BDS-3 Satellites Research Articles

Improved SSA-Based GRU Neural Network for BDS-3 Satellite Clock Bias Forecasting.

Satellite clock error is a key factor affecting the positioning accuracy of a global navigation satellite system (GNSS). In this paper, we use a gated recurrent unit (GRU) neural network to construct a satellite clock bias forecasting model for the BDS-3 navigation system. In order to further improve the prediction accuracy and stability of the GRU, this paper proposes a satellite clock bias forecasting model, termed ITSSA-GRU, which combines the improved sparrow search algorithm (SSA) and the GRU, avoiding the problems of GRU's sensitivity to hyperparameters and its tendency to fall into local optimal solutions. The model improves the initialization population phase of the SSA by introducing iterative chaotic mapping and adopts an iterative update strategy based on t-step optimization to enhance the optimization ability of the SSA. Five models, namely, ITSSA-GRU, SSA-GRU, GRU, LSTM, and GM(1,1), are used to forecast the satellite clock bias data in three different types of orbits of the BDS-3 system: MEO, IGSO, and GEO. The experimental results show that, as compared with the other four models, the ITSSA-GRU model has a stronger generalization ability and forecasting effect in the clock bias forecasting of all three types of satellites. Therefore, the ITSSA-GRU model can provide a new means of improving the accuracy of navigation satellite clock bias forecasting to meet the needs of high-precision positioning.

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%.

Estimation of phase center corrections for BDS satellites aligned to the IGS20 frame

Estimation of phase center corrections for BDS satellites aligned to the IGS20 frame

Precise orbit determination of Haiyang-2D using onboard BDS-3 B1C/B2a observations with ambiguity resolution

The Haiyang-2D altimetry mission of China is one of the first Low Earth Orbit (LEO) satellites that can receive new B1C/B2a signals from the BeiDou-3 Navigation Satellite System (BDS-3) for Precise Orbit Determination (POD). In this work, the achievable accuracy of the single-receiver ambiguity resolution for onboard LEO satellites is studied based on the real measurements of new BDS-3 frequencies. Under normal conditions, six BDS-3 satellites on average are visible. However, the multipath of the B1C/B2a code observations presents some patchy patterns that cause near-field variations with an amplitude of approximately 40 cm and deteriorate the ambiguity-fixed rate. By modeling those errors, for the B2a code, a remarkable reduction of 53% in the Root Mean Square (RMS) is achieved at high elevations, along with an increase of 8% in the ambiguity-fixed rates. Additionally, an analysis of the onboard antenna's phase center offsets reveals that when compared to the solutions with float ambiguities, the estimated values in the antenna’s Z direction in the solutions with fixed ambiguities are notably smaller. The independent validation of the resulting POD using satellite laser ranging at 16 selected high-performance stations shows that the residuals are reduced by a minimum of 15.4% for ambiguity-fixed solutions with an RMS consistency of approximately 2.2 cm. Furthermore, when compared to the DORIS-derived orbits, a 4.3 cm 3D RMS consistency is achieved for the BDS-3-derived orbits, and the along-track bias is reduced from 2.9 to 0.4 cm using ambiguity fixing.

An Improved Carrier-Smoothing Code Algorithm for BDS Satellites with SICB

Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent.

Uncalibrated phase delay estimation and ambiguity resolution for BDS-3 six-frequency uncombined PPP with legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals

Multi-frequency integration can accelerate the ambiguity resolution (AR) and shorten the convergence time of precise point positioning (PPP). BDS-3 satellites can broadcast legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals, which facilitates the multi-frequency PPP. An uncalibrated phase delay (UPD) estimation method and a fast AR method are extended for BDS-3 six-frequency uncombined PPP. The characteristics of UPD estimates are analyzed in terms of stability, ambiguity residuals, and usage rate. The data sets on seven consecutive days from 224 globally distributed stations are selected for UPD estimation, and those from 21 stations are employed for PPP AR. The results indicate that the static convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions (with a threshold of 10 cm) can reach 8.2, 4.0, and 13.4 min in the east, north, and up directions, respectively, and the three-dimensional (3D) convergence time is shortened by 21.1 % and 26.5 % compared with the six-frequency ambiguity-float solutions and the dual-frequency ambiguity-fixed solutions, respectively. The corresponding kinematic convergence time can reach 13.0, 7.0, and 33.2 min in three directions, respectively, and the corresponding improvement rates are 21.0 % and 33.7 %, respectively. In addition, the convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions can be slightly shortened even compared with the five-frequency case. The static and kinematic positioning accuracy of BDS-3 six-frequency PPP ambiguity-fixed solutions can reach 4, 3, and 9 mm, and 18, 14, and 38 mm in three directions, respectively, which is slightly better than other cases.

Advancing Precise Orbit Determination and Precise Point Positioning of BDS-3 Satellites from B1IB3I to B1CB2a: Comparison and Analysis

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time.

A Study of Solar Radiation Pressure Model in BDS-3 Precise Orbit Determination

For the BDS (BeiDou Navigation Satellite System) satellites, the solar radiation pressure is the major non-gravitational perturbation the satellites suffer. Due to the influence of multiple factors, accurate modeling the solar radiation pressure acting on these satellites is difficult to accomplish. The solar radiation pressure perturbation is an essential source of error in the precise orbit determination (POD) and orbit prediction processes of the BDS satellites. As the ECOMC (Empirical CODE Orbit Model 1 and 2 Combined) model adopts the advantageous features of the ECOM1 (Empirical CODE Orbit Model 1) model and the ECOM2 (Empirical CODE Orbit Model 2) model, a greater number of parameters have been introduced into the model, leading to strong correlation between the ECOMC model parameters. In response to the deficiency of the ECOMC model, the authors collected the BDS-3 satellite precise ephemeris data that were provided by Wuhan University (WHU) from January 2019 to April 2022. And by these ephemeris data, the ECOMC model’s 13 parameters were obtained through the dynamic orbit fitting method. By conducting these time sequence diagrams analysis of the ECOMC model parameters, this thesis affords the selection strategies of the solar radiation pressure parameters of the ECOMC model for BDS-3 inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellite. And the rationality of the selection strategies of the solar radiation pressure parameters for the ECOMC model was verified by orbit fitting and orbit prediction experiments. The results show that using the improved ECOMC model gains the best orbit fitting effects for BDS-3 IGSO and MEO satellite, and can also enhance the accuracy of medium and long-term orbit prediction of BDS-3 IGSO and MEO satellite.

An Analysis of Satellite Multichannel Differential Code Bias for BeiDou SPP and PPP

Differential code bias (DCB) of satellite is an error that cannot be ignored in precise positioning, timing, ionospheric modeling, satellite clock correction, and ambiguity resolution. The completion of the third generation of BeiDou Navigation Satellite System (BDS-3) has extended DCB to multichannel code bias observations and observable-specific signal bias (OSB). In this paper, the DCB and OSB products provided by the Chinese Academy of Sciences (CAS) are analyzed and compared. The DCB parameters for the BDS satellites are applied in both single- and dual-frequency single point positioning (SPP), and the results are intensively investigated. Based on the satellite DCB parameters of the BDS, the performance of precise point positioning (PPP) with different frequency combinations is also analyzed in terms of positioning accuracy and convergence time. The standard deviations (STDs) of DCBs at each signal pair fluctuate from 0.2 ns to 1.5 ns. The DCBs of BDS-2 are slightly more stable than those of BDS-3. The mean values and STDs of C2I and C7I OSBs for BDS-2 are at the same level and are numerically smaller than their counterparts for the C6I OSBs. The mean OSBs for each signal of the BDS-3, excluding C2I, fluctuate between 12.35 ns and 12.94 ns, and the STD fluctuates between 2.11 ns and 3.10 ns. The DCBs and OSBs of the BDS-3 of the IGSO satellites are more stable than those of the MEO satellites. The corrections for TGD and DCB are able to improve the accuracy of single-frequency SPP by 44.09% and 44.07%, respectively, and improve the accuracy of dual-frequency SPP by 6.44% and 12.85%, respectively. The most significant improvements from DCB correction are seen in single-frequency positioning with B1I and dual-frequency positioning with B2a+B3I. DCB correction can improve the horizontal and three-dimensional positioning accuracy of the dual-frequency PPP of different ionosphere-free combinations by 13.53% and 13.84% on average, respectively, although the convergence is slowed.

An improved satellite-induced code bias correction model for BDS un-GEO satellites in consideration of elevation and azimuth angles

The satellite-induced code bias (SICB) resulting in code-phase divergences of nearly 1.0 m has been observed in the code measurements of BeiDou navigation satellite system (BDS). Since the SICB is proved to be elevation- and frequency-dependent, several SICB correction models have been proposed to remove the systematic bias, but most of them only consider elevation angles, overlooking the influence of azimuth angles, which would limit the accuracy of the correction models, especially for Medium Earth Orbit (MEO) satellites. To deal with this problem, we proposed an improved SICB piecewise correction model as a function of elevation and azimuth angles and estimated parameters for each BDS un-GEO (Geostationary Earth Orbit) satellite and each available frequency with node-separation of 1°. The epoch-difference method is employed to remove the effect of stable terms, such as phase-ambiguities, receiver- and satellite-dependent hardware delays. Moreover, to reduce the effect of code noise and multipath at low-elevation conditions, the threshold of elevation angle for the improved model is determined based on the statistics of Multipath (MP) combinations. Besides, weight-average algorithm is used to obtain the optimal MP deviations and improve the accuracy of proposed correction model in consideration of signal-to-noise (SNR). The experiment results with real GNSS data show that the SICB models are more suitable for BDS-2 MEO satellites than Inclined Geosynchronous Orbit (IGSO) satellites. The code measurements on B1 signal are more susceptible to the SICB than that on B3 signal. After applying the improved SICB correction models, the RMS errors of MP series are significantly reduced for BDS-2 un-GEO satellites. However, for BDS-3 satellites, only centimeter-level SICB deviations can be detected for all frequency-bands, and the RMS of MP variations have slight changes after applying the SICB corrections, indicating that the systematic bias in MP combinations is not obvious, especially for BDS-3 MEO satellites.

Improvement Analysis of a Height‐Deviation Compensation‐Based Linear Interpolation Method for Multi‐Station Regional Troposphere

AbstractIn network real‐time kinematic positioning of multi‐reference station, the spatial and temporal distribution of tropospheric delay is affected by both horizontal and elevation. The traditional modeling strategy of regional troposphere takes more consideration of the horizontal factor, and the incomplete consideration of the elevation factor will lead to the problem of reduced modeling accuracy, especially in the face of the scene with large regional height deviation. Based on the traditional linear interpolation method (LIM), a simple and effective height‐deviation compensation‐based linear interpolation method (HCLIM) for regional tropospheric is proposed. The modeling accuracy of troposphere and the positioning accuracy of user RTK in large height deviation region are significantly improved. The method was verified based on six experimental subnets with large height deviations from a provincial continuously operating GNSS reference stations network in central China. The results showed that: For GPS satellite modeling, compared with the traditional LIM method, the average modeling accuracy improvement rate of HCLIM method is (84.5%, 75.5%, 59.3%, 26.7%) in the elevation angle range of (10–30°/30–40°/40–50°/50–90°). For BDS satellite, the average modeling accuracy improvement rate of HCLIM method in the above four elevation angles is (83.3%, 70%, 50%, 23.5%). For the positioning performance of user RTK, The horizontal positioning accuracy and RTK fixing rate were similar under the two methods, while HCLIM method showed only slight improvement. However, in the U direction, LIM method showed obvious systematic bias, while HCLIM method showed consistent positioning accuracy, which was improved to 82.8% compared with LIM method.

Estimating inter-satellite link Ka-band antenna phase center offsets to improve BDS-3 satellite orbit determination

Satellite antenna phase center offset (PCO) correction is essential not noly for L-band ground-tracking GNSS high-precision data processing, but also for Ka-band inter-satellite link (ISL) observations. The Ka-band ISL and L-band satellite-ground observations of 90 days from 25 November 2020 to 23 February 2021 are used for the Ka-band PCO estimation and precise orbit determination (POD) validation for BDS-3 satellites. The results show that the standard deviations of the estimated Ka-band PCOs for 29 BDS-3 satellites are 1.73, 2.63 and 3.58 cm in the X, Y and Z components, respectively. The accuracy of the Ka-band PCO estimates for medium Earth orbit satellites (MEO) is better than those of inclined geosynchronous orbit (IGSO) and geostationary Earth orbit (GEO) satellites due to a better observation geometry. The POD validation results indicate that using the estimated Ka-band PCOs can improve the ISL-based orbit determination performance. Using Ka-band ISL and L-band satellite-ground observations with 40 global stations for combined POD, the orbit overlap comparison shows that the average three-dimensional (3D) root mean square (RMS) error for 29 BDS-3 satellites is decreased from 12.6 to 6.6 cm with a reduction of 47.6%, and satellite laser ranging (SLR) validation for 4 BDS-3 satellites shows an accuracy improvement from 6 to 5 cm in RMS. When using ISL and only 7 regional ground stations are used, the average 3D RMS of orbit overlap errors is decreased from 15.9 to 10.9 cm with a reduction of 31.6%, and the RMS of SLR residuals for 4 BDS-3 satellites is decreased from 6.7 to 5.6 cm. For ISL-only POD, the average 3D RMS of orbit overlap errors is decreased from 18.0 to 12.4 cm with a reduction of 31.1%, and the RMS of SLR residuals for 4 BDS-3 satellites is decreased from 7.1 to 6.9 cm.

Adapting empirical solar radiation pressure model for BDS-3 medium Earth orbit satellites

For the precise orbit determination (POD) of global navigation satellite systems (GNSS) constellation, it is very difficult to precisely model the solar radiation pressure (SRP) force acting on GNSS satellites. For GPS satellites, the ECOM model developed by the Center for Orbit Determination in Europe has been utilized by most of International GNSS Service (IGS) analysis centers. However, it should be adapted and optimized to the characteristics of satellites of each GNSS system or even individual satellites. It was extended to the ECOM2 model for GLONASS satellites and then for Galileo satellites by employing a box–wing model. Since November 2020, the third generation of the BeiDou satellite system (BDS-3) has been in its full operation and there are about 200 globally distributed IGS ground stations tracking BDS-3 signals, which creates a great potential to evaluate and optimize its SRP modeling. From the POD processing carried out in this study, we found significant fluctuations of up to 20 cm in overlapping orbit differences for satellites over eclipses in the radial direction and of about 20 and 50 cm in the cross and along directions for ECOM2 and ECOM models. Then, based on numerical analyses we demonstrate that the fourth- and sixth-order sine terms in the Sun direction can significantly reduce the overlapping orbit differences of ECOM. Therefore, an adapted SRP model by adding the fourth- and sixth-order sine periodical terms in the Sun direction to the ECOM model is presented. The adapted model is then validated for BDS-3 POD and orbit prediction. Results show that fluctuations in the amplitude of overlapping estimated orbits using ECOM models are reduced from 20 to < 10 cm in the radial-track component and satellite laser ranging residuals are reduced to half by the adapted SRP model. For the predicted BDS-3 satellite orbits, the RMS values over deep eclipses can be improved from about 7, 14 and 26 cm to about 3, 5 and 12 cm, in the radial, cross and along directions, respectively, compared to the ECOM model.

An Improved Doppler-Aided Smoothing Code Algorithm for BeiDou-2/BeiDou-3 un-Geostationary Earth Orbit Satellites in Consideration of Satellite Code Bias

The extensive use of carrier-aided smoothing code (CSC) filters has led to a reduction in the noise level of raw code measurements in GNSS positioning and navigation applications. However, the existing CSC technique is sensitive to the changes in the integer ambiguity, and then the smoothing procedure needs to be restarted in the presence of cycle slips. As the Doppler shift is instantaneously observed and immune to cycle slips, the Doppler-aided smoothing code (DSC) algorithm would be more promising in a challenged environment. Based on the Hatch filter, an optimal DSC approach is proposed with the principle of minimum variance. Meanwhile, to inhibit the effect of the integral cumulative error of the Doppler, a balance factor is adopted to adjust the contributions of raw code and DSC. The noise level of code observable is not only affected by thermal noise, but also limited by systematic bias. Satellite code bias (SCB) was identified in the raw code observable on each frequency for each BDS-2 satellite. By minimizing the sum of the absolute value of residuals, the polynomial segment fitting algorithm as a function of elevation angles is applied to establish the SCB correction model based on epoch-differenced multipath (MP) deviations. Finally, different types of experiments demonstrate the validity and efficiency of the refined DSC filter with SCB corrections on each available frequency for BDS un-GEO satellites.

BDS Dual-Frequency Carrier Phase Multipath Hemispherical Map Model and Its Application in Real-Time Deformation Monitoring.

The BDS multipath delay error is highly related to the surrounding monitoring environment, which cannot be eliminated or mitigated by applying the double difference observation model. In the actual monitoring environment, due to the complexity of the BDS constellation, it is difficult for existing algorithms to consider GEO, IGSO, MEO and other different orbital types of satellites for real-time and efficient multipath error reduction. Therefore, we propose a novel BDS dual-frequency multipath error reduction method for real deformation monitoring for BDS considering various satellite orbit types. This method extracts the single error residual of each satellite based on the assumption of "zero mean" and divides the appropriate grid density of GEO and IGSO/MEO, respectively, to construct a dual-frequency multipath hemispherical map model suitable for BDS satellites with different orbital types. This method can realize the multipath error elimination of the observed values of different orbits and different frequencies. The results of simulation experiments and real deformation monitoring data demonstrate that this method can effectively eliminate low-frequency multipath delay errors in the observation domain and coordinate domain. After multipath correction, the precision of the horizontal coordinates and height coordinates are 1.7 mm and 4.6 mm. The precision of the horizontal coordinate and height coordinate is increased by 50% and 60%, respectively. The fixed rate of ambiguity increased by 5-7%.

The Extraction and Characterization of Pseudorange Multipath Based on BDS-3 Multi-Frequency Observations.

Global Navigation Satellite System (GNSS) observations are subject to various errors during their propagation process. A reasonable correction of these errors can improve the positioning, navigation, and timing (PNT) service capability. The impact of multipaths on pseudorange observations can reach a decimeters or even meters level. However, their mechanism is complex and there is currently no universally accepted high-precision correction model. The correlation between the pseudorange multipaths (MP) of BDS-2 satellites and satellite elevation has been confirmed, while there have been fewer analyses of the MP characteristics for different frequencies of BDS-3 satellites. The broadcasting of multi-frequency observations in BDS-3 should theoretically make the extracted MP more accurate compared to traditional methods. Based on this, in this contribution, a multi-frequency MP extraction algorithm based on the least squares principle is proposed, which can simultaneously eliminate the influence of higher-order ionospheric delay. The analytical expression for only eliminating first-order ionospheric delay is successfully derived. Subsequently, the characteristics of the MPs extracted from different frequency combinations and the impact of combination noise on the extraction accuracy are discussed. The influence of second-order ionospheric delay on the MPs for each frequency under different combination noises, as well as the periodic behavior exhibited in long-term observations of the BDS-3 medium earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites, are also analyzed. Finally, the correlations between the MPs of each frequency of BDS satellite and elevation are quantitatively analyzed based on observations from 35 stations. Overall, this work has positive implications for the study of the MP characteristics of BDS-3 and subsequent modeling efforts.

Analysis on BDS-3 Autonomous Navigation Performance Based on the LEO Constellation and Regional Stations

The global navigation satellite system (GNSS) is developing rapidly, and the related market applications and scientific research are increasing. Studies based on large low Earth orbit (LEO) satellite constellations have become research hotspots. The global coverage of the LEO constellation can reduce the dependence of navigation satellites on ground-monitoring stations and improve the precise orbit determination (POD) accuracy of navigation satellites. In this paper, we simulate various LEO satellite constellations (with 12, 30, and 60 satellites), along with ground stations’ observation data, to examine the impact of LEO satellites on the precision of the BeiDou-3 Global Navigation Satellite System (BDS-3) in terms of its POD accuracy. Using the simulated observation data of both LEO satellites and ground-monitoring stations, we analyze the integrated orbit determination for the LEO and BDS-3 satellites. The findings reveal that the 3D orbital accuracy of BDS-3 is 9.51 dm by using only seven ground-monitoring stations, and it is improved to a centimeter level after adding the LEO constellations. As the number of LEO constellation satellites increases, the impact on improving accuracy gradually diminishes. In terms of time synchronization accuracy in the BDS-3, compared to the results of clock offset using only ground stations, the addition of 12 LEO satellites resulted in an improvement of 49% for RMS1(root mean square) and 52% for RMS2 (standard deviation), the addition of 30 LEO satellites resulted in an improvement of 66% for RMS1 and 70% for RMS2, and the addition of 60 LEO satellites resulted in an improvement of 87% for RMS1 and 90% for RMS2. The integrated orbit determination of the LEO and BDS-3 satellites constellation greatly improves the accuracy of time synchronization. In addition, we also use simulated inter-satellite link (ISL) data to perform enhanced BDS-3 satellites POD and time synchronization experiments. The experiments showed that the orbit determination accuracy of the seven sta (seven stations) and ISL scheme is comparable to that of the seven sta and LEO12 scheme, and that the time synchronization accuracy of the seven sta and ISL scheme is slightly worse. The preliminary experiments showed that the LEO satellite could enhance the orbit determination accuracy of BDS-3 and obtain a higher time synchronization accuracy.

An improved approach for rapid filter convergence of GNSS satellite real-time orbit determination

Introduction: The real-time precise satellite orbit of Global Navigation Satellite System (GNSS) usually takes a long time to converge to a stable state using the filter method. The ultra-rapid orbit products are helpful to improve convergence speed by introducing them as external constraints. Reasonably determination of stochastic model of the constraint equation from the ultra-rapid products is the key for a better performance of convergence whereas it has not been well solved.Methods: We propose to establish the stochastic model of the orbit constraint equation by analyzing the differences between the predicted part of the ultra-rapid orbit and the filter orbit after convergence. To improve the orbit accuracy during the convergence, the constant stochastic model of the constraint equation is first determined for each system by averaging the root mean square (RMS) time-series of the differences between predicted orbit from the ultra-rapid products and the SRIF orbit after convergence in different time ranges. Besides, a time-dependent stochastic model of the constraint equation is then determined by analyzing the variation of the RMS time-series. To validate the proposed method, a month of multi-constellation data collected from 80 globally distributed stations is processed using the Square Root Information Filter (SRIF) algorithm.Results: Orbit results without introducing external orbit constraints show that the convergence time in the radial direction is 13.75, 15.25 and 17.75 h for GPS, Galileo and BDS-3 satellite, respectively. For the scheme of constant stochastic model using the average RMS over 6 h, results show that there is no significant convergence phenomenon for each system in all directions. The one-dimensional (1D) RMS during the constraint period is improved by 86.5%, 84.8%, 96.8% for GPS, Galileo and BDS-3 satellites when compared to the results without introducing external orbit constraints. As for the scheme of time-dependent stochastic model, results show that the quadratic function is suitable for modeling the RMS time-series for each system, and the accuracy of results during the constraint period has a further improvement of 1.3%, 3.7% in 1D direction for GPS, BDS-3 satellites when compared to the constant stochastic model using the average RMS over 6 h. In addition, the orbit accuracy with external orbit constraint is slightly better than those without external orbit constraint after the constraint period.Discussion: The above results show that when introducing the ultra-rapid product as the external constraint, there is basically no convergence phenomenon for GNSS satellite, while the orbit accuracy for time-dependent stochastic model has further improvement than constant stochastic model. These results indicate that the proposed method can significantly improve the convergence performance without damaging the orbit accuracy after convergence, and time-dependent stochastic model is better than constant stochastic model.

Estimation of antenna phase center offsets for BDS-3 satellites with the metadata and receiver antenna calibrations

Estimation of antenna phase center offsets for BDS-3 satellites with the metadata and receiver antenna calibrations

BDS-3 new signals observable-specific phase biases estimation and PPP ambiguity resolution

Nowadays, the BDS-3 satellites transmit new signals B1c and B2a that are compatible with GPS and Galileo, which is meaningful to fully take advantage of the BDS positioning capability. However, further research and analysis are needed to investigate the precise point positioning ambiguity resolution (PPP-AR) performance of the new BDS-3 signal combination. In this manuscript, the characteristics and quality of differential code bias (DCB), inter frequency clock bias (IFCB) and uncalibrated phase delay (UPD) of BDS-3 new signals are analyzed based on 30 days observation data from 70 multi GNSS experiment (MGEX) stations. The results show that the mean value of IFCB between B1I/B3I and B1C/B2a is 1.18 cm, which indicates that the IFCB can be ignored when performing the clock errors reference conversion of BDS-3 satellites. Besides, the DCB of the new BDS-3 signals varies within 0.2 ns over 30 days, and with a difference of 0.08 ns compared to the DCB product provided by chinese academy of science (CAS). The percentage of the estimated residuals less than 0.25 cycles for new signals WL UPD and less than 0.15 cycles for new signals NL UPD are 99.76% and 97.19%, respectively. The above results demonstrate the reliability of the DCB and UPD products, which can be used to estimate the carrier phase observable specific signal bias (OSB) product for the new signals. The average positioning errors of the BDS-3 new signals static PPP-AR in the N, E and U directions is 0.50 cm, 0.43 cm and 1.62 cm respectively, with an improvement of 18.3%, 28.3% and 11.5% compared to the ambiguity float static PPP. The average positioning errors of the kinematic PPP-AR are 2.09 cm, 2.67 cm and 4.79 cm in three directions, respectively, with an improvement of 17.1%, 23.9% and 15.7% compared to the ambiguity float PPP. The convergence time of the static and kinematic PPP-AR are 26.36 min and 29.12 min, respectively.