Search Results (14)

The BeiDou Navigation Satellite System (BDS) has developed rapidly, and the combination of BDS Phase II (BDS-2) and BDS Phase III (BDS-3) has attracted wide attention. It is found that there are code ISBs between BDS-2 and BDS-3, which may have a certain impact on the BDS-2 and BDS-3 combined positioning. This paper focuses on the performance of BDS-2/BDS-3 combined B1I single-frequency pseudorange positioning and investigates the positioning performance with and without code ISBs correction for different types of receivers, include geodetic GNSS receivers and low-cost receivers. The results show the following: (1) For geodetic GNSS receivers, the code ISBs of each receiver is about −0.3 m to −0.8 m, and the position deviation is reduced by 7% after correcting code ISBs. The code ISBs in the baseline with homogeneous receivers has a little influence on the positioning result, which can be ignored. The code ISBs in the baseline with heterogeneous receivers is about −0.5 m, and the position deviation is reduced by 4% after correcting code ISBs. (2) The code ISBs in the low-cost receivers are significantly larger than those in the geodetic GNSS receivers, and the impact on the positioning performance of the low-cost receivers is significantly greater than that on the geodetic GNSS receivers. After correcting the code ISBs, the position deviation of low-cost receivers can be reduced by around 12% for both undifferenced and differenced modes. (3) For low-cost receivers, correcting the code ISBs can increase the number of epochs successfully solved, which effectively improves the low-cost navigation and positioning performance. (4) The carrier-phase-smoothing method can effectively reduce the distribution dispersion of code ISBs and make the estimation of ISBs more accurate. The STD values of estimated code ISBs in geodetic GNSS receivers are reduced by about 40% after carrier-phase smoothing, while the corresponding values are reduced by about 7% in low-cost receivers due to their poor carrier-phase observation quality. Full article

Nowadays, BDS-3 and Galileo are still developing and have global service capabilities. This study aims to provide a comprehensive analysis of pseudorange-based/single point positioning (SPP) among GPS, BDS-3, and Galileo on a global scale. First, the positioning accuracy distribution of adding IGSO and GEO to the MEO of BDS-3 is analyzed. The results show that after adding IGSO and GEO, the accuracy of 3D in the Asia-Pacific region is significantly improved. Then, the positioning accuracy of the single-system and single-frequency SPP was validated and compared. The experimental results showed that the median RMS values for the GPS, Galileo, and BDS-3 are 1.10/1.10/1.30 m and 2.57/2.69/2.71 m in the horizontal and vertical components, respectively. For the horizontal component, the GPS and Galileo had better positioning accuracy in the middle- and high-latitude regions, while BDS-3 had better positioning accuracy in the Asia-Pacific region. For the vertical component, poorer positioning accuracy could be seen near the North Pole and the equator for all three systems. Meanwhile, in comparison with the single-system and single-frequency SPP, the contribution of adding pseudorange observations from the other satellite system and frequency band was analyzed fully. Overall, the positioning accuracy can be improved to varying degrees. Due to the observation of noise amplification, the positioning errors derived from dual-frequency SPP were much noisier than those from single-frequency SPP. Moreover, the positioning performance of single-frequency SPP with the ionosphere delay corrected with CODE final (COD), rapid (COR), 1-day predicted (C1P), and 2-day predicted (C2P) global ionospheric map (GIM) products was investigated. The results showed that SPP with COD had the best positioning accuracy, SPP with COR ranked second, while C1P and C2P were comparable and slightly worse than SPP with COR. SPP with GIM products demonstrated a better positioning accuracy than that of the single- and dual-frequency SPP. The stability and variability of the inter-system biases (ISBs) derived from the single-frequency and dual-frequency SPP were compared and analyzed, demonstrating that they were stable in a short time. The differences in ISBs among different receivers with single-frequency SPP are smaller than that of dual-frequency SPP. Full article

Several global navigation satellite systems (GNSS) broadcast overlapping frequencies to enhance interoperability, allowing tight integration with only one reference satellite for every system with the same frequency. The key to realizing tight integration is estimating and utilizing differential intersystem biases, which allows the integer characteristic of the differenced ambiguity of two satellites from different systems to be retrieved. In this study, a detailed algorithm flow of a tight integration kinematic uncalibrated phase delay (UPD)-based PPP ambiguity resolution (PPP-AR) method, which includes multiple parts, is introduced. Subsequently, PPP-AR numerical experiments were conducted in a high-shade observation environment to determine the performance. In comparison with traditional methods, our results indicate that the average success fix rate improves from 83% to 100% after using the tight integration method in an environment where only three satellites are observed for each system. Moreover, for fewer than nine satellites, the tight integration method can still consistently maintain a fixed state. However, for comparison, the traditional loose integration method could no longer be implemented. Full article

The Chinese BeiDou global satellite system (BDS-3) and regional system (BDS-2) are predicted to coexist over the next decade. Intersystem biases (ISBs) in BDS-2/BDS-3 play a key role in maintaining the consistency and continuity from the BDS-2 to BDS-3 time transfer. Here, we discuss the temporal characteristics, parameter composition, generation mechanism, and the effect of ISBs in BDS-2/BDS-3 on time and frequency transfer. The satellite orbits and clock products from three international GNSS service analysis centers, namely Wuhan University (WUM, China), GeoForschungsZentrum Potsdam (GFZ, Germany), and the Center for Orbit Determination in Europe (CODE), were employed to investigate the time-transfer stability of ISBs when BDS-2 and BDS-3 were used in combination. We analyzed the intrinsic characteristics of ISBs, the receiver types, antennas, and frequency standards. Our first results showed that ISBs are stable for different analysis center products, although the mean values of daily results differed markedly for the three analysis centers. With respect to the relationship between station attribution and ISB difference for a time link, the receiver type, antenna, and frequency standard influence the ISB differences in time and frequency transfer. The effect of three ISB stochastic models was evaluated with respect to time and frequency transfer. The “walk” and “constant” schemes were slightly superior to “noise”, with the improvement in their frequency stability being approximately 5% compared with that of “noise”. Full article

For the development of a global navigation satellite system (GNSS), the third generation of BeiDou Navigation Satellite System (BDS-3) achieved full constellation for worldwide service on 23 June 2020. The new signals, B1C and B2a of BDS-3, further enhance the compatibility and interoperability between different GNSSs. In this study, we first assessed the quality of all the signals in BDS-3/GPS/Galileo. Then, to achieve the interoperability among BDS-3/GPS/Galileo, the inter-system bias (ISB), which appears if an inter-system difference exists between two GNSSs, was estimated at overlapping frequencies. Finally, we used the estimated ISBs in real-time kinematic (RTK) positioning. The results show the higher quality of the overlapping frequency B2a/L5/E5a than B1C/L1/E1 in terms of pseudo range multipath. The ISBs are stable both in the short term for one day and in the long term for over a year, which fit a zero-mean normal distribution well when the identical type of receiver is applied. Thus, it is reasonable to ignore the ISBs in the inter-system differences. With the estimated ISBs, the inter-system double-difference RTK can be achieved, which is called a tightly combined model (TCM) RTK. Compared with the traditional intra-system double-difference RTK, which is called a loosely combined model (LCM) RTK, the TCM RTK can achieve a higher success rate (SR) in terms of ambiguity resolution and higher positioning accuracy. In addition, the higher the cutoff elevation angle set, the greater the promotion can be obtained in SR. Even with a cutoff elevation angle of 50°, the SR of TCM is over 80%. Thus, it is important to apply TCM RTK when the observation conditions are limited, such as in dense jungles or the urban canyons. Full article

The restart of the receiver will lead to the change in the non-overlapping frequency inter-system biases (ISB), which will make it difficult to apply the tightly combined RTK method of pre-calibrating ISB to the actual scene. Particle swarm optimization (PSO) algorithm can be used to estimate the fractional part of the inter-system phase bias (F-ISPB) in real time, which is not affected by the receiver restart. However, the standard PSO can easily fall into local optimum and cannot accurately estimate the value of F-ISPB. In this contribution, based on the characteristics of F-ISPB, we propose an improved PSO with adaptive search space and elite reservation strategy to estimate the F-ISPB in real time. When the value of F-ISPB is close to the boundary of the search space, the improved PSO will transform the search space so that F-ISPB will be located near the central region of the new search space, which will greatly reduce the situation of the standard PSO easily falling into local optimum. Since F-ISPB is very stable, an elite retention strategy will help us to estimate F-ISPB faster and more accurately. Three sets of short baseline static data were selected for testing. The results show that the inter-system differenced model based on the improved PSO has a higher ambiguity fixed rate and positioning accuracy than the inter-system differenced model based on the standard PSO and the classical intra-system differenced model, and the fewer the number of satellites, the more obvious the effect. Full article

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. Full article

In this study, an uncombined precise point positioning (PPP) model was established and was used for estimating fractional cycle bias (FCB) products and for achieving ambiguity resolution (AR), using GPS, BDS-2, and Galileo raw observations. The uncombined PPP model is flexible and efficient for positioning services and generating FCB. The FCBs for GPS, BDS-2, and Galileo were estimated using the uncombined PPP model with observations from the Multi-GNSS Experiment (MGEX) stations. The root mean squares (RMSs) of the float ambiguity a posteriori residuals associated with all of the three GNSS constellations, i.e., GPS, BDS-2, and Galileo, are less than 0.1 cycles for both narrow-lane (NL) and wide-lane (WL) combinations. The standard deviation (STD) of the WL combination FCB series is 0.015, 0.013, and 0.006 cycles for GPS, BDS-2, and Galileo, respectively, and the counterpart for the NL combination FCB series is 0.030 and 0.0184 cycles for GPS and Galileo, respectively. For the BDS-2 NL combination FCB series, the STD of the inclined geosynchronous orbit (IGSO) satellites is 0.0156 cycles, while the value for the medium Earth orbit (MEO) satellites is 0.073 cycles. The AR solutions produced by the uncombined multi-GNSS PPP model were evaluated from the positioning biases and the success fixing rate of ambiguity. The experimental results demonstrate that the growth of the amount of available satellites significantly improves the PPP performance. The three-dimensional (3D) positioning accuracies associated with the PPP ambiguity-fixed solutions for the respective only-GPS, GPS/BDS-2, GPS/Galileo, and GPS/BDS-2/Galileo models are 1.34, 1.19, 1.21, and 1.14 cm, respectively, and more than a 30% improvement is achieved when compared to the results related to the ambiguity-float solutions. Additionally, the convergence time based on the GPS/BDS-2/Galileo observations is only 7.5 min for the ambiguity-fixed solutions, and the results exhibit a 53% improvement in comparison to the ambiguity-float solutions. The values of convergence time based on the only-GPS observations are estimated as 22 and 10.5 min for the ambiguity-float and ambiguity-fixed solutions, respectively. Lastly, the success fixing rate of ambiguity is also dramatically raised for the multi-GNSS PPP AR. For example, the percentage is approximately 99% for the GPS/BDS-2/Galileo solution over a 10 min processing period. In addition, the inter-system bias (ISB) between GPS, BDS-2, and Galileo, which is carefully considered in the uncombined multi-GNSS PPP method, is modeled as a white noise process. The differences of the ISB series between BDS-2 and Galileo indicate that the clock datum bias of the satellite clock offset estimation accounts for the variation of the ISB series. Full article

With the development of precise positioning with multi-GNSS, the inter-system bias (ISB) has become an issue that cannot be ignored. ISB is introduced from the differences among satellite reference clocks and different receiver hardware delay biases. To analyze the characteristics of multi-GNSS ISB, the precise point positioning (PPP) with full-rank uncombined model was derived for GLONASS, BDS, GALILEO, while the GPS receiver clock was selected as the reference. In addition, a recommended ISB parameter processing model was adopted. Data of 28-days from the Multi-GNSS Experiment (MGEX) station was used to estimate and analyze the ISB parameters. Based on a statistical analysis of the acquired data, results demonstrate that: (a) The rms of multi-GNSS PPP positional bias can reach 4.6 mm, 3.4 mm and 8.5 mm for E, N and U directions, respectively, which guarantees the reliability and accuracy of the ISB parameter solution. (b) The intra-day ISB time series of the three groups is relatively stable with standard deviations less than 0.6 ns. The ISB parameters between the GALILEO and GPS system are the most stable and the standard deviation was the smallest, at about 0.37 ns, which may be related to the good signal quality of the GALILEO system. (c) The mean of the single-day solution of the ISB parameter is not stable and the amplitude of the jump can be up to 60 ns. However, each station shows a similar variation for the same ISB parameter on the same day. The situation is independent of the type of receiver and antenna; however, it may be affected by the satellite reference clock of different systems. (d) There is a clear relationship between the ISB parameters and receiver types. Full article

In this contribution, we assess, for the first time, the tightly combined real-time kinematic (RTK) with GPS, Galileo, and BDS-3 operational satellites using observations from their overlapping L1-E1-B1C/L5-E5a-B2a frequencies. First, the characteristics of B1C/B2a signals from BDS-3 operational satellites is evaluated compared to GPS/Galileo L1-E1/L5-E5a signals in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, as well as double-differenced carrier phase and code residuals using data collected with scientific geodetic iGMAS and commercial M300Pro receivers. It’s demonstrated that the observational quality of B1C/B2a signals from BDS-3 operational satellites is comparable to that of GPS/Galileo L1-E1/L5-E5a signals. Then, we investigate the size and stability of phase and code differential inter-system bias (ISB) between BDS-3/GPS/Galileo B1C-L1-E1/B2a-L5-E5a signals using short baseline data collected with both identical and different receiver types. It is verified that the BDS-3/GPS/Galileo ISBs are indeed close to zero when identical type of receivers are used at both ends of a baseline. Moreover, they are generally present and stable in the time domain for baselines with different receiver types, which can be easily calibrated and corrected in advance. Finally, we present initial assessment of single-epoch tightly combined BDS-3/GPS/Galileo RTK with single-frequency and dual-frequency observations using a formal and empirical analysis, consisting of ambiguity dilution of precision (ADOP), ratio values, the empirical ambiguity resolution success rate, and the positioning accuracy. Experimental results demonstrate that the tightly combined model can deliver much lower ADOP and higher ratio values with respect to the classical loosely combined model whether for GPS/BDS-3 or GPS/Galileo/BDS-3 solutions. The positioning accuracy and the empirical ambiguity resolution success rate are remarkably improved as well, which could reach up to approximately 10%∼60% under poor observational conditions. Full article

Multi- system and multi-frequency are two key factors that determine the performance of precise point positioning. Both multi-frequency and multi-system lead to new biases, which are not solved systematically. This paper concentrates on mathematical models of biases, influences of these biases, and positioning performance analysis of different observation models. The biases comprise the inter-frequency clock bias in multi-frequency and the inter-system clock bias in multi-system. The former is the residual differential code biases (DCBs) from receiver clock and satellite clock and usually occurs at the third frequency, the latter is the deviation of the receiver clock errors in different systems. Unified mathematical models of the biases are presented by analyzing the general formula of observation equations. The influences of these biases are validated by experiments with corresponding observation models. Subsequently, the experiments, which are based on the data at five globally distributed stations in Multi-Global Navigation Satellite System (GNSS) Experiment (MGEX) on day of year 100, 2018, assess positioning performance of different observation models with combination of frequencies (dual-frequency or triple- frequency) and systems (BeiDou Navigation Satellite System (BDS) or Global Positioning System (GPS)). The results show that the performances of triple-frequency models are almost as the same level as the dual-frequency models. They provide scientific support for the triple-frequency ambiguity-fixed solution which has a better convergence characteristic than dual-frequency ambiguity-fixed solution. Furthermore, the biases are expressed as an unified form that gives an important and valuable reference for future research on multi-frequency and multi-system precise point positioning. Full article

An inter-system differencing model between two Global Navigation Satellite Systems (GNSS) enables only one reference satellite for all observations. If the associated differential inter-system biases (DISBs) are priori known, double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can also be fixed to integers. This can provide more redundancies for the observation model, and thus will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning. However, for Global Positioning System (GPS) and the regional BeiDou Navigation Satellite System (BDS-2), there are no overlapping frequencies. Tight combination of GPS and BDS needs to process not only the DISBs but also the single-difference ambiguity of the reference satellite, which is caused by the influence of different frequencies. In this paper, we propose a tightly combined dual-frequency GPS and BDS RTK positioning model for medium baselines with real-time estimation of DISBs. The stability of the pseudorange and phase DISBs is analyzed firstly using several baselines with the same or different receiver types. The dual-frequency ionosphere-free model with parameterization of GPS-BDS DISBs is proposed, where the single-difference ambiguity is estimated jointly with the phase DISB parameter from epoch to epoch. The performance of combined GPS and BDS RTK positioning for medium baselines is evaluated with simulated obstructed environments. Experimental results show that with the inter-system differencing model, the accuracy and reliability of RTK positioning can be effectively improved, especially for the obstructed environments with a small number of satellites available. Full article

Precise Point Positioning (PPP) technique enables stand-alone receivers to obtain cm-level positioning accuracy. Observations from multi-GNSS systems can augment users with improved positioning accuracy, reliability and availability. In this paper, we present and evaluate the GPS/BDS combined PPP models, including the traditional model and a simplified model, where the inter-system bias (ISB) is treated in different way. To evaluate the performance of combined GPS/BDS PPP, kinematic and static PPP positions are compared to the IGS daily estimates, where 1 month GPS/BDS data of 11 IGS Multi-GNSS Experiment (MGEX) stations are used. The results indicate apparent improvement of GPS/BDS combined PPP solutions in both static and kinematic cases, where much smaller standard deviations are presented in the magnitude distribution of coordinates RMS statistics. Comparisons between the traditional and simplified combined PPP models show no difference in coordinate estimations, and the inter system biases between the GPS/BDS system are assimilated into receiver clock, ambiguities and pseudo-range residuals accordingly. Full article

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations from three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. Combining measurements from different GNSS systems introduces additional biases, including inter-system bias and hardware delays, which require rigorous modelling. Our model is based on the un-differenced and between-satellite single-difference (BSSD) linear combinations. BSSD linear combination cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. Forming the BSSD linear combination requires a reference satellite, which can be selected from any of the GPS, Galileo, and BeiDou systems. In this paper three BSSD scenarios are tested; each considers a reference satellite from a different GNSS constellation. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets collected at four different IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) network are used to correct the GPS, Galileo, and BeiDou measurements in the post-processing PPP mode. A real-time PPP solution is also obtained, which is referred to as RT-PPP in the sequel, through the use of the IGS real-time service (RTS) for satellite orbit and clock corrections. However, only GPS and Galileo observations are used for the RT-PPP solution, as the RTS-IGS satellite products are not presently available for BeiDou system. All post-processed and real-time PPP solutions are compared with the traditional un-differenced GPS-only counterparts. It is shown that combining the GPS, Galileo, and BeiDou observations in the post-processing mode improves the PPP convergence time by 25% compared with the GPS-only counterpart, regardless of the linear combination used. The use of BSSD linear combination improves the precision of the estimated positioning parameters by about 25% in comparison with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for the BSSD model, which represents about 50% reduction, in comparison with the GPS-only PPP solution. The GNSS RT-PPP solution, on the other hand, shows a similar convergence time and precision to the GPS-only counterpart. Full article