Inter-system Bias Research Articles

Single-epoch RTK performance assessment of tightly combined BDS-2 and newly complete BDS-3

The BeiDou global navigation satellite system (BDS-3) constellation deployment has been completed on June 23, 2020, with a full constellation comprising 30 satellites. In this study, we present the performance assessment of single-epoch Real-Time Kinematic (RTK) positioning with tightly combined BeiDou regional navigation satellite system (BDS-2) and BDS-3. We first investigate whether code and phase Differential Inter-System Biases (DISBs) exist between the legacy B1I/B3I signals of BDS-3/BDS-2. It is discovered that the DISBs are in fact about zero for the baselines with the same or different receiver types at their endpoints. These results imply that BDS-3 and BDS-2 are fully interoperable and can be regarded as one constellation without additional DISBs when the legacy B1I/B3I signals are used for precise relative positioning. Then we preliminarily evaluate the single-epoch short baseline RTK performance of tightly combined BDS-2 and the newly completed BDS-3. The performance is evaluated through ambiguity resolution success rate, ambiguity dilution of precision, as well as positioning accuracy in kinematic and static modes using the datasets collected in Wuhan. Experimental results demonstrate that the current BDS-3 only solutions can deliver comparable ambiguity resolution performance and much better positioning accuracy with respect to BDS-2 only solutions. Moreover, the RTK performance is much improved with tightly combined BDS-3/BDS-2, particularly in challenging or harsh conditions. The single-frequency single-epoch tightly combined BDS-3/BDS-2 solution could deliver an ambiguity resolution success rate of 96.9% even with an elevation cut-off angle of 40°, indicating that the tightly combined BDS-3/BDS-2 could achieve superior RTK positioning performance in the Asia–Pacific region. Meanwhile, the three-dimensional (East/North/Up) positioning accuracy of BDS-3 only solution (0.52 cm/0.39 cm/2.14 cm) in the kinematic test is significantly better than that of the BDS-2 only solution (0.85 cm/1.02 cm/3.01 cm) due to the better geometry of the current BDS-3 constellation. The tightly combined BDS-3/BDS-2 solution can provide the positioning accuracy of 0.52 cm, 0.22 cm, and 1.80 cm, respectively.

Modelling and assessment of Galileo and Galileo/GPS velocity determination with stand-alone receiver

AbstractReasonable stochastic model and function model are the premise of accurate velocity determination, especially in the time-differenced carrier-phase (TDCP) method. This paper presents, first, an elevation-dependent stochastic model (ESM), and then gives a simplified and unified Galileo/GPS combined TDCP function model, where the inter-system bias (ISB) variations are analysed based on correlation coefficients and the scaled sensitivity matrix. To evaluate the performance of the proposed models, datasets collected at 10 multi-GNSS experiment (MGEX) stations and a vehicle kinematic experiment are employed. The results indicate that the ESM model can improve the accuracy of the velocity solution, especially for the Galileo/GPS combined system, in comparison with the equivalent weight ratio method. In contrast to the Galileo-only velocity solution, the Galileo/GPS combined velocity solution can bring improvements of about 1–1⋅5 mm/s, 0⋅5 mm/s and 1⋅5–2⋅5 mm/s in East, North and Up components, respectively. Compared with the traditional Galileo/GPS TDCP model, the simplified and unified model shows no obvious differences in all components in the environment with more visible satellites, but it performs better in a challenging environment with few visible satellites.

Multi-GNSS inter-system model for complex environments based on optimal state estimation

When calibrating inter-system biases (ISB), especially the fractional part of inter-system phase biases (F-ISPB), a multi-GNSS inter-system model can effectively improve positioning performance under a complex environment. Usually, the F-ISPB is estimated after fixing the intra-system ambiguities. However, this approach seems inapplicable when it is difficult to obtain intra-system ambiguities under a complex environment. A multi-dimensional particle filter (PF)-based F-ISPB estimate method has been proposed to overcome the problem. Nevertheless, the multi-dimensional PF involves a great quantity of computations. In this contribution, four state optimal estimate-based F-ISPB handling schemes are proposed: step-by-step PF, step-by-step particle swarm optimization (PSO), multi-dimensional PF, and multi-dimensional PSO-based F-ISPB estimate methods. Two baselines were selected to investigate the F-ISPB estimate performance in both open and complex environments. The results show that due to the potential of the wrong F-ISPB to bring about the maximum ratio for a long time during the initial stage, the step-by-step PF method can achieve better performance than step-by-step PSO. Besides, the two-dimensional results show that all of the F-ISPB still cannot be extracted under complex environments by multi-dimensional PSO. Furthermore, compared with step-by-step PF, the multi-dimensional PF method costs too much to obtain the right value. For example, in the two-dimensional case, the step-by-step PF searches 200 times for each epoch, while the two-dimensional PF requires 40 000 times for each epoch, so it is difficult for receivers to provide hardware support for this method. In addition, the step-by-step PF can obtain the right F-ISPB with about 100 epochs no matter what scenario. Thus, under challenging observation scenarios, a step-by-step PF method is recommended to extract the F-ISPB.

Tightly combined triple-frequency GPS and BDS for rapid wide-lane RTK positioning with consideration of carrier-phase differential inter-system bias

Multi-frequency signals have been accessible for most Global Navigation Satellite Systems . Existing studies have verified that using multi-frequency extra-wide-lane and wide-lane observations can realize decimeter, sub-decimeter and even centimeter rapid positioning. In this paper, a tightly combined wide-lane real-time kinematic positioning method using triple-frequency GPS and BDS is proposed. The differential inter-system bias is taken into consideration so that an inter-system differencing model is formed. Due to the influence of different frequencies between GPS and BDS, the double-difference wide-lane ambiguity between GPS and BDS reference satellites and the single-difference ambiguity of the BDS reference satellite are estimated jointly with the wide-lane differential inter-system bias. Thus, a full-rank model can be obtained without any external calibration. Using the stability of wide-lane differential inter-system bias in the estimation from epoch to epoch, redundant observations can be introduced, therefore the strength of the positioning model can be enhanced. Positioning performance under simulated obstructed environments is evaluated. The results show that the inter-system model can effectively improve the positioning compared with the conventional intra-system model for the severely obstructed situations.

Modeling and Analysis of BDS-2 and BDS-3 Combined Precise Time and Frequency Transfer Considering Stochastic Models of Inter-System Bias

BeiDou global navigation satellite system (BDS) began to provide positioning, navigation, and timing (PNT) services to global users officially on 31 July, 2020. BDS constellations consist of regional (BDS-2) and global navigation satellites (BDS-3). Due to the difference of modulations and characteristics for the BDS-2 and BDS-3 default civil service signals (B1I/B3I) and the increase of new signals (B1C/B2a) for BDS-3, a systemically bias exists in the receiver-end when receiving and processing BDS-2 and BDS-3 signals, which leads to the inter-system bias (ISB) between BDS-2 and BDS-3 on the receiver side. To fully utilize BDS, the BDS-2 and BDS-3 combined precise time and frequency transfer are investigated considering the effect of the ISB. Four kinds of ISB stochastic models are presented, which are ignoring ISB (ISBNO), estimating ISB as random constant (ISBCV), random walk process (ISBRW), and white noise process (ISBWN). The results demonstrate that the datum of receiver clock offsets can be unified and the ISB deduced datum confusion can be avoided by estimating the ISB. The ISBCV and ISBRW models are superior to ISBWN. For the BDS-2 and BDS-3 combined precise time and frequency transfer using ISBNO, ISBCV, ISBRW, and ISBWN, the stability of clock differences of old signals can be enhanced by 20.18%, 23.89%, 23.96%, and 11.46% over BDS-2-only, respectively. For new signals, the enhancements are −50.77%, 20.22%, 17.53%, and −3.69%, respectively. Moreover, ISBCV and ISBRW models have the better frequency transfer stability. Consequently, we recommended the optimal ISBCV or suboptimal ISBRW model for BDS-2 and BDS-3 combined precise time and frequency transfer when processing the old as well as the new signals.

Impact of Galileo-to-GPS-Time-Offset accuracy on multi-GNSS positioning and timing

The combined use of multi-GNSS systems in positioning, navigation and timing requires taking into account the variable time offset between the individual system times. This offset can be determined at the user level as an additional unknown in the position-velocity-time (PVT) solution when a sufficient number of satellites is visible. However, a known value of the inter-system bias can also be injected in the PVT algorithm. We investigate in which situation determining the Galileo-to-GPS-Time-Offset (GGTO) or fixing this parameter to a known value provides the best PVT solution and quantify the impact of a biased fixed GGTO value on the PVT solutions. Our results indicate that the recommendation on fixing or determining the GGTO, as well as the impact of a biased fixed GGTO value, heavily depends on the receiver noise level. In high visibility conditions, fixing the GGTO provides a similar or better solution than determining the GGTO if the accuracy of the fixed GGTO is better than 2 ns for a high precision receiver and 7 ns for a smartphone. Furthermore, an extreme bias of 20 ns on the fixed GGTO with respect to the true value induces an increase in the position or timing errors lower than 50% for a smartphone, while up to 150% for a high precision receiver. As a consequence, fixing the GGTO should be preferred in mass-market receivers, while determining the GGTO should be preferred in high precision receivers. The study also shows that there is no significant correlation between the superiority of determining or fixing the GGTO and either the dilution of precision or the number of visible satellites.

Interference mitigation: impact on GNSS timing

While interference mitigation techniques can significantly improve the performance of a Global Navigation Satellite System (GNSS) receiver in the presence of jamming, they can also introduce distortions, biases and delays on the GNSS measurements and on the final receiver solution. We analyze the impact of five interference mitigation techniques on the solution provided by a GNSS timing receiver that operates in a known location and under static conditions. In this configuration, the receiver only estimates its clock bias and drift, which can be potentially affected by interference mitigation. The analysis has been performed considering a multiconstellation case, including GPS L1 Coarse Acquisition (C/A), Galileo E1b/c and Beidou B1c signals. Tests were also conducted on the wideband Galileo E5b modulation. In all cases, real jammers were used to challenge GNSS signal reception. The techniques analyzed are four Robust Interference Mitigation (RIM) approaches and the Adaptive Notch Filter (ANF). From the analysis, it emerges that RIM techniques do not affect the receiver clock bias and drift. On the other hand, the ANF introduces a modulation-dependent delay on the clock bias. This delay is difficult to predict and is common to signals adopting modulations with similar spectral characteristics. In this respect, interoperable signals such as the Galileo E1b/c and Beidou B1c components are affected in the same way by the ANF, which leaves the Galileo–Beidou intersystem bias unaltered. Stability analysis has also been performed: interference mitigation does not significantly increase the short-term characteristics of the estimated clock bias and drift for low jamming levels.

Multi-GNSS real-time precise clock estimation considering the correction of inter-satellite code biases

For reasons mostly related to chip shape distortions, global navigation satellite system (GNSS) observations are corrupted by receiver-dependent biases. These are often stable in the long term, though numerically different depending on the signal frequency, satellite system and receiver manufacturer. Based on the mixed-differenced model combining undifferenced pseudorange with epoch-differenced carrier phase observations, we present a multi-GNSS real-time precise clock estimation model considering correction of inter-satellite code biases (ISCBs). Pre-estimated receiver-dependent ISCB corrections are introduced to correct the inter-receiver, inter-satellite and inter-system biases largely. Then the number of estimated parameters is reduced to a manageable level for real-time estimation. Comparisons with post-processed data show that compared to undifferenced, epoch-differenced and non-bias-corrected mixed-differenced models, the proposed bias-corrected model can greatly reduce the precise clock offset systematic biases, especially for GLONASS and BeiDou. The test results show the root mean square data reductions are improved by up to 96% for GLONASS, 78% for BeiDou and 40% for GPS and Galileo.

Analysis of differential code biases and inter-system biases for GPS and NavIC satellite constellations

<abstract> <p>Multi Global Navigation Satellite System (GNSS) plays an essential role in navigation and geodesy fields for positioning, Navigation, and Timing (PNT) services. The predominant challenge of multi-GNSS is hardware bias errors such as Differential code Bias (DCB) and Inter System Biases (ISB). The estimation of DCB and ISB are essential for analyzing the GNSS system performance to improve the positional accuracy. Navigation with the Indian Constellation (NavIC) system consists of the entire constellation of seven Geo-Stationary satellites to cater to Position Navigation Time (PNT) services over India and adjacent areas. In this paper, the relation between DCB and ISB of Global Positioning System (GPS) and NavIC systems is investigated using two ground-based NovAtel GPS and three Accords NavIC Receivers data (January to April 2019) at Koneru Lakshamaiah Education Foundation (K.L. Deemed to University), Guntur, India (16.47°N, 80.61°E). The correlation results indicate that NavIC GSO satellites are more stable than GEO satellites from DCB and ISB analysis due to low elevation angles and multipath effects. A systematic bias error is observed between NavIC and GPS satellite systems from ISB and DCB results. The current research work outcome would be beneficial for modeling GNSS ionospheric Total Electron Content (TEC) for high precision multi-constellation and multi-frequency GNSS systems.</p> </abstract>

Incorporating Inter-System Bias in Single Point Positioning Based on GPS, Galileo and BeiDou System

The increasing number of satellites provides new opportunities. In the experiment presented in this paper, the Single Point Positioning technique is tested. Data from four different receivers were used in the tests. The GPS, Galileo and BeiDou System observations were collected over a three day long observational session. The computational process was carried out using self‑made software and point positions were obtained as the result. The goal of the test was to verify the impact of the Inter‑System Bias (ISB) on the final results. For this purpose, two cases of processing data were compared: with estimating ISB and without taking into account this parameter. In the paper the formulas of the mathematical models used are presented and, in both of the considered cases, a combination of GPS, BDS and Galileo was used. The results show that in the case where the ISB was taken into account, the accuracy and precision in the positioning was much better than in the approach where the ISB was not considered. Estimating the ISB allows for more precise positioning results to be obtained for car-navigation or GIS purposes.

Assessment and Analysis of the Four-Satellite QZSS Precise Point Positioning and the Integrated Data Processing With GPS

The Quasi-Zenith Satellite System (QZSS), which serves Japan and its surrounding areas, is a regional navigation satellite system developed by Japan Aerospace Exploration Agency. The system is now in a four-satellite constellation with preliminary standalone navigation and positioning capabilities. In this paper, the performance of QZSS-only precise point positioning (PPP) in both static and kinematic modes is initially evaluated using the datasets spanning 11 days from 11 tracking stations in Asia-Pacific regions and the final precise orbit and clock products from the analysis centers GFZ and WUM. For completeness, the GPS/QZSS integrated data processing with GFZ and WUM final products as well as the L6E real-time orbit and clock corrections is also analyzed. The results indicate that the static positioning accuracy of QZSS-only PPP is approximately 4, 2 and 15 cm in the east, north and up directions, respectively, and the static convergence time of QZSS-only PPP with WUM and GFZ products can be 75.2, 44.3 and 45.6 min, and 153.5, 201.6 and 162.8 min in the three directions, respectively. As for the QZSS-only kinematic PPP solutions, the re-convergence repeatedly occurs due to limited available satellites. To achieve more reliable solutions, the inter-system bias parameter in GPS/QZSS PPP processing is recommended to be estimated as random walk process or white noise process. The improvement of post-processed GPS/QZSS PPP over GPS-only case is marginal on position accuracies, but can be several minutes on convergence time. Compared with post-processed GPS/QZSS PPP, the real-time one achieves worse position accuracies but comparable convergence time.

Long Baseline Tightly Coupled DGNSS Positioning with Ionosphere-Free Inter-System Bias Calibration

Based on the statistical stability of the inter-system bias (ISB), we propose a tightly coupled Differential Global Navigation Satellite System (DGNSS) positioning method by using ionosphere-free combination for the long baseline applications. The proposed method is compatible with the traditional Radio Beacon (RBN) base station implementation. The tightly coupled DGNSS positioning method is utilized at the long baseline rover by eliminating the effect of ionosphere delay with ionosphere-free (IF) based differential ISB calibration. The improved positioning model strength can be obtained with the proposed method when compared with the traditional loosely coupled method, particularly under the satellite-deprived environment. GNSS datasets of different baselines were collected to test the proposed method. The results of the ISB stability show that the ISB has long-term stability and needs to be calibrated when the receiver is rebooted. The positioning results show that when compared with the IF-based loosely coupled method, the IF-based tightly coupled DGNSS method based on ISB calibration can obtain better positioning performance of accuracy and continuity within 240 km baselines.

A single difference-based multi-GNSS inter-system model with consideration of inter-frequency bias and inter-system bias

By calibrating the inter-system bias (ISB), an inter-system model can be achieved to improve the performance of multi-global navigation satellite system (GNSS) positioning. A number of studies were carried out to compose inter-system models among code division multiple access (CDMA) systems. However, due to the frequency division multiple access (FDMA) technique, GLONASS phase and code observations suffer from inter-frequency phase bias (IFPB) and inter-frequency code bias (IFCB) respectively, which make it difficult to obtain the ISB among GLONASS and CDMA systems. In addition, most of the current inter-system models are unable to handle mixed frequencies. A new single difference-based uniform inter-system model suitable for all of the CDMA and FDMA frequency combinations is proposed in this study. We first utilize a particle filter approach to extract the IFPB rate. Afterwards, the multi-ISB parameters can be estimated by the proposed model simultaneously. Four short baselines containing the signals of GLONASS, GPS, BDS3, BDS2, Galileo, and QZSS are selected to validate the model. The quantitative results indicate that the IFPB rate can be extracted precisely by a particle filter within ten epochs. The inter-system phase bias valuations are sufficiently stable on a daily scale and have standard deviation near 0.01 cycles. After de-weighting the GLONASS code observations to reduce the influence of IFCB, the inter-system code bias is also stable. Furthermore, imposing the stable ISB on the multi-GNSS inter-system model can effectively improve the single-frequency real-time kinematic positioning accuracy and reliability for severely obstructed situations with only a small number of satellites observed.

A comprehensive assessment of four-satellite QZSS constellation: navigation signals, broadcast ephemeris, availability, SPP, interoperability with GPS, and ISB against GPS

In this study, a comprehensive assessment of four-satellite Quasi-Zenith Satellite System (QZSS) constellation is conducted, including the quality of navigation signals, the accuracy of broadcast ephemeris, the availability of satellite constellation, the performance of single point positioning (SPP), the interoperability with GPS, and the inter-system bias (ISB) against GPS. Regarding the signal quality, no significant difference between QZSS and GPS can be found. The signal-in-space ranging error (SISRE) of QZSS satellites is 0.59–0.62 m. The service rate of QZSS-only positioning is 69.8–77.8% in QZSS service areas. A positioning accuracy of 5.70, 3.20 and 6.99 m in east, north and up directions can be achieved for the QZSS-only SPP. After introducing QZSS observations into GPS-only SPP processing, the positioning accuracy can be slightly improved. The ISB with a short-term stability of 1.75 ns behaves like systematic biases, and thus cannot be ignored in the GPS/QZSS combined SPP.

Characterization of biases between BDS-3 and BDS-2, GPS, Galileo and GLONASS observations and their effect on precise time and frequency transfer

With the development of the Chinese BeiDou Navigation Satellite System (BDS), from a regional system BDS-2 to a global system BDS-3, more satellites can now be employed in the domain of globally precise time and frequency transfer. However, if the current BDS-3 and BDS-2, Global Positioning System (GPS), Galileo and GLObal NAvigation satellite system (GLONASS) are combined for multi-global navigation satellite system (multi-GNSS) time transfer, the characteristics of inter-system biases (ISBs) remain unclear. In this study, we analyzed the characteristics of ISBs between BDS-3 and BDS-2, GPS, Galileo and GLONASS, and revealed that their ISB series is not constant and that all the daily ISB series of the multi-GNSS show some systematic characteristics among different stations. Therefore, three stochastic models for ISBs of white noise process, random constant process and random walk process expressed as ‘White’, ‘Hour’ and ‘Walk’, respectively, were employed to assess the performance of the time and frequency transfer using the time link accuracy and frequency stability indicators. The results show that the models for the ‘Hour’ and ‘Walk’ schemes are notably better than that for the ‘White’ scheme by 10.4% and 16.8%, respectively, for the least noisy time link of WTZZ-BRCH. Furthermore, the improvements in the ‘Hour’ and ‘Walk’ schemes are 2.1% and 3.5%, respectively, for the TP01-BRCH time link, when compared with that of the ‘White’ scheme. With respect to frequency stability, the ‘Hour’ and ‘Walk’ schemes also perform better in terms of frequency stability than the ‘White’ scheme at different time intervals. Similarly, the improvements over the ‘White’ scheme are 5.05% and 4.97% for the TP01-BRCH time link and are 24.01% and 32.48% for the WTZZ-BRCH time link.

On the temperature sensitivity of multi-GNSS intra- and inter-system biases and the impact on RTK positioning

The intra-system biases, including differential code biases (DCBs) and differential phase biases (DPBs), are generally defined as the receiver-dependent hardware delays between different frequencies in a single global navigation satellite system (GNSS) constellation. Likewise, the inter-system biases (ISBs) are the differential code and phase hardware delays between different GNSSs, which are of great relevance for combined processing of multi-GNSS and multi-frequency observations. Although the two biases are usually assumed to remain unchanged for at least 1 day, they sometimes can exhibit remarkable intraday variability, likely due to environmental factors, particularly the ambient temperature. It has been proved that the possible short-term temporal variations of receiver DCBs and DPBs are directly related to ambient temperature fluctuation. We analyze whether the variability of the biases is sensitive to temperature and further identify how this affects the performance of real-time kinematic (RTK) positioning. Our numerical tests, carried out using GPS, BDS-3, Galileo and QZSS observations collected by zero and short baselines, suggest two major findings. First, we found that while ISBs associated with overlapping frequencies are fairly stable, those associated with non-overlapping frequencies can exhibit remarkable variability over a rather short period of time, driven by the changes of ambient temperature. Second, by pre-calibrating and modeling of the biases for the baselines at hand, the empirical success rates and positioning performance can be significantly improved when compared to classical and inter-system differencing, with both models assuming time-invariant receiver DCBs, DPBs and ISBs.

Maximum Ratio Principle-Based Estimation of Difference Inter-System Bias

The tight combination model improves the positioning accuracy of the Global Navigation Satellite System (GNSS) in complex environments by increasing the redundancy of observation. However, the ambiguity cannot be calculated directly because of the correlation between it and the phase difference inter-system bias (DISB) in the model. This paper proposes a method of DISB estimation based on the principle of maximum ratio. From the data analysis, for the standard deviation of code DISB, the improvement of the method can up to 0·179 m with the poor quality data. In addition, compared to the parameter combination method, the standard deviation of all the phase DISB was deceased with the method in the paper. About the phase DISB of GPS L1/Galileo E1, the standard deviation decreased from 0·014/0·022/0·009/0·051 cycles to 0·006/0·015/0·004/0·029 cycles of four baselines, which represents the improvement of 57·14/31·82/55·56/43·14%. About the phase DISB of GPS L1/BDS B1, the standard deviation decreased from 0·014/0·061/0·010/0·052 cycles to 0·002/0·005/0·009/0·004 cycles of four baselines, which represents the improvement of 85·71/91·80/10·00/92·31%.

Characterization of Inter-System Biases in GPS + BDS Precise Point Positioning

With the combination of multi-GNSS data, the precise-point positioning (PPP) technique can improve its accuracy, availability and reliability: Inter-system bias (ISB) is the non-negligible parameter in multi-GNSS PPP. To further enhance the performance of multi-GNSS PPP, it is crucial to analyze the characterization of inter system biases (ISBs) and model them properly. In this contribution, we comprehensively investigate the characterization of ISBs between global positioning system (GPS) and BeiDou navigation satellite system (BDS) in different situations. (1) We estimate ISB by using different precise products from the Center for Orbit Determination (CODE), Deutsches GeoForschungsZentrum (GFZ) and Wuhan University (WHU). The results indicate that the one-day estimates of ISB are stable when using CODE and WHU products, whereas the estimates based on GFZ products vary remarkably. As for the three-day time series of ISB, a sudden jump exists between two adjacent days, which is due to the change of satellite clock datum; (2) We investigate the ISB characterization affected by the ambient environments of the receivers. The result shows that the ISBs estimated from receivers (and antennas) with same type are still inconsistent, which indicates that the ambient environment, probably the temperature, influences the ISB characterization as well, since the receivers are in different areas; (3) We analyze the ISB characterization affected by receiver and antenna type with the same ambient environment. To ensure the same ambient environment, the ultra-short baselines were applied to investigate the ISB characterization affected by the receiver and antenna type. With the insights into ISB characterizations, we carry out combined GPS and BDS PPP with modeling the ISB as time constant, random walk process and white noise. The results suggest that the random walk process outperforms in most cases, since it strengthens the model to some extend and, at the same time, considers the variation of ISBs.

Evaluation of Inter-System Bias between BDS-2 and BDS-3 Satellites and Its Impact on Precise Point Positioning

The BeiDou navigation satellite system (BDS) currently has 41 satellites in orbits and will reach its full constellation following the launch of the last BDS satellite in June 2020 to provide navigation, positioning, and timing (PNT) services for global users. In this contribution, we investigate the characteristics of inter-system bias (ISB) between BDS-2 and BDS-3 and verify whether an additional ISB parameter should be introduced for the BDS-2 and BDS-3 precise point positioning (PPP). The results reveal that because of different clock references applied for BDS-2 and BDS-3 in the International GNSS Service (IGS) precise satellites clock products and the inconsistent code hardware delays of BDS-2 and BDS-3 for some receiver types, an ISB parameter needs to be introduced for BDS-2 and BDS-3 PPP. Further, the results show that the ISB can be regarded as a constant within a day, the value of which is closely related to the receiver type. The ISB values of the stations with the same receiver type are similar to each other, but a great difference may be presented for different receiver types, up to several meters. In addition, the impact of ISB on PPP has also been studied, which demonstrates that the performance of kinematic PPP could be improved when ISB is introduced.

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.