo solutions were 11.4 min and 8.0 min, respectively, and both of their mean RMS for positioning accuracy reached 0.79, 0.95, and 1.48 cm for the E, N, and U components, respectively. However, the addition of BDS did not further enhance the performance of multi-GNSS PPP-AR in either the kinematic or static positioning mode due to the poor quality of the real-time BDS products. More importantly, a prediction method was proposed to avoid re-convergence and to enhance the reliability of PPP-AR in the event of short-time missing real-time OSB products and to improve the positioning accuracy and the ambiguity fixed rate.

In-Flight Performance Assessment of the Single-Frequency GPS/BDS Receiver for Yaogan-30 Series Satellites Real-Time Navigation

Within the Yaogan-30 series satellites, the low-cost single-frequency Global Positioning System/BeiDou Navigation Satellite System (GPS/BDS) receiver was employed for onboard real-time navigation. This article presents the in-flight performance of the single-frequency GPS/BDS receiver, including the tracking of GPS/BDS satellites, the noise of measurements, and the orbit accuracy of onboard real-time navigation results. First, in terms of satellites tracking, no BDS-2 satellites are tracked in 30–40% of all the time, four to seven BDS-2 satellites can be observed for less than 15% of the time, and only one to three BDS-2 satellites are available for the rest time, whereas 7–12 GPS satellites are tracked for the vast majority of the time. Obviously, the GPS observations play a more important role than BDS-2 data in real-time navigation and precise orbit determination (POD). Although the receivers only provide the single-frequency C/A-code pseudorange measurements without carrier-phases output, the accuracies of postprocessed POD could arrive at the level of 10–25 cm in terms of 3-D position. Hence, the post precise orbits are used as the reference for the assessment of real-time navigation accuracy. The assessment results demonstrate that the onboard real-time navigation accuracies of 2.0–3.5 m for 3-D position and 10.0–13.0 mm/s for 3-D velocity are achievable. At the same time, the statistics on the C/A-code pseudorange residuals after POD processing reflects that the noises of measurements from GPS and BDS-2 satellites are at the same level of 0.5–1.6 m. It should be noted that there is a notable velocity deviation of up to about 7.6 mm/s. Nevertheless, even with this obvious systematic error, the current velocity accuracy could still meet the real-time requirements of the small Yaogan-30 series satellites. In addition, some offline simulative solutions with tuned strategy settings are tested to validate the potential real-time navigation accuracy improvement. The simulation experiment tests results illustrate that a higher real-time orbit accuracy of roughly 1.0 m for 3-D position and 1.0 mm/s for 3-D velocity could be obtainable, if an optimized power spectral density of estimated empirical accelerations and a slightly higher order and degree of gravity model (50×50) are adopted. All the above analyses show that the single-frequency pseudorange Global Navigation Satellite System receiver is a high cost-effective sensor and has a wide horizon of application in the aerospace market.

BDS-3 Broadcast Ephemeris Orbit Correction Model Based on Improved PSO Combined with BP Neural Network.

During the operation of navigation satellites, errors in the broadcast ephemeris orbits are caused by the influence of ingress factors and other factors. To address this phenomenon, this paper examines the use of the computational intelligence (CI) methods to implement track correction and to develop an optimized BP neural network model based on an improved particle swarm algorithm. The model improves the inertia weights and learning factor parameters of the particle swarm optimization (PSO) algorithm to improve the global optimization capability and accelerate the convergence speed. The improved PSO (IPSO) algorithm is used to perform a global optimization search for the hyperparameters of the BP neural network, and then the neural network model is trained by broadcast ephemeris Keplerian root number and regression parameters. The model is validated using the broadcast ephemeris data of the BDS-3 MEO and IGSO satellites, and the mean square error correction rate of multiple satellites with different correction models shows that the error correction rate of the IPSO-BPNN model can reach 70.2–84% and the error correction rate can be improved by 14.2–56.8% compared with the PSO-BPNN model. The proposed algorithm provides an important reference for BDS-3 and other global navigation satellite systems for improving the accuracy of satellite orbit determination.

Analysis of the Long-Term Characteristics of BDS On-Orbit Satellite Atomic Clock: Since BDS-3 Was Officially Commissioned

Satellite atomic clocks are the key elements for position, navigation, and timing services of the Global navigation satellite system (GNSS); it is necessary to research the characteristics of BDS-3 on-orbit satellite atomic clocks for their further optimization. In this study, clock offset data with a duration of 620 days since BDS-3 was officially commissioned were applied to long-term characteristic analysis. To begin with, the precision clock offset data of Deutsches geoforschungs zentrum (GFZ) processed by a MAD-based method were used as reliable test data. Herein, the working principle and main characteristics of satellite atomic clocks are analyzed and discussed, and thus, a comprehensive long-term characteristic analysis scheme is designed. On this basis, the performance indicators—mainly including physical parameters, periodic characteristics, frequency drift rate, frequency accuracy, frequency stability—were calculated and analyzed respectively, revealing the long-term characteristics of the BDS in orbit satellite atomic clocks during the test period. The results of experimental data testify that the performance of BDS-3 satellite atomic clocks is significantly superior to that of BDS-2, especially in terms of drift rate and frequency stability, and the performance of passive hydrogen maser (PHM) is generally superior to that of rubidium atomic frequency standards (RAFS). Within about half a year since BDS-3 was officially commissioned, the frequency stability of BDS-3 satellite atomic clock gradually improved and then reached the order of 10−15, reflecting the effectiveness of system maintenance and inter-satellite link. Furthermore, some novel conclusions are drawn, such as the long-term period term of the fitting residual and drift rate, which may be caused by the earth’s revolution.

Real-Time Multi-GNSS Precise Orbit Determination Based on the Hourly Updated Ultra-Rapid Orbit Prediction Method

Offering real-time precise point positioning (PPP) services for global and large areas based on global navigation satellite systems (GNSS) has drawn more and more attention from institutions and companies. A precise and reliable satellite orbit is a core premise for multi-GNSS real-time services, especially for the GPS and GLONASS, which are undergoing modernization, whereas the Galileo, BDS and QZSS have just fulfilled the construction stage. In this contribution, a real-time precise orbit determination (POD) strategy for the five operational constellations based on the hourly updated ultrarapid orbit prediction method is presented. After combination of 72 h arc through three adjacent 24 h arc normal equations, the predicted orbits are finally generated (hourly updated). The POD results indicate that the mean one-dimensional (1-D) root mean square (RMS) values compared with the Deutsches GeoForschungsZentrum (GFZ) final multi-GNSS orbits are approximately 3.7 cm, 10.2 cm, 5.8 cm, 5.7 cm, 4.1 cm and 25.1 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The mean 1-D RMS values of the hourly updated ultrarapid orbit boundary overlapping comparison are approximately 1.6 cm, 6.9 cm, 3.2 cm, 2.7 cm, 1.8 cm and 22.2 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The satellite laser ranging (SLR) validation illuminates that the mean RMS values are approximately 4.53 cm and 4.73 cm for the four MEOs of BDS-3 and four BDS-2 satellites, respectively.

Assessment of Real-Time GPS/BDS-2/BDS-3 Single-Frequency PPP and INS Tight Integration Using Different RTS Products

Due to the virtues of low-cost and high positioning accuracy, Single-Frequency Precise Point Positioning (SF-PPP) is becoming a prospective technique. However, SF-PPP is not as widely used as dual-frequency and triple-frequency PPP at present, owing to the effect of ionospheric delay residuals after model rectification. In recent years, with the evolution of multi-constellation Global Navigation Satellite Systems (multi-GNSS, i.e., GPS, BDS-2, and BDS-3), it has become possible to obtain credible and continuous positioning results using SF-PPP. However, such performance would be significantly degraded in challenging environments (i.e., boulevards, tunnels, and tall buildings). Under these circumstances, GNSS signals are obstructed, and it is difficult to provide sufficient observations for SF-PPP. Therefore, the Inertial Navigation System (INS) is employed to promote the positioning performance of SF-PPP. The PPP/INS integration is regarded as one of the most efficient approaches in GNSS-denied environments. To satisfy the request of supplying real-time positioning information, the Real-Time Services (RTS) of the International GNSS Service (IGS) provide real-time precise orbit and clock products for globally distributed users through the internet. In this paper, a real-time GPS/BDS-2/BDS-3 SF-PPP and INS tight integration model is proposed, and it is assessed using the data gathered by vehicle and real-time products afforded by CAS (Chinese Academy of Sciences), GFZ (Deutsche GeoForschungsZentrum), and WHU (Wuhan University). The outcomes illustrate the following: (1) GPS + BDS SF-PPP/INS can provide more accurate and continuous positioning solutions compared with those of GPS + BDS SF-PPP, with improvements of 52.8%, 31.1%, and 42.8% in the north, east, and vertical components, respectively. (2) In general, the orbit and clock products’ accuracies in terms of GPS afforded by the three analysis centers are consistent with each other. For BDS, the orbit product from WHU is more accurate compared to those of CAS and GFZ. However, the accuracy of the clock product afforded by WHU is lower compared with those provided by the other two centers, especially for BDS-2 satellites. (3) The positioning accuracy in terms of Root Mean Square (RMS) values based on GFZ products are much higher than the results based on CAS and WHU products in the three directions.

Precise orbit determination and precision comparison for FY3C and FY3D with receiver antenna GPS and BDS PCV using spaceborne BDS and GPS observation data

The FY3C and FY3D satellites were equipped with global navigation satellite occultation detector (GNOS) receivers that received both GPS and BDS-2 signals. For further improving precise orbit determination (POD) precisions, we estimated receiver GPS and BDS signal phase center variations (PCV) models with 2° and 5° resolutions and set the different weights for GPS and BDS-2 observations in the combined POD. The BDS-based POD precision using BDS-2 satellite antenna phase center offset (PCO) values from the China Satellite Navigation Office (CSNO) are not as accurate as those obtained from the International GNSS Service (IGS) Multi-GNSS experiments project (MGEX). The estimated receiver GPS and BDS PCV models with 2° and 5° resolutions were estimated from the GPS phase residuals of GPS-based POD and BDS phase residuals of combined POD, respectively. In most cases, the POD precisions using the estimated PCVs with 2° resolution are superior to those with 5° resolution. The precisions of the BDS-based POD and combined POD were both improved by introducing the receiver BDS PCV models. The weighting for GPS and BDS-2 observations can further improve the precision of the combined POD. The tested results of selected weights are better than those with equal weight in the combined POD. The experiment results show that orbital precisions of FY3C are worse than those of FY3D.

Impacts of Arc Length and ECOM Solar Radiation Pressure Models on BDS-3 Orbit Prediction

The BeiDou global navigation satellite system (BDS-3) has already provided worldwide navigation and positioning services for which the high-precision BDS-3-predicting orbit is the foundation. The arc length of the observed orbits and the solar radiation pressure (SRP) are two important factors for producing precise orbit predictions. The contribution studies the influences of these factors on BDS-3 orbit prediction. Three-month data from 1 July 2021 to 30 September 2021 are used to analyze optimal arc lengths and different ECOM SRP models for obtaining precise BDS-3 orbit predictions. The results show that the best-fitting arc length for the BDS-3 MEO/IGSO satellite is 42–48 h by comparing the final precise ephemeris and SLR validation. Furthermore, the ECOM9 SRP model shows improved orbit-prediction accuracy than that of the ECOM5 SRP model when the satellites move in and out of the eclipse season. As for the ECOM9 SRP model, the user range error (URE) accuracy of 6 h orbit predictions when satellites are in and outside of the eclipse season is 0.036 m and 0.030 m, respectively. In addition, the orbit prediction accuracy of the BDS-3 satellites does not decrease significantly since BDS-3 satellites apply the continuous yaw-steering (CYS) attitude mode during the eclipse season.

BeiDou Satellite Radiation Force Models for Precise Orbit Determination and Geodetic Applications

China's BeiDou satellite navigation system (BDS) has completed its full constellation in orbit since June 2020. Services have been evolved from regional (BDS-2) to global (BDS-3). This contribution evaluates the impact of solar radiation pressure (SRP) modeling on satellite orbits and geodetic parameters. To that end, we process 2 years of BDS observations (2019-2021), collected by a network of 100 ground stations. A physical a priori box-wing model based on the estimated optical properties is introduced. Various physical effects, such as radiator emission and thermal radiation of solar panels are considered. The ECOM (Empirical CODE orbit Model), ECOM+along-track and ECOM2 models are employed on top in the experiment. We show that without the use of the a priori box-wing model, the ECOM+along-track model shows clear better orbit solutions during eclipse seasons for BDS-3 satellites. This is proven to be mainly due to the thermal radiation of the solar panels. However, the along-track acceleration is highly correlated with LOD (length of day) and ECOM parameters. LOD estimates in this case are contaminated. When using the physical a priori box-wing model satellite orbital errors are greatly reduced for all the ECOM models. For instance, orbit misclosures of BDS-3 CAST (China Academy of Space Technology) satellites improve by a factor of two for the ECOM model during eclipse seasons. Furthermore, the use of the a priori box-wing model mitigates a great majority of the spurious signals in the geodetic parameters.

On the potential contribution of BeiDou-3 to the realization of the terrestrial reference frame scale

Since the release of the phase center calibrations for both the receivers and the satellites, the BeiDou Navigation Satellite System (BDS) became a new potential contributor to the realization of the terrestrial reference frame (TRF) scale of future International Terrestrial Reference Frame releases. This study focuses on the evaluation of the potential usage of the BDS-3 Medium Earth Orbit (MEO) constellation to the definition of the TRF scale. To that aim, we used ground calibrated BDS-3 satellite PCOs provided by the China Satellite Navigation Office and multi-GNSS robot calibrations for the ground antennas conducted by Geo++. Two ionosphere-free linear combinations of signals, namely B1I/B3I and B1C/B2a, have been investigated to find out whether using different frequencies may lead to different TRF scale definitions. Differences between the z components of the satellite phase offsets as given by manufacturer calibrations and those estimated based on IGS14 scale amount to 6.55 ± 12.56 cm and − 0.32 ± 10.99 cm for B1I/B3I and B1C/B2a frequency pairs, respectively. On the one hand, the substantial deviation from the mean reflects the disparities in the quality of calibrations for the individual spacecraft, especially those manufactured by the Shanghai Engineering Center for Microsatellites (SECM). On the other hand, the difference between the two frequency pairs arises to a great extent from the doubtful quality of the SECM PCO calibrations, which certainly do not reflect the frequency dependence of the PCOs. Eventually, the mean scale bias with respect to IGS14 equals + 0.546 ± 0.085 ppb and + 0.026 ± 0.085 ppb for B1I/B3I and B1C/B2a solutions, respectively, when using all 24 BDS-3 MEO satellites.

Emerging errors in the orientation of the constellation in GNSS autonomous orbit determination based on inter-satellite link measurements

The emergence of inter-satellite link (ISL) technology, which realizes the high-precision measurement of the inter-satellite distances and forms a spatial geometric constraint within the constellation, enables the high-precision autonomous orbit determination of the GNSS satellites. Firstly, according to the fact that ISL adjustment is singular to the satellite orbit state vector, a distributed autonomous orbit determination algorithm employing the long-term forecast ephemeris to constrain the constellation orientation is designed in this paper. Then, the autonomous orbit determination using 60-day onboard ISL observations of the whole constellation is carried out. Then, the resulting orbits accuracy is evaluated by comparing them with a precise orbit determination using a global reference network with an accuracy of 0.10 m. The results show that the mean root mean square (RMS) of the user range error (URE) over a 60-day period of the 24 BDS-3 satellites in the constellation is 3.22 m. The characteristics of orbit errors for individual satellite are very similar, which is mainly caused by the overall orientation errors of the constellation. After eliminating these orientation errors, the corresponding mean RMS of URE is reduced to 0.68 m. The prediction errors of the Earth rotation parameters and the determination errors of the parameters of the state vectors, which compose the orientation errors, are further investigated. The Earth rotation parameter prediction errors mainly cause errors in the estimates of the longitude of ascending node, of which the 60-day error can reach 2.5e-5°. The determination errors of the parameters of the state vectors -- the inclination and the right ascension of ascending node, can reach 2.4e-5° and 5.1e-5° rad, respectively.

Estimation and analysis of BDS-3 satellite yaw attitude using inter-satellite link observations

Estimation and analysis of BDS-3 satellite yaw attitude using inter-satellite link observations

Precise point positioning with BDS-2 and BDS-3 constellations: ambiguity resolution and positioning comparison

The full operational capability of the Chinese BeiDou Satellite Navigation System (BDS) has injected additional energy into the GNSS field. Along with the visibility of more BDS satellites, as well as the precise products generated by analysis centers, ambguity float and fixed Precise Point Positioning (PPP) performance with the complete BDS constellation are evaluated in this study. Inter-system biases (ISBs) between BDS-2 and BDS-3 are first evaluated, and Fractional Cycle Bias (FCB) with and without consideration of ISBs are assessed. Results show that when considering ISBs, the standard deviations of ambiguity residuals are smaller, thus the ISB parameter should be taken into consideration in BDS PPP. BDS-3 FCBs are more stable than those of BDS-2, at the same time, the ambiguity residuals are smaller for BDS-3 satellites. In terms of PPP performance, BDS-3 outperforms BDS-2 in positioning accuracy, convergence time and time to first fix. For the test data, the convergence time of BDS-2 static solution is 48.8 min, while for BDS-2 + 3 it is 19.7 min, representing an improvement of 59.6% when BDS-3 satellites are included. The positioning accuracy of static BDS-2, BDS-3 and BDS-2 + 3 PPP can reach the same millimeter-level after a long time of convergence, while kinematic solution with BDS-2 + 3 has the highest accuracy compared to BDS-2 and BDS-3, which could reach 1.7, 1.3 and 4.3 cm in East, North and Up components, respectively, in fixed solution. The performance of BDS PPP with the whole constellation is comparable with that of GPS and Galileo, and the PPP performance is promising with receiver updates for MGEX stations in the near future.

Improving BDS broadcast ephemeris accuracy using ground-satellite-link observations

The BeiDou Navigation Satellite System (BDS) employs a hybrid constellation including GEO (Geosynchronous Earth Orbit), IGSO (Inclined Geosynchronous Orbit), and MEO (Medium Earth Orbit) satellites, where the GEO and IGSO satellites are critical to providing continuous and reliable Positioning, Navigation, and Timing (PNT) services in the Asia–Pacific region. To handle the inconsistency between the satellite orbits and clocks in the broadcast ephemeris, which are determined by the Orbit Determination and Time Synchronization (ODTS) and the Two-way Satellite Time Frequency Transfer (TWSTFT) technique, respectively, we present the strategies using ground-satellite-link observations to improve the accuracy of broadcast ephemeris. The clock differences between the ODTS and TWSTFT techniques are used for correcting the radial orbit component to derive the refined orbits, which are used to generate the refined broadcast ephemeris. The test results show the precision of the refined orbits is improved by 50–60% in the 3-h to 12-h predicted arcs for the GEO satellites, and by 40–50% for the IGSO satellites. Moreover, the validation using satellite laser ranging observations shows the mean precision of the refined broadcast ephemeris is improved by 27% compared to the original one. Applying the proposed strategies in the BDS Operational Control Segment (OCS), the time evolution of BDS Single Point Positioning (SPP) in the period from Jan. 2016 to April 2021 is evaluated. The SPP accuracy is improved from 1.94, 2.06 and 3.29 m to 1.39, 1.85, and 2.39 m in the north, east, and up components, respectively. Further update with the inclusion of BDS-3 satellites improve the corresponding SPP precision to 0.68, 0.70 and 1.91 m.