Signal-in-space Range Error Research Articles

Real-time LEO satellite clock estimation with predicted LEO satellite orbits constrained

Low Earth Orbit (LEO) satellites can augment the traditional GNSS-based positioning, navigation and timing services, which require real-time high-precision LEO satellite clock products. As the complicated systematic effects contained in the LEO satellite clock estimates limit their high-precision mid- to long-term prediction, high-frequency LEO satellite clocks need to be estimated within a Kalman filter, resulting in a short prediction time for real-time applications. Compared to the clock estimation using Batch Least-Squares (BLS) adjustment, filter-based clock estimation experiences a lower precision. Increasing the model strength by introducing external orbital information, thus, de-correlating the orbital and clock parameters, will benefit real-time clock precision. In this contribution, reduced-dynamic LEO satellite orbits are first estimated using BLS adjustment in near real-time and predicted in the short term. The predicted orbits are then constrained during the Kalman-filter-based clock estimation process. The variance–covariance matrix of the introduced orbital errors is tested for different sets of values in the radial, along-track and cross-track directions when constraining orbits of different prediction times. One week of GPS data from the Sentinel-3B satellite in 2018 was used for validation of the proposed method. When weakly constraining high-accuracy predicted orbits within a prediction time of 20 min, i.e., with a standard deviation of the constraint set to 2–3 dm in the radial and cross-track directions, and 4–6 dm in the along-track direction, the estimated clock accuracy can be improved from about 0.27 to 0.23 ns, with a 13.4% improvement. Depending on the prediction period of the introduced orbits, the Signal-In-Space Range Error (SISRE) of the LEO satellite to Earth can also be improved, from about 9.59 cm without constraints, to 7.38–8.07 cm after constraining the predicted orbits, with an improvement of 16–23%. The improvements in the SISRE also indicate a better consistency between the real-time clock and orbital estimates.

A kinematic real-time PPP approach with estimating signal in space range errors

Since 2013, the International GNSS Service (IGS) real-time service (RTS) has been providing precise orbit and clock corrections for ten years, which enables real-time positioning at the decimeter level. High precision positioning relies heavily on accurate orbit and clock. However, constrained by the relatively short observation duration, the accuracy of real-time products are often worse than the final products. Previous studies indicate that compensating for errors in orbit and clock can improve positioning accuracy. Based on this theory, we proposed an improved positioning model, which incorporates the signal-in-space range error (SISRE) into the ionosphere-free combination observation equation and treats it as a parameter in the Kalman filter. Through the analysis of SISRE, we find that the time-varying characteristic of the parameter follows a random walk assumption. To find the optimal parameter settings of the SISRE parameters, a two-dimensional sensitivity analysis is employed, and a set of recommended values are provided. In the simulated kinematic positioning experiments, the proposed method achieves positioning accuracies of 17.3 cm, 19.6 cm, and 18.0 cm for GPS, BDS-3, and Galileo, respectively, representing a 10–20 % improvement over traditional methods. In real-time PPP experiment, the accuracy reaches 21.7 cm, indicating a 12.9 % improvement compared to traditional methods.

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%.

Evaluation of timing and time transfer with PPP using Galileo High Accuracy Service

The Galileo High Accuracy Service (HAS) provides free corrections for real-time precise point positioning (PPP) worldwide. PPP can provide high-stability time dissemination and remote clock comparisons, and consequently is widely adopted in time metrology. We collected HAS data of 134 days to present a comprehensive performance evaluation in timing and time transfer. Concerning the signal-in-space range error (SISRE), HAS corrections reach orbital/total root mean square errors (RMSE) of 3.0/6.0 cm and 4.2/13.7 cm for Galileo and GPS, respectively. The timing results show overlapping Allan deviation (OADEV) values 1 · 10-12–5 · 10-15 for Galileo and 4 · 10-12–1 · 10-14 for GPS, for intervals 30–100,000 s, and RMSE of PPP timing 1.9 ns and 1.4 ns for Galileo and GPS, respectively. For remote clock comparisons, the OADEV values are 5 · 10-13–5 · 10-15 for Galileo and 7 · 10-13–4 · 10-15 for GPS.

Performance evaluation of real-time orbit determination for LUTAN-01B satellite using broadcast earth orientation parameters and multi-GNSS combination

Real-time orbit determination (RTOD) for spacecraft using the space-borne GNSS technique needs earth orientation parameters (EOPs) for the required coordinate transformation between earth-fixed and inertial reference frames. GPS and BDS transmit EOPs in modernized navigation messages, which enables GNSS-equipped spacecraft to update EOPs onboard and improves the RTOD automaticity. However, the impact of broadcast EOP errors on RTOD has not yet been evaluated. With the GPS and BDS-3 observations collected from a Chinese low-earth orbit (LEO) mission, the LUTAN-01B satellite, we analyze the LEO RTOD performance with broadcast EOPs and GPS/BDS-3 combination for the first time. In RTOD, we parameterize the ephemeris signal-in-space range error (SISRE) to account for its slow-varying signature and to compensate for the EOP errors. Without estimating SISRE, the RTOD precision using broadcast EOPs is 70.1 cm with only GPS observations and 42.4 cm with only BDS-3, revealing degradations of 5.1 cm (7.8%) and 3.3 cm (8.4%) compared to those using the precise C04 EOPs, respectively. With SISRE estimated, the impact of broadcast EOP error is compensated and the RTOD precisions with broadcast EOPs show identical results to those with C04, reaching 36.3 cm with GPS and 25.8 cm with BDS-3. Combining GPS and BDS-3 further improves the RTOD precision to 23.9 cm. Furthermore, we show that the RTOD precision can be further improved by using GPS and BDS broadcast EOPs’ differences to correct ephemeris rotation errors. With this correction, the precision improvement of BDS-3 independent and GPS/BDS-3 combined RTOD increases significantly when BDS-3 broadcast EOPs suffer large errors due to long update intervals. During the experiment period, their maximum orbital improvements reach 10.2 and 7.7 cm, respectively, while the average improvements are both around 1.5 cm.

Signal-in-Space Range Error of the Global BeiDou Navigation Satellite System and Comparison with GPS, GLONASS, Galileo, and QZSS

Based on the standard of precise multisystem orbit and clock offset, the evaluation methods of satellite orbit, satellite clock offset and the signal-in-space range error (SISRE) from broadcast ephemeris were given in this study. The SISRE was used as a key performance index to compare the global BeiDou navigation satellite system (BDS-3) with the regional navigation satellite system (BDS-2), Global Positioning System (GPS), Galileo, Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS), and Quasi-Zenith Satellite System (QZSS). Through the combination of domestic tracking stations and inter satellite links, the orbit determination accuracy of BDS-3 has been significantly improved. The radial (R), tangential (T) and normal (N) direction orbit accuracies of BDS-3 medium Earth orbit (MEO) satellites were 0.08, 0.37, and 0.34 m, respectively, which were considerably better than those of other satellite navigation systems. The R-, T-, and N-direction orbit accuracies of BDS-3 inclined geosynchronous orbit (IGSO) satellites were 0.17, 0.59, and 0.56 m, respectively, which were better than those of QZSS IGSO satellites. The R-, T-, and N-direction orbit accuracies of BDS-3 geostationary earth orbit (GEO) satellites were 0.27, 3.42, and 1.29 m, respectively, revealing considerable accuracy advantages in the R and N directions compared with QZSS GEO, although performance in the T direction was inferior. For the clock offset, the BDS-3 MEO satellites had an accuracy of 1.83 ns, which was noticeably superior, similar, slightly inferior, and superior to those of BDS-2, GPS, Galileo, and GLONASS. The clock offset accuracies of BDS-3 IGSO and GEO satellites were 3.13 and 3.17 ns, respectively, which were slightly better than those of QZSS IGSO and GEO satellites but did not have an obvious advantage over BDS-2. The primary reason could be that the launch time of the two types of BDS-3 satellites was close to the analysis period, and therefore, the clocks may be still in the aging process. Considering only orbit error, the average SISRE (orb) of BDS-3 MEO, Galileo, GPS, and GLONASS was 0.10, 0.28, 0.57, and 1.03 m, respectively. The SISRE (orb) of BDS-3 IGSO was 0.19 m, which was marginally greater than that of BDS-3 MEO but smaller than those of the other systems and considerably smaller than that (0.90 m) of QZSS IGSO. The SISRE (orb) of BDS-3 GEO was 0.60 m, which was comparable to that of GPS (0.59 m) and considerably smaller than that of QZSS GEO (0.91 m) satellites. Considering both orbit and clock offset error, the SISRE of BDS-3 MEO satellites was 0.52 m, which was slightly greater than that of Galileo (0.40 m), marginally smaller than that of GPS (0.59 m), and considerably smaller than that of GLONASS (2.33 m). The BDS-3 IGSO satellites had a SISRE of 0.90 m, which was greater than those of GPS and Galileo but comparable to that of QZSS IGSO (0.92 m). The average SISRE of BDS-3 GEO satellites was 1.15 m, which was greater than those of GPS and Galileo and slightly greater than that of QZSS0.95 m GEO satellites, but smaller than that of GLONASS.

Analysis of Precise Orbit Determination of BDS-3 MEO and IGSO Satellites Based on Several Dual-Frequency Measurement Combinations

The Chinese BeiDou-3 navigation satellite system (BDS-3) is capable of transmitting both old B1I, B3I signals and new B1C, B2a, B2b signals. Current BDS-3 precise orbits are generally calculated using a B1I/B3I combination considering overlap with the BeiDou-2 navigation satellite system (BDS-2). In this contribution, the observation quality of BDS-3 medium earth orbit (MEO) satellites and inclined geosynchronous orbit (IGSO) satellites are analyzed based on three aspects, i.e., carrier to noise ratio (C/N0), pseudo-range noise and pseudo-range multipath (MP). The C/N0 of the MEO satellite is 2~3 dB higher than that of the IGSO satellite at the same elevation angle. Meanwhile, the order of the Root Mean Square (RMS) values of both pseudo-range noise and MP is B1I < B1C < B3I < B2a ≈ B2b. Three kinds of combinations, i.e., B1CB2a, B1CB2b and B1IB3I, are selected for the BDS-3 precise orbit determination (POD) experiment. Orbits are assessed by the orbit-only signal-in-space range error (SISRE) computed between pairs of the three kinds of combinations in this contribution, CODE and GFZ final orbits. Orbit-only SISRE assessment shows that B1CB2a/CODE, B1CB2b/CODE, B1CB2a/GFZ and B1CB2b/GFZ are at the same level with CODE/GFZ, and the orbit-only SISRE is at the level of 5 cm for MEOs and 9 cm for IGSOs, respectively. Meanwhile, B1IB3I/CODE and B1IB3I/GFZ are about 1–2 cm worse. Inter-solution comparison between B1CB2a, B1CB2b and B1IB3I also indicate that B1CB2a and B1CB2b have good consistency, while B1IB3I shows poor performance. Satellite laser ranging (SLR) residuals indicate that the mean RMS is 3–4 cm for the four BDS-3 MEOs for CODE final orbit, GFZ final orbit, B1CB2a and B1CB2b combinations, while the mean RMS value for B1IB3I combination is a few millimeters worse, at approximately 4–5 cm.

Enhanced precise orbit determination of BDS-3 MEO satellites based on ambiguity resolution with B1C/B2a dual-frequency combination

Broadcasting the multi-frequency signals is one of the outstanding advantages of BDS-3 (BeiDou Navigation Satellite System). In addition to the legacy signals B1I and B3I, we are interested in the performance of two new signals B1C and B2a. For the purpose of improving the orbit accuracy of BDS-3 backbone MEOs (Medium Earth Orbits), this study focuses on Precise Orbit Determination (POD) using B1C/B2a dual-frequency measurements. First, the performance of POD will be benefit from an increasing observation quantity and qualities. Observations from the public MGEX (Multi-GNSS Experiment) network are statistically collected, and the number of stations able to track B1C and B2a signals is analyzed. In recent years, the sustainable growth number of stations is up to more than one hundred, which brings the new chance to improve the POD accuracy based on B1C/B2a linear combination. Then, the multipath and post-fit residuals of observations are compared between B1C/B2a and B1I/B3I to investigate the observation qualities. Second, as a key strategy, the ambiguities are successfully fixed during POD processing of BDS-3 MEOs. The ambiguity fixing percentage is as high as 93.1% on average using B1C/B2a combination. Compared with float solutions, the improvements of ambiguity fixed orbits reach 36.2%, 19.9% and 36.6% on the radial, along-track and cross-track components, respectively. For the fixed solutions of B1I/B3I and B1C/B2a, it is noticed that the orbits achieve further benefits from B1C/B2a combination for 8.4%, 6.9% and 8.0% on the radial, along-track and cross-track components, respectively. Finally, the performance of B1C/B2a combination POD is validated by orbital overlapping, the orbit signal-in-space range error (SISRE) analysis, independent technology Satellite Laser Ranging (SLR) and Precise Point Positioning (PPP), respectively. SLR residuals show the radial orbital accuracy has an improvement of 8.0% for C20, C21, C29 and C30 on average when employing B1C/B2a measurements. Compared with B1I/B3I, both static and kinematic PPP based on B1C/B2a orbits indicate the improvement on the vertical component. And a faster and more stable convergence performance is also observed using B1C/B2a combination.

Signal-in-space range error and positioning accuracy of BDS-3

Being the first mixed-constellation global navigation system, the global BeiDou navigation system (BDS-3) designs new signals, the service performance of which has attracted extensive attention. In the present study, the Signal-in-space range error (SISRE) computation method for different types of navigation satellites was presented. The differential code bias (DCB) correction method for BDS-3 new signals was deduced. Based on these, analysis and evaluation were done by adopting the actual measured data after the official launching of BDS-3. The results showed that BDS-3 performed better than the regional navigation satellite system (BDS-2) in terms of SISRE. Specifically, the SISRE of the BDS-3 medium earth orbit (MEO) satellites reached 0.52 m, slightly inferior compared to 0.4 m from Galileo, marginally better than 0.59 m from GPS, and significantly better than 2.33 m from GLONASS. The BDS-3 inclined geostationary orbit (IGSO) satellites achieved the SISRE of 0.90 m, on par with that (0.92 m) of the QZSS IGSO satellites. However, the average SISRE of BDS-3 geostationary earth orbit (GEO) satellites was 1.15 m, which was marginally inferior to that of the QZSS GEO satellite (0.91 m). In terms of positioning accuracy, the new signals B1C and B2a are considered together with the transition signals B1I and B3I. The overall three-dimensional single-frequency standard point positioning (SPP) accuracy of BDS-3 B1C, B2a, B1I, and B3I gained an accuracy level better than 5 m. Moreover, the B1I signal exhibited the best positioning accuracy in the Asian-Pacific region, while the B1C signal set forth the best positioning accuracy in the other regions. Owing to the advantage in signal frequency, the dual-frequency SPP accuracy of B1C + B2a surpassed that of the transitional signal of B1I + B3I. Since there are more visible satellites in Asia–Pacific, the positioning accuracy of BDS-3 was moderately superior to that of GPS. The precise point positioning (PPP) accuracy of BDS-3 B1C + B2a or B1I + B3I converged to the order of centimeters, marginally inferior to that of the GPS L1 + L2. However, these three combinations had a similar convergence time of approximately 30 min.

Signal-in-Space and Positioning Performance of BDS Open Augmentation Service

As a typical augmentation satellite system for centimeter-level positioning, PPP (Precise Point Positioning) service based on PPP-B2b signal of China’s new generation BeiDou system (BDS-3) was released for Asia-Pacific area on July, 2020. This paper first introduces the recovery theory of PPP-B2b SSR (State Space Representation) messages and then implements a real-time PPP-B2b precise positioning terminal to decode and obtain the PPP-B2b SSR orbit, clock, and biases. On those bases, the coverage, signal-in-space, and positioning performance of PPP-B2b SSR are evaluated. The results show that PPP-B2b SSR of BDS-3 can cover the most area of 50°E-180°E, 30°S-70°N and improve signal-in-space accuracy significantly. The improvement rate on BDS clock offset can reach 77%, which far exceeds average 40% improvement on BDS orbit, while it is opposite for GPS with 80% improvement rate on orbit and 61% on clock offset. Average SISRE (signal-in-space range error) of PPP-B2b SSR is better than 10 cm. The 95% positioning results show that centimeter- to decimeter-level positioning can be achieved after a few minutes of convergence based on PPP-B2b SSR, which satisfies the BDS open service performance standard. Comparing to BDS PPP based on PPP-B2b SSR, BDS + GPS PPP can promote convergence significantly with average 40% improvement rate for 95% epochs and can further improve positioning accuracy with 30%-35% improvement rate in horizontal and 10%–15% in vertical direction.

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.

Characterization and Performance Assessment of BeiDou-2 and BeiDou-3 Satellite Group Delays

<h3>Abstract</h3> Based on one year of data, a comprehensive assessment of broadcast group delays and differential code biases (DCBs) from network solutions is presented for all open BeiDou signals. Daily DCB estimates exhibit a precision of 0.1 ns, which also places a limit on long-term variations of the satellite group delays. On the other hand, the estimated DCBs show a notable dependence on the employed receivers, which causes inconsistencies at the few-nanosecond level between BeiDou-2 and BeiDou-3 satellites. Systematic satellite-specific offsets can likewise be identified in broadcast group delay values and clock offsets. These constitute the dominant contribution of the signal-in-space range error (SISRE) budget and are a limiting factor for single point positioning and timing. Use of the modernized B1C/B2a signals is therefore recommended instead of B1I/B3I. This offers a SISRE reduction from about 0.6 m to 0.45 m and also improves the consistency of precise clock and bias products derived from heterogeneous receiver networks.

Precise point positioning with GPS and Galileo broadcast ephemerides

For more than 20 years, precise point positioning (PPP) has been a well-established technique for carrier phase-based navigation. Traditionally, it relies on precise orbit and clock products to achieve accuracies in the order of centimeters. With the modernization of legacy GNSS constellations and the introduction of new systems such as Galileo, a continued reduction in the signal-in-space range error (SISRE) can be observed. Supported by this fact, we analyze the feasibility and performance of PPP with broadcast ephemerides and observations of Galileo and GPS. Two different functional models for compensation of SISREs are assessed: process noise in the ambiguity states and the explicit estimation of a SISRE state for each channel. Tests performed with permanent reference stations show that the position can be estimated in kinematic conditions with an average three-dimensional (3D) root mean square (RMS) error of 29 cm for Galileo and 63 cm for GPS. Dual-constellation solutions can further improve the accuracy to 25 cm. Compared to standard algorithms without SISRE compensation, the proposed PPP approaches offer a 40% performance improvement for Galileo and 70% for GPS when working with broadcast ephemerides. An additional test with observations taken on a boat ride yielded 3D RMS accuracy of 39 cm for Galileo, 41 cm for GPS, and 27 cm for dual-constellation processing compared to a real-time kinematic reference solution. Compared to the use of process noise in the phase ambiguity estimation, the explicit estimation of SISRE states yields a slightly improved robustness and accuracy at the expense of increased algorithmic complexity. Overall, the test results demonstrate that the application of broadcast ephemerides in a PPP model is feasible with modern GNSS constellations and able to reach accuracies in the order of few decimeters when using proper SISRE compensation techniques.

Analysis and Assessment of BDS-2 and BDS-3 Broadcast Ephemeris: Accuracy, the Datum of Broadcast Clocks and Its Impact on Single Point Positioning

For the global ordinary users, the broadcast ephemeris plays important roles in positioning, navigation and timing (PNT) services. With the construction of a new generation of the BeiDou navigation satellite system (BDS), the development of BDS has entered the era of globalization. It is meaningful for global users to analyze and assess the BDS-2 and BDS-3 broadcast ephemeris. Therefore, the satellite orbits and clock offsets calculated by broadcast ephemeris are compared with the precise orbit and clock offset products provided by three analysis centers (i.e., Helmholtz Centre Potsdam German Research Center for Geosciences (GFZ), Wuhan University (WHU) and Shanghai Astronomical Observatory (SHA)), and the corresponding signal-in-space range error (SISRE) and the orbit-only SISRE are analyzed to assess the accuracy of BDS broadcast ephemeris. Due to the upgrade of BDS-3 satellite hardware technology and inter-satellite links payload and the development of satellite orbit determination algorithm, the accuracy of broadcast orbit and clock offsets has been greatly improved. The root mean square (RMS) of BDS-3 broadcast orbit errors is improved by 86.30%, 89.47% and 76.86%, and the standard deviation (STD) is improved by 79.41%, 77.00% and 76.78% compared with BDS-2 in the radial, along-track and cross-track directions. The corresponding RMS and STD of all BDS-3 satellite clock offsets are improved by 40.34% and 52.49% than that of BDS-2, respectively. Meanwhile, the mean RMS and STD are 1.78 m and 0.40 m for BDS-2 SISRE, 1.72 m and 0.34 m for BDS-2 orbit-only SISRE, 0.50 m and 0.14 m for BDS-3 SISRE, and 0.17 m and 0.04 m for BDS-3 orbit-only SISRE. It is noteworthy that the average broadcast-minus-precise (BMP) clock values of BDS-2 and BDS-3 are inconsistent, which can indirectly prove that the datum of broadcast clock offsets for BDS-2 and BDS-3 are inconsistent. The inconsistency of the datum of satellite clock offsets and receiver hardware delay bias between BDS-2 and BDS-3 will result in the inter-system bias (ISB) on the receiver segment. For JAVAD TRE_3 receivers, the ISB is relatively small and thus can be ignored. However, for the TRIMBLE ALLOY, SEPT POLARX5, CETC-54-GMR-4016, CETC-54-GMR-4011, GNSS-GGR and UB4B0-13478 receivers, estimating ISB can improve the positioning accuracy of single point positioning (SPP) by 20.15%, 19.81% and 12.76% in north, east and up directions, respectively.

The update of BDS-2 TGD and its impact on positioning

Timing group delay (TGD) is an important parameter that affects the positioning performance of global navigation satellite systems (GNSS). The BeiDou navigation satellite system (BDS) broadcasts TGD corrections from B3I frequency to B1I and B2I frequencies, namely TGD1 and TGD2. On July 21, 2017, BDS updated TGD values with a maximum change of more than 4 ns. In this contribution, we explain the motivation for the BDS TGD update, which is due to the systematic bias between narrowly correlated and widely correlated pseudo-ranges in BDS monitoring receivers. To investigate the impact of the updated TGD, BDS signal-in-space range error (SISRE) and user positioning performance regarding single point positioning (SPP) and precise point positioning (PPP) are analyzed. Results show that after the update of TGD, the difference between the new TGD and multi-GNSS experiment (MGEX) differential code bias (DCB) decreases from 1.38 ns to 0.29 ns on TGD1 and from 0.40 ns to 0.25 ns on TGD2. With the contribution of more accurate TGD, the systematic bias of BDS radial SISRE no longer exists, and the overall BDS SISRE also reduces from 1.33 m to 0.87 m on B1I/B2I frequency, from 1.05 m to 0.89 m on B1I frequency, from 0.92 m to 0.91 m on B2I frequency, respectively, which proves the similar precision of BDS TGD and MGEX DCB. One week of statistical results from 28 globally distributed MGEX stations shows that the SPP performance improves on non-B3I frequencies after the TGD update, with a maximum improvement of more than 22% for the B1I/B2I or B1I/B3I combination. The new TGD mainly reduces SPP positioning bias in the East component. The updated TGD also slightly improves the PPP convergence performance for the B1I/B3I combination, but mostly contributes to a more accurate estimation of the receiver clock and ambiguities.

Analysis of Galileo signal-in-space range error and positioning performance during 2015\u20132018

A long-term analysis of signal-in-space range error (SISRE) is presented for all healthy Galileo satellites, and the first pair of full operational capability satellites in wrong elliptical orbits. Both orbit and clock errors for Galileo show an obvious convergence trend over time. The annual statistical analyses show that the average root mean squares (RMSs) of SISRE for the Galileo constellation are 0.58 m (2015), 0.29 m (2016), 0.23 m (2017), and 0.22 m (2018). Currently, the accuracy of the Galileo signal-in-space is superior to that of the global positioning system (GPS) Block IIF (0.35 m). In addition, the orbit error accounts for the majority of Galileo SISRE, while the clock error accounts for approximately one-third of SISRE due to the high stability of the onboard atomic clock. Single point positioning results show that Galileo achieves an accuracy of 2–3 m, which is comparable to that of GPS despite the smaller number of satellites and worse geometry. Interestingly, the vertical accuracy of Galileo, which uses the NeQuick ionospheric model, is higher than that of GPS. Positioning with single frequency E1 and E5 show a higher precision than E5a and E5b signals. Regarding precise point positioning (PPP), the results indicate that a comparable positioning accuracy can be achieved among different stations with the current Galileo constellation. For static PPP, the RMS values of Galileo-only solutions are within 1 cm horizontally, and the vertical RMSs are mostly within 2 cm horizontally. For kinematic PPP, the RMSs of Galileo-only solutions are mostly within 4 cm horizontally and 6 cm vertically.

Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias

The accuracy of the timing group delay (TGD) transmitted in the broadcast ephemeris is an important factor that affects the service performance of a GNSS system. In this contribution, an apparent bias is found by comparing the orbit and clock difference using half-year data of the BeiDou navigation satellite system (BDS) broadcast ephemeris and precise post-processed products. The bias differs at each satellite on each frequency and shows a general systematic difference between BDS-2 and BDS-3. We attribute this to the satellite-dependent TGD bias of the BDS broadcast ephemeris, which is subsequently calibrated. Moreover, to calibrate the bias independently, a network solution strategy is proposed based on 87 globally distributed multi-GNSS experiment (MGEX) stations spanning 25 weeks. The estimated bias shows good agreement with the values observed from the orbit and clock comparison. For the validation of the bias, we compared the signal-in-space range error (SISRE) performance with and without the TGD bias correction. The results show that the SISRE of the BDS improved from 0.71, 0.81, and 1.40 m to 0.64, 0.66, and 0.64 m in the B1I, B3I, and B1I/B3I frequencies. For BDS-3, the SISRE is well within 0.50 m after the bias correction. To further validate the bias, a week’s data were collected at 97 globally distributed MGEX stations. When the TGD bias is corrected, the root mean square (RMS) of single point positioning (SPP) can be improved by 5.6, 8.4, and 21.6% in the B1I, B3I, and B1I/B3I frequencies. Meanwhile, the SISRE and SPP assessment results also indicate that the TGD bias should be corrected by each satellite rather than only corrected between BDS-2 and BDS-3.

Apparent clock and TGD biases between BDS-2 and BDS-3

With the official commencement of the BDS-3 service, the BeiDou navigation satellite system (BDS) has become a global navigation satellite system. The characteristics of the new BDS-3 satellites, including code bias, are worth investigating. An apparent pair of clock and timing group delay (TGD) biases between BDS-2 and BDS-3 are found when assessing the BDS signal-in-space range error (SISRE) with 5-months of data spanning day of year (DOY) 6 to 145 in 2019, which results from the system bias between the broadcast ephemeris and the precise products provided by Wuhan University and the Chinese Academy of Science. The biases of the broadcast ephemeris are therefore calibrated when aligning to precise products. When these biases are corrected, the overall performance of the BDS SISRE decreases from 1.41 to 0.84 m for the B1I/B3I frequency. To further investigate the biases, we analyze 68 multi-GNSS experiment stations equipped with different receivers based on raw pseudorange measurements. It is found that the clock bias seems similar at each receiver, while the TGD bias from B3I to B1I depends on receiver type, with a value of − 0.48, − 0.98, and − 1.60 m for Javad, Trimble, and Septentrio receiver, respectively. The estimated average clock and TGD biases show good agreement with that from broadcast ephemeris and precise product comparison. When the calibrated clock and TGD biases are corrected in the BDS-3 satellites, the SPP performance improves from 0.3 to 31.8%, depending on frequency and receiver type. For real-time kinematic positioning, when the clock and TGD biases are corrected, the ratio value for ambiguity resolution increases and the fixing rate also improves from 59.79 to 74.44% at B1I frequency.

Initial assessment of BDS-3 preliminary system signal-in-space range error

The basic constellation of the BeiDou global satellite navigation system (BDS-3) had been successfully completed by the end of 2018. It included 18 medium earth orbit satellites and 1 geostationary orbit satellite. An initial assessment of BDS-3 broadcast orbit and clock accuracy based on 55 days of broadcast message data is presented in this contribution. Satellite positions and clock offsets derived from broadcast ephemeris are compared with precise orbit determination orbits and clock offsets. Furthermore, the corresponding signal-in-space range error (SISRE), which is of most interest to navigation users, is computed. Thanks to the new inter-satellite link payloads on BDS-3 satellites, the statistics of age-of-data-ephemeris and age-of-data-clock demonstrate that more than 98% of ephemerides and 93% of clock parameters are updated within only one hour. Experimental results show that the 3D root mean square (RMS) of broadcast orbit errors is less than 0.6 m for the overall constellation. The broadcast orbit is also assessed by satellite laser ranging measurements, giving an RMS of 7.3 cm. The orbit-only SISRE is about 0.1 m. With respect to clock errors, the timescale differences between two clock products are eliminated to assess the accuracy of broadcast clock offsets. The standard deviation value of 0.25 m shows a good performance, but the RMS value is regrettably nearly 0.5 m due to a nonzero mean bias. RMS of BDS-3 SISRE amounts to approximately 0.5 m, which is largely attributed to clock errors. Finally, a positioning experiment is conducted to analyze the accuracy of single point positioning (SPP). With 95% confidence level, the horizontal accuracy is less than 5 m, and the vertical accuracy is close to 6 m. Considering that the nonzero mean bias in clock errors may affect the performance of SPP, we correct the nonzero mean value by a satellite-specific constant to analyze the influence of clock bias on the SPP performance. The results show that improvement in the 3D position accuracy can be up to 11%, especially in the up direction.

Initial Positioning Assessment of BDS New Satellites and New Signals

With the official announcement of open service since the end of 2018, the BeiDou navigation satellite system (BDS) has started to provide global positioning, navigation and timing (PNT) services. Thus, it is worth assessing the positioning service of new BDS satellites and signals. In this paper, we comprehensively assess the system status and the global positioning performance of BDS regarding single point positioning (SPP) and real-time kinematic (RTK) performance. Results show that the signal in space range error (SISRE) of BDS-3 satellites is superior to that of BDS-2 satellites, showing an overall accuracy of 0.71 m versus 0.97 m, which is competitive with GPS and Galileo. With the contribution of BDS-3, the number of global average visible satellites has increased from 5.1 to 10.7, which provides a mean global position dilution of precision (PDOP) value better than 6 at 99.88% and the mean availability of basic PNT performance is also improved from 35.25% to 98.84%. One week of statistical results from 54 globally distributed international GNSS service (IGS) stations show that the root mean square (RMS) of SPP accuracy is 1.1 m in horizontal and 2.2 m in vertical, which is at the same level of GPS. The new B1c and B2a signals show a smaller observation noise than B1I, and SPP performance of B1c is similar to that of B1I. However, the positioning precision is slightly worse at the B2a frequency, which may be due to the inaccurate BDS ionosphere correction. As for short baseline RTK, baseline accuracy is also improved due to the increased number of new BDS satellites.