BDS-3 Satellites Research Articles

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.

Progress of global ARAIM availability of BDS-2/BDS-3 with TGD and ISB

Advanced RAIM (ARAIM) is an extension of Receiver Autonomous Integrity Monitoring (RAIM) by enhancing the vertical navigation capabilities, so it can be applied to higher-level precision applications. But when the observation data of the second-generation BDS (BDS-2) and the third-generation BDS (BDS-3) are combined to evaluate the ARAIM availability, the evaluation be affected by the Timing Group Delay (TGD) of different satellite signals and the Inter-system Bias (ISB) between BDS-2 and BDS-3, which is ignored by the existing literature. Therefore, in this article, we deduced the mathematical model of ARAIM and the calculation formula of Vertical Protection Level (VPL) by considering the combined influence of TGD and ISB. We used the BDS observation data and ephemeris files of 374 International GNSS Service (IGS) stations around world on July 29, 2021 to calculate the VPL of these stations and evaluate the global ARAIM availability. The results show that the number of visible BDS satellites is 8.033 and the Geometric Dilution of Precision (GDOP) is 1.721, which can meet the basic needs of global ARAIM calculations. Furthermore, when considering the combined influence of TGD and ISB, the evaluation of ARAIM availability by Multiple Hypothesis Solution Separation (MHSS) is significantly better than that without considering the combined TGD and ISB influence or their individual influence. The average VPL values at these IGS stations in four cases are 124.925 m, 13.882 m, 32.610 m and 9.962 m, and the corresponding ARAIM availability percentages are 90.839%, 95.241%, 96.751% and 99.660%, respectively. Finally, the minimum coverage of ARAIM availability based on BDS can reach 90.839%, which can meet the aviation demand for ARAIM availability in most regions and times.

Enhancing Short-Term Prediction of BDS-3 Satellite Clock Bias Based with BSO Optimized BP Neural Network

The satellite clock bias (SCB) prediction plays an important role in high-accuracy and real-time navigation and positioning. When predicting the SCB, the performance of the BP neural network is affected by the local optimum due to inaccurate initial parameters. Therefore, we propose an improved BP neural network based on the beetle swarm optimization (BSO-BP) algorithm to improve the performance of SCB prediction in third-generation Beidou satellite navigation system (BDS-3). The proposed model takes advantage of group learning strategy to optimize the initialization parameters of the BP neural network and obtains globally optimized parameters. In order to verify the proposed BSO-BP model, 15 BDS satellites are analyzed in terms of prediction accuracy and stability of SCB. The experimental results show that when predicting 1 hour SCB based on a 12 hours SCB data, the prediction accuracy of the BSO-BP model is the best, with an average accuracy of 0.064 ns. As compared with the LP, QP, and GM models, the average prediction accuracy of the proposed BSO-BP model increases by about 72.6%, 43.4%, and 86%, respectively. As the prediction time increases, the influence of the inaccurate initial parameters on SCB prediction gradually decreases, and the prediction accuracy improves. The proposed BSO-BP model has the best accuracy and stability when predicting the 1 h SCB based on the same data. The prediction stability of the proposed BSO-BP model improves by more than 36% as compared with LP, QP, and GM models. In addition, the prediction accuracies of PHM clock and Rb-II clock improved by more than 47%, as compared with that of the Rb clock. Therefore, the overall performance of the atomic clock based on BDS-3 is better than BDS-2. The positioning accuracy of the BSO-BP model can reach the centimeter level in east, north, and up directions.

GNSS real-time precise point positioning with BDS-3 global short message communication devices

Global short-message communication (GSMC) service is a new function of BeiDou-3 global navigation satellite system (BDS-3). Broadcasting precise orbit and clock corrections via GSMC provides an opportunity for real-time precise point positioning (PPP), especially in the areas where internet-based communication is not available, such as deserts and oceans. This research achieves a real-time multi-GNSS PPP based on the precise orbit and clock corrections broadcast via BDS-3 GSMC. To reduce the data size, the precise corrections of only visible GNSS satellites are broadcast, and three messages are used to broadcast the corrections of GPS, Galileo and BDS satellites. The encoding strategy of corrections is designed and a procedure for real-time PPP with BDS-3 GSMC is described. To evaluate the positioning performance of the proposed real-time PPP scheme, the simulated kinematic real-time PPP experiments with BDS-3 GSMC corrections and Centre National d’Etudes Spatiales (CNES) real-time precise orbit and clock products are carried out by using observations of 7 days from 12 globally distributed IGS stations. The positioning accuracy in E, N and U components reach up to 3.3, 3.8 and 5.9 cm with GSMC corrections, which is comparable to that with CNES real-time products. Furthermore, a vehicle real-time PPP experiment is conducted using the devices with the function of BDS-3 GSMC and the positioning accuracy reach up to 4.1, 2.2 and 7.1 cm in E, N and U components after convergence.

THE PERFORMANCE ANALYSIS OF BDS POSITIONING IN NORDIC AREAS BASED ON THE SMARTPHONE

Abstract. Nowadays, the Global Navigation Satellite System (GNSS) is widely used in many applications. As a new system, China's BeiDou navigation system (BDS) is emerging in recent years. The last satellite of the third generation global BeiDou navigation system (BDS-3) has been successfully launched on June 23 in 2020, which means that BDS can offer navigation services worldwide. We evaluate the quality of BDS signals and analyze the performance of BDS positioning based on the smartphone in Espoo, Finland. The static and kinematic experiments were implemented in the parking lot of the Finish Geospatial Research Institute (FGI) and a highway route in Espoo, respectively. Experimental results show that BDS has good satellite visibility and geometric distribution. The signal carrier-to-noise density ratio (C/N0) of BDS-2 reaches 34.22 dB-Hz, which is comparable to the Global Positioning System (GPS). However, the signal carrier-to-noise density of BDS-3 is slightly lower than BDS-2, which is due to the significant number of BDS-3 satellites at low elevation angles. The horizontal precision of BDS positioning in the static and kinematic experiment is comparable to GPS in the east direction and slightly inferior to GPS in the north direction. However, the BDS shows poor precision in the up direction. In addition, the integration of BDS with other GNSS systems can significantly improve the positioning precision. This study intends to provide a reference for further research on the BDS global Positioning, Navigation, and Timing (PNT) services, particularly for LBS and smartphone positioning.

Augmentation Performance Analysis of Beidou-3 SBAS under Single Frequency and Dual Frequency

Abstract Based on the principle of satellite based augmentation information positioning, this paper uses the standard positioning algorithm of SBAS, IGMAS site data and augmentation information messages to evaluate the single point positioning performance of BDS satellite based augmentation information in China. From the results, the accuracy of single frequency augmentation information for single point positioning is improved by about 30%, which is equivalent to that of EGNOS. The accuracy of dual frequency augmentation information for single point positioning is improved by nearly 40%, which is better than that of single frequency.

Ambiguity Resolution for Long Baseline in a Network with BDS-3 Quad-Frequency Ionosphere-Weighted Model

For long baseline in a network, the traditional combined ionosphere-free (IF) + wide-lane (WL) strategy is commonly used, but the residual tropospheric delays and larger noise hamper the basic ambiguity resolution (AR). With the completion of the BeiDou global navigation satellite system (BDS-3) and the quad-frequency signals provided by BDS-3 satellites, we can construct more combinations that are conducive to ambiguity resolution. Compared with ionosphere-free linear combinations, we estimated ionospheric delay using three independent WL observations, and formed an ionosphere-weighted model using uncombined code and phase observations, which proved to be quite effective. Based on the real quad-frequency BDS-3 observations of two CORS (Continuously Operating Reference Stations) and two user stations, we processed eight days of data to study the formal and empirical ambiguity success rates and user positioning errors. The rounding success rate of WL ambiguity was significantly improved with ionospheric correction. The success rate of the basic ambiguity increased from 94.4 and 96.1% to 98.0% using the quad-frequency ionosphere-weighted (QFIW) model compared with the double-frequency ionosphere-free (DFIF) model and the triple-frequency geometry-based (TFGB) model. Furthermore, the user E/N/U positioning accuracy improved by 20.6/31.5/13.1% and 6.3/22.9/5.8%, respectively.

Principle and performance of BDSBAS and PPP-B2b of BDS-3

Within the framework of differential augmentation, this paper introduces the basic technical framework and performance of the BeiDou Global Navigation Satellite System (BDS-3) Satellite-Based Augmentation System (BDSBAS), including orbit products, satellite clock offset products, ionosphere and its integrity performance. The basic principle of BDS-3 Precise Point Positioning (PPP-B2b) is expounded, the similarities and differences between the PPP service provided by BDS-3 and International Global Navigation Satellite System (GNSS) Service (IGS) are discussed, and the limitations of PPP-B2b are analyzed. Since both the BDSBAS and PPP-B2b utilize a ground monitoring station network to determine the satellite orbits and clock offset corrections, and broadcast differential corrections through the three Geostationary Orbit (GEO) satellites of BDS-3, the feasibility of the co-construction of BDSBAS and PPP-B2b is analyzed, strategies for the infrastructure sharing and correction broadcasting are presented, and the influences of BDSBAS correction broadcasting strategy adjustment are evaluated. In addition, it assesses the possibility of broadcasting differential corrections through the Inclined Geosynchronous Orbit (IGSO) satellites of BDS-3, and the feasibility of augmenting satellite navigation with Low Earth Orbit (LEO) satellites.

Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between −2×10−18 and 2×10−18 s/s2. The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is 4.0 × 10−14 s/s at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites.

Accounting for biases between BDS-3 and BDS-2 overlapping B1I/B3I signals in BeiDou global ionospheric modeling and DCB determination

The receiver pseudo-range biases between BDS-2 and BDS-3 in global ionospheric modeling and differential code bias (DCB) determination are investigated by using the overlapping B1I/B3I signals. The BDS receiver DCB estimations from global ionospheric modeling and the results of single-differences of short-baselines reveal that the receiver pseudo-range bias differences between BDS-3 and BDS-2 B1I/B3I observations are related to receiver types, and the maximum of the bias differences can be up to 8.6 ns. It means that the receiver DCB differences between BDS-3 and BDS-2 B1I/B3I observations should be considered in BDS-3/BDS-2 ionospheric modeling and DCB determination. Compared with DCB products from Chinese Academy of Sciences (CAS), the RMS is better than 0.3 ns when the receiver pseudo-range bias differences between BDS-3 and BDS-2 are ignored, while the RMS is about 0.51 ns when the receiver pseudo-range bias differences are considered. Based on the analysis of the BDS-3 and BDS-2 receiver pseudo-range bias differences, it indicates there are significant deviations in existing CAS satellite DCB products for BDS B1I/B3I observations. In terms of the stability of BDS satellite DCB estimations, the monthly STDs of BDS-3 DCB estimations improves by 20.2% on average when the receiver pseudo-range bias differences between BDS-3 and BDS-2 are considered. Taking the final Global Ionospheric Maps (GIMs) from Centre for Orbit Determination in Europe (CODE) as references, the accuracy of BDS-only global ionospheric modeling is 2.4 total electron content unit (TECU) when the receiver DCB differences between BDS-3 and BDS-2 are considered, and improves by 9.3% compared with the results which ignores the receiver pseudo-range bias differences between BDS-3 and BDS-2.

Comprehensive Analyses of PPP-B2b Performance in China and Surrounding Areas

BeiDou Global Navigation Satellite System (BDS-3) provides a regional Precise Point Positioning (PPP) service, called PPP-B2b, for users in China and surrounding areas through B2b signal transmitted from its three geostationary earth orbit (GEO) satellites. The information broadcasted by the B2b signal include satellite orbit corrections, satellite clock offset corrections, and differential code bias (DCB) corrections of BDS-3 satellites. In this study, the accuracies of PPP-B2b corrections along with real-time PPP performance are comprehensively evaluated referenced to precise orbit and clock products from GFZ and the precise DCB products from CAS. The result indicates that the accuracy of the BDS-3 broadcast orbit is similar to that of the PPP-B2b real-time orbit. The PPP-B2b clock offset correction improved the satellite clock offset precision of the BDS-3 broadcast ephemeris. The Signal-in-Space Range Error (SISRE) of broadcast ephemeris and PPP-B2b are calculated, which are 0.536 and 1.24 m, respectively. The large SISRE value of PPP-B2b is caused by the satellite-specified systematic bias to IGS final products. The positioning performance evaluation of real-time PPP with B2b service is carried out and compared with the real-time product provided by Wuhan University (WHU) based on the eight IGS MGEX stations in China and surrounding countries. The positioning accuracy of static positioning mode with PPP-B2b service achieved centimeter-level accuracy in the selected station, and that of kinematic positioning mode achieved decimeter-level accuracy. The availability rate of PPP-B2b corrections in the surrounding area of China, however, degrades from 88.76% to 60.91% in the selected stations. The accuracy of the PPP solution using PPP-B2b correction is better than that of using WHU real-time product within China. The positioning performance of stations located at the boundary of the PPP-B2b service area, however, is affected by the number of PPP-B2b available satellites. The positioning accuracy in kinematic positioning mode is worse than that of using WHU real-time precise product.

Variation Characteristics of Multi-Channel Differential Code Biases from New BDS-3 Signal Observations

A multi-frequency Global Navigation Satellite System (GNSS) provides greater opportunities for positioning and navigation applications, particularly the BeiDou Global Navigation Satellite System (BDS-3) satellites. However, multi-frequency signals import more pseudorange channels, which introduce more multi-channel Differential Code Biases (DCBs). The satellite and receiver DCBs from the new BDS-3 signals are not clear. In this study, 9 DCB types of the new BDS-3 signals from 30-days Multi-GNSS Experiment (MGEX) observations are estimated and investigated. Compared with the DCB values provided by the Chinese Academy of Science (CAS) products, the mean bias and root mean squares (RMS) error of new BDS-3 satellite DCBs are within ±0.20 and 0.30 ns, respectively. The satellite DCBs are mostly within ±0.40 ns with respect to the product of the Deutsches Zentrum für Luft- und Raumfahrt (DLR). The four sets of constructed closure errors and their mean values are within ±0.30 ns and ±0.15 ns, respectively. The mean standard deviation (STD) of the estimated satellite DCBs is less than 0.10 ns. In particular, our estimated satellite DCBs are more stable than DCB products provided by CAS and DLR. Unlike satellite DCBs, the receiver DCBs have poor compliance and show an obvious relationship with the geographic latitude when compared to the CAS products. The STDs of our estimated receiver DCBs are less than 1.00 ns. According to different types of receiver DCBs, the distribution of STDs indicates that the coefficient of the ionospheric correction has an influence on the stability of the receiver DCBs under the ionosphere with the same accuracy level. In addition, the type of receiver shows no regular effects on the stability of receiver DCBs.

Characterization and Calibration of Spaceborne GNSS-R Observations Over the Ocean From Different BeiDou Satellite Types

The Global Navigation Satellite System Reflectometry (GNSS-R) technique can measure ocean surface winds and other geophysical parameters from forward scattered GNSS (GPS, BeiDou, Galileo, etc.) signals. However, most early spaceborne missions only captured GPS signals while the study of spaceborne reflectometry using BeiDou signals (BDS-R) is limited. The GNOS-II payload onboard China’s FY-3E satellite has been operationally collecting a large number of BDS-R data since July 10, 2021. BDS is different from GPS in the orbit, signal frequency, chipping rate and Effective Isotropic Radiated Power (EIRP). Furthermore, BDS satellites have different generations and orbits. This paper, for the first time, comprehensively characterizes the spaceborne BDS-R observations over the ocean using the FY-3E GNOS-II data from different BDS satellite types including BDS-2 IGSO, BDS-2 MEO, BDS-3 IGSO and BDS-3 MEO. Their spatial coverage, spatial resolution, effective scattering area, incidence angle, range corrected gain, EIRP and signal-to-noise ratio have been analyzed and compared to those of GPS-R. Spaceborne BDS-R shows a lot of uniquenesses compared to GPS-R. The BDS-R observables are then calibrated separately for each type. An intercalibration is also applied to correct extra calibration errors. After the calibration, BDS-R observables and retrieved winds are consistent between each type and compared to those of GPS-R. Calibrated observables from FY-3E GNOS-II are also evaluated by comparing them to those measured by the Cyclone Global Navigation Satellite System (CYGNSS) mission and a theoretical model. The results of this paper can provide a reference for future BDS-R studies and spaceborne GNSS-R mission design.

Initial assessment of BDS-3 precise point positioning service on GEO B2b signal

The China BeiDou global navigation satellite system (BDS-3) has started to provide free and open precise positioning services to users in China and surrounding areas since Jul 2020 on the GEO B2b signal. The initial assessment of BDS-3 PPP-B2b products and the PPP performance over a period of near five months from Jul 26, 2020 to Dec 19, 2020 was carried out in this work. Taking the GBM products as a reference, the average signal-in-space ranging error (SISRE) of the disseminated orbit and clock products is approximately 82.3 cm (RMS) and 3.9 cm (STD) for BDS-3 satellites, and about 135.8 cm (RMS) and 7.5 cm (STD) for GPS. The average positioning error RMS at six permanent stations in China is about 2.1 (1.8) and 2.6 (2.1) cm in the horizontal and vertical components respectively for BDS-only (BDS + GPS) static PPP. In the kinematic PPP mode, the average positioning error (95%) at the same six stations is about 21.5 (15.2) and 33.4 (30.3) cm in the horizontal and vertical component respectively for BDS-only (BDS + GPS), with an average convergence time of 17.4 (16.2) min. In addition, two vehicle-based kinematic PPP tests show average position error (95%) of about 23.5 (18.6) and 48.8 (37.1) cm in horizontal and vertical respectively, and an average convergence time of 10.4 (14.2) min for BDS-only (BDS + GPS) PPP. The assessment results are overall in accordance with the official claim of centimeter-level in static mode and decimeter-level in kinematic mode from BDS-3 PPP service.

Signal-to-Noise Ratio Analyses of Spaceborne GNSS-Reflectometry from Galileo and BeiDou Satellites

In recent years, Global Navigation Satellite System Reflectometry (GNSS-R) technology has made considerable progress with the increasing of GNSS-R satellites in orbit, the improvements of GNSS-R data processing technology, and the expansion of its geophysical applications. Meanwhile, with the modernization and evolution of GNSS systems, more signal sources and signal modulation modes are available. The effective use of the signals at different frequencies or from new GNSS systems can improve the accuracy, reliability, and resolution of the GNSS-R data products. This paper analyses the signal-to-noise ratio (SNR) of the GNSS-R measurements from Galileo and BeiDou-3 (BDS-3) systems, which is one of the important indicators to measure the quality of GNSS-R data. The multi-GNSS (GPS, Galileo and BDS-3) complex waveform products generated from the raw intermediate frequency data from TechDemoSat-1 (TDS-1) satellite and Cyclone Global Navigation Satellite System (CYGNSS) constellation are used for such analyses. The SNR and normalized SNR (NSNR) of the reflected signals from Galileo and BDS-3 satellites are compared to these from GPS. Preliminary results show that the GNSS-R SNRs from Galileo and BDS-3 are ∼1–2 dB lower than the GNSS-R measurements from GPS, which could be due to the power of the transmitted power and the bandwidth of the receiver. In addition, the effect of coherent integration time on GNSS-R SNR is also assessed for different GNSS signals. It is shown that the SNR of the reflected signals can be improved by using longer coherent integration time (∼0.4–0.8 dB with 2 ms coherent integration and ∼0.6–1.2 dB with 4 ms coherent integration). In addition, it is also shown that the SNR can be improved more efficiently (∼0.2–0.4 dB) for reflected BDS-3 and Galileo signals than for GPS. These results can provide useful references for the design of future spaceborne GNSS-R instrument compatible with reflections from multi-GNSS constellations.

Evaluation of BDS-2 and BDS-3 Satellite Atomic Clock Products and Their Effects on Positioning

The BeiDou Navigation Satellite System (BDS) has completed third phase construction and currently provides global services, with a mixed constellation of BDS-2 and BDS-3. The newly launched BDS-3 satellites are equipped with rubidium and passive hydrogen maser (PHM) atomic clocks. The performance of atomic clocks is one of the cores of satellite navigation system, which will affect the performance of positioning, navigation and timing (PNT). In this paper, we systematically analyze the characteristics of BDS-2 and BDS-3 atomic clocks, based on more than one year of precise satellite clock products and broadcast ephemeris. Firstly, the results of overlapping Allan variations demonstrate that BDS-3 Rb and PHM clocks improve better in stability than BDS-2 Rb clock and are comparable to GPS IIF Rb and Galileo PHM clocks. Accordingly, the STDs of BDS-3 broadcast satellite clock are better than GPS and BDS-2, which are at the same level with that of Galileo. Secondly, the inter-system bias (ISB) between BDS-2 and BDS-3 is analyzed by satellite clock datum comparison and precise point positioning (PPP). Surprisingly, the discrepancy between BDS-2 and BDS-3 satellite clock datum has a great difference between products that could reach up to about 10 ns for WHU satellite clock products and broadcast ephemeris. Moreover, the ISBs between BDS-2 and BDS-3 satellite clocks are quite stable over one-year periods. Thirdly, due to the improved stability of BDS-3 atomic clock, the 68% positioning accuracy is better than 0.65 m at 10 min for BDS-3 PPP, based on broadcast ephemeris. Besides, the non-negligible bias between BDS-2 and BDS-3 will greatly affect the BDS precise data processing. The accuracy of positioning is greatly improved when considering the ISB.

Combined BDS-2/BDS-3 real-time satellite clock estimation with the overlapping B1I/B3I signals

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

Correction Model of BDS-3 Satellite Pseudorange Multipath Delays and Its Impact on Single-Frequency Precise Point Positioning

Precise point positioning (PPP) is used in many fields. However, pseudorange multipath delay is an important error that restricts its accuracy. Pseudorange multipath delay can be considered as the combination of effective information and observation noise; it can be modeled after removing the observation noise. In this work, elastic nets (EN) regularization denoising method is proposed and compared with L2-norm regularization denoising method. Then, quadratic polynomial (QP) model plus autoregressive (AR) model (QP + AR) are used to model the denoised pseudorange multipath delays. Finally, the modeling results are corrected to the observations to verify the improvement of BDS-3 single-frequency PPP accuracy. Three single-frequency PPP schemes are designed to verify the effectiveness of denoising method and QP + AR model. The experimental results show that the accuracy improvement of B3I and B2a is more obvious than that of B1I and B1C when the modeling values are corrected to the pseudorange observations. The improvement of B3I and B2a in the east (E) and up (U) directions can reach 10.6%∼34.4% and 5.9%∼65.7%, and the improvement of the north (N) direction is mostly less than 10.0%. The accuracy of B1I and B1C in E and U directions can be improved by 0%∼30.7% and 0.4%∼28.6%, respectively, while the accuracy of N direction can be improved slightly or even decreased. Using EN regularization denoising and QP + AR model correction, single-frequency PPP performs better at B3I and B2a, while L2-norm regularization denoising and QP + AR model correction perform better at B1I and B1C. The accuracy improvement of B2a and B3I is more obvious than that of B1I and B1C. The convergence time after MP correction of each frequency is slightly shorter. Overall, the proposed pseudorange multipath delays processing strategy is beneficial in improving the single-frequency PPP of BDS-3 satellite.

Modeling and assessment of multi-frequency GPS/BDS-2/BDS-3 kinematic precise point positioning based on vehicle-borne data

BeiDou Navigation Satellite System (BDS) has got the global service capability after the launch of the 55th BDS-3 satellite on June 23, 2020. Currently, BDS is operated based on both the second generation BDS (BDS-2, with 15 satellites transmitting triple frequency signals) and the third generation BDS (BDS-3, with 30 satellites providing services from five frequency signals). To make full use of BDS-2 + BDS-3 signals (B1I, B2I, B3I, B1C, and B2a), this paper introduces an undifferenced and uncombined Precise Point Positioning (PPP) model by using single/dual/triple frequencies BDS-2/BDS-3 data. Results illustrate that the Root Mean Square (RMS) values of BDS-3 PPP based on new signals are better than BDS-2 (B1I + B3I), but worse than BDS-3 (B1I + B3I). Generally, triple-frequency PPP is close to that of dual-frequency PPP, but it is improved significantly in the north, east and vertical components comparing with single-frequency PPP. Compared to the positioning accuracy of GPS + BDS-2 PPP, those of GPS + BDS-3 PPP are improved obviously, especially in the horizontal components. While using BDS-2 and BDS-3 together, the positioning performance of GPS + BDS-2 + BDS-3 is upgraded significantly in both horizontal and vertical directions. Moreover, the convergence time of BDS-3 (especially B1C + B2a) and BDS-2 + BDS-3 PPP are accelerated visibly comparing with that of BDS-2 PPP.

Identification of BDS Satellite Clock Periodic Signals Based on Lomb-Scargle Power Spectrum and Continuous Wavelet Transform

Onboard satellite clocks are the basis of Global Navigation Satellite Systems (GNSS) operation, and their revolution periods are at the level of 2 per day (about 12 h) in the case of the Medium Earth Orbit (MEO) satellites. In this work, the authors analysed the entire BeiDou Navigation Satellite System (BDS) space segment (BDS-2 and BDS-3) in terms of the occurrence of periodic, repetitive signals in the clock products, and checked if they coincide with the orbital periods or their multiples. The Lomb-Scargle (L-S) power spectrum was used as a tool to determine the periods present in the BDS clock products, allowing for analyses based on incomplete input data; in this case, the incomplete data were the phase data with jumps and outliers removed. In addition, continuous wavelet transform (CWT) was used to produce a time−frequency representation showing the more complex behaviour of the satellite clock products. As shown in the case of geostationary and geosynchronous inclined orbit satellites, the main period was 23.935 h, while for the Medium Earth Orbit it was 12.887 h, with the BDS satellite orbital period being 12 h 53 m (12.883 h). Some effects connected with reference clock swapping are also visible in the power spectrum. The conducted analyses showed that the BDS-2 satellite clocks have much higher noise than the BDS-3 satellite clocks, meaning that the number of designated periods is greater, but their reliability is significantly lower. BDS-3 satellites have only been in operation for a very short time, thus this is the first analysis to include this type of data. Moreover, such a wide and complex analysis has not been carried out to date.