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18 pages, 11941 KiB  
Article
Performance Evaluation and Application Field Analysis of Precise Point Positioning Based on Different Real-Time Augmentation Information
by Mengjun Wu, Le Wang, Wei Xie, Fan Yue and Bobin Cui
Remote Sens. 2024, 16(8), 1349; https://doi.org/10.3390/rs16081349 - 11 Apr 2024
Viewed by 1064
Abstract
The most commonly used real-time augmentation services in China are the International GNSS Service’s (IGS) real-time service (RTS), PPP-B2b service, and Double-Frequency Multi-Constellation (DFMC) service of the BeiDou Satellite-Based Augmentation System (BDSBAS) service. However, research on the performance evaluation, comparison, and application scope [...] Read more.
The most commonly used real-time augmentation services in China are the International GNSS Service’s (IGS) real-time service (RTS), PPP-B2b service, and Double-Frequency Multi-Constellation (DFMC) service of the BeiDou Satellite-Based Augmentation System (BDSBAS) service. However, research on the performance evaluation, comparison, and application scope of these three products is still incomplete. This article introduces methods for obtaining real-time augmentation information and real-time orbit and clock offset recovery. Based on real-time orbit and clock offset accuracy, positioning accuracy, and positioning availability, this article systematically evaluates the performance and analyzes the application fields of Centre National d’Études Spatiales (CNES), PPP-B2b, and BDSBAS augmentation information. The results of the evaluation revealed that the radial accuracy of the CNES and PPP-B2b real-time orbit product is consistent, and the Root Mean Square (RMS) is better than 5 cm. The CNES real-time orbit product can achieve centimeter-level accuracy in both along-track and cross-track components, surpassing PPP-B2b’s decimeter-level accuracy. Both services demonstrate consistent accuracy in the real-time clock offset, with PPP-B2b showing similar standard deviations (STDs) of 0.16 ns for different satellites. However, for CNES, the STD of the real-time clock offset varies, with values of 0.10 ns, 0.19 ns, and 0.60 ns, respectively, for GPS, BDS-3 Medium Earth Orbit (MEO), and BDS-3 Inclined Geosynchronous Satellite Orbit (IGSO) satellites. Centimeter-level accuracy is achieved after convergence and positioning availability exceeds 99% for CNES and PPP-B2b services. Therefore, the difference between the two services in application areas depends on the acquisition of augmentation information. However, BDSBAS, which concentrates on code observations, demonstrates inferior performance in real-time orbit, clock offset, positioning accuracy, and positioning availability when compared to the other two services. Its primary application is in the aviation and maritime domains, where there is a greater need for service integrity, continuity, and reliability. Full article
(This article belongs to the Section Engineering Remote Sensing)
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12 pages, 5013 KiB  
Communication
SISRE of BDS-3 MEO: Evolution as Well as Comparison between D1 and B-CNAV (B-CNAV1, B-CNAV2) Navigation Messages
by Zhenghua Dong and Songlin Zhang
Remote Sens. 2024, 16(3), 484; https://doi.org/10.3390/rs16030484 - 26 Jan 2024
Viewed by 1282
Abstract
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 [...] Read more.
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%. Full article
(This article belongs to the Special Issue Remote Sensing in Space Geodesy and Cartography Methods II)
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17 pages, 6333 KiB  
Article
Advancing Precise Orbit Determination and Precise Point Positioning of BDS-3 Satellites from B1IB3I to B1CB2a: Comparison and Analysis
by Chen Wang, Tengjie Luo, Shitong Chen and Pan Li
Remote Sens. 2023, 15(20), 4926; https://doi.org/10.3390/rs15204926 - 12 Oct 2023
Cited by 1 | Viewed by 1408
Abstract
The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions [...] Read more.
The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time. Full article
(This article belongs to the Special Issue Beidou/GNSS Precise Positioning and Atmospheric Modeling II)
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18 pages, 2339 KiB  
Article
Analytical Solutions and a Clock for Orbital Progress Based on Symmetry of the Ellipse
by Robert E. Criss and Anne M. Hofmeister
Symmetry 2023, 15(3), 641; https://doi.org/10.3390/sym15030641 - 3 Mar 2023
Viewed by 1604
Abstract
Kepler’s discoveries were permitted by his remarkable insight to place the Sun at the focus of an elliptical planetary orbit. This coordinate system reduces a 2-dimensional orbit to a single spatial dimension. We consider an alternative coordinate system centered on the “image focus,” [...] Read more.
Kepler’s discoveries were permitted by his remarkable insight to place the Sun at the focus of an elliptical planetary orbit. This coordinate system reduces a 2-dimensional orbit to a single spatial dimension. We consider an alternative coordinate system centered on the “image focus,” which is the symmetrical (mirror) counterpart of the “real focus” occupied by the Sun. Our analytical approach provides new purely geometric formulae and an exact relationship for the dynamic property of orbital time. In addition, considering the mirror symmetry of the ellipse leads to a simple approximation: the radial hand of an orbital clock rotates counterclockwise at a nearly steady angular velocity 2π/T about the “image focus,” where T is the orbital period. This approximation is a useful pedagogic tool and has good accuracy for orbits with low to moderate eccentricities, since the deviation from the exact result goes as eccentricity squared. Planetary comparisons are made. In particular, the angular speeds of Mercury and Jupiter are highly variable in the geocentric and heliocentric reference frames, but are nearly constant in the image focus reference frame. Our findings resolve whether the image focus is the location for observing uniform motion of an elliptical orbit, and pertain to their stability. Full article
(This article belongs to the Section Physics)
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21 pages, 7897 KiB  
Article
Analysis of BDS-3 PPP-B2b Positioning and Time Transfer Service
by Runzhi Zhang, Zaimin He, Langming Ma, Gongwei Xiao, Wei Guang, Yulong Ge, Xiangbo Zhang, Jihai Zhang, Jian Tang and Xueqing Li
Remote Sens. 2022, 14(12), 2769; https://doi.org/10.3390/rs14122769 - 9 Jun 2022
Cited by 11 | Viewed by 2755
Abstract
With the completion of the BeiDou global navigation satellite system (BDS-3), the BeiDou Navigation Satellite System Signal In Space Interface Control Document Precise Point Positioning Service Signal PPP-B2b (Version 1.0) was officially announced, and BDS-3 officially broadcast PPP-B2b correction to broadcast ephemeris through [...] Read more.
With the completion of the BeiDou global navigation satellite system (BDS-3), the BeiDou Navigation Satellite System Signal In Space Interface Control Document Precise Point Positioning Service Signal PPP-B2b (Version 1.0) was officially announced, and BDS-3 officially broadcast PPP-B2b correction to broadcast ephemeris through geostationary earth orbit (GEO) satellites to provide precise point positioning services for users in the Asia–Pacific region. This study comprehensively analyzes the application of the PPP-B2b product to time transfer and positioning. On a daily basis, the PPP-B2b positioning accuracy after convergence is calculated using the four ionosphere-free (IF) combinations in static and simulated kinematic modes: BDS B1I/B3I, BDS B1C/B2a, BDS B1I/B3I + GPS, and BDS B1C/B2a + GPS. Observations of time laboratories including the National Time Service Center of the Chinese Academy of Sciences (NTSC) and the Telecommunication Laboratories (TL) are employed to conduct zero-baseline common clock difference (CCD) time comparison experiments and long-baseline time comparison experiments using the PPP-B2b product and the GBM product. The results indicate that the PPP-B2b position accuracy in static mode by only BDS is 1.5/2.7/3.9 cm, and by GPS + BDS is within 1.5/2.5/3.5 cm in North, East, and Up directions, respectively. Regarding simulated kinematic PPP-B2b, the average root mean square (RMS) values of the position errors in the North, East, and Up directions for the combination of BDS B1I/B3I + GPS and BDS B1I/B3I are 3.4/5.8/7.6 cm and 3.8/6.6/7.8 cm, respectively. Simultaneously, the average RMS values of position errors using BDS B1C/B2a + GPS and BDS B1C/B2a are 3.6/4.9/8.1 cm and 4/6.1/8.5 cm. In the time comparison study, the results of zero-baseline CCD using the PPP-B2b product and the GBM product are within the fluctuation range of 0.1 ns, respectively. Particularly, the long-baseline time comparison difference between results employing the PPP-B2b product and the GBM product is within the range of ±0.5 ns. Full article
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18 pages, 9465 KiB  
Article
Undifferenced Kinematic Precise Orbit Determination of Swarm and GRACE-FO Satellites from GNSS Observations
by Peng Luo, Shuanggen Jin and Qiqi Shi
Sensors 2022, 22(3), 1071; https://doi.org/10.3390/s22031071 - 29 Jan 2022
Cited by 5 | Viewed by 2989
Abstract
Low Earth Orbit (LEO) satellites can be used for remote sensing and gravity field recovery, while precise orbit determination (POD) is vital for LEO satellite applications. However, there are some systematic errors when using the LEO satellite orbits released by different agencies in [...] Read more.
Low Earth Orbit (LEO) satellites can be used for remote sensing and gravity field recovery, while precise orbit determination (POD) is vital for LEO satellite applications. However, there are some systematic errors when using the LEO satellite orbits released by different agencies in multi-satellite-based applications, e.g., Swarm and Gravity Recovery and Climate Experiment-Follow-On (GRACE-FO), as different GNSS precise orbit and clock products are used as well as processing strategies and software. In this paper, we performed undifferenced kinematic PODs for Swarm and GRACE-FO satellites simultaneously over a total of 14 days by using consistent International Global Navigation Satellite System (GNSS) Service (IGS) precise orbit and clock products. The processing strategy based on an undifferenced ionosphere-free combination and a least squares method was applied for Swarm and GRACE-FO satellites. Furthermore, the quality control for the kinematic orbits was adopted to mitigate abrupt position offsets. Moreover, the accuracy of the kinematic orbits solution was evaluated by carrier phase residual analysis and Satellite Laser Ranging (SLR) observations, as well as comparison with official orbits. The results show that the kinematic orbits solution is better than 4 cm, according to the SLR validation. With quality control, the accuracy of the kinematic orbit solution is improved by 2.49 % for the Swarm-C satellite and 6.98 % for the GRACE-D satellite when compared with their precise orbits. By analyzing the accuracy of the undifferenced kinematic orbit solution, the reliability of the LEO orbit determination is presented in terms of processing strategies and quality control procedures. Full article
(This article belongs to the Section Remote Sensors)
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26 pages, 9037 KiB  
Article
Stability of CubeSat Clocks and Their Impacts on GNSS Radio Occultation
by Amir Allahvirdi-Zadeh, Joseph Awange, Ahmed El-Mowafy, Tong Ding and Kan Wang
Remote Sens. 2022, 14(2), 362; https://doi.org/10.3390/rs14020362 - 13 Jan 2022
Cited by 7 | Viewed by 3852
Abstract
Global Navigation Satellite Systems’ radio occultation (GNSS-RO) provides the upper troposphere-lower stratosphere (UTLS) vertical atmospheric profiles that are complementing radiosonde and reanalysis data. Such data are employed in the numerical weather prediction (NWP) models used to forecast global weather as well as in [...] Read more.
Global Navigation Satellite Systems’ radio occultation (GNSS-RO) provides the upper troposphere-lower stratosphere (UTLS) vertical atmospheric profiles that are complementing radiosonde and reanalysis data. Such data are employed in the numerical weather prediction (NWP) models used to forecast global weather as well as in climate change studies. Typically, GNSS-RO operates by remotely sensing the bending angles of an occulting GNSS signal measured by larger low Earth orbit (LEO) satellites. However, these satellites are faced with complexities in their design and costs. CubeSats, on the other hand, are emerging small and cheap satellites; the low prices of building them and the advancements in their components make them favorable for the GNSS-RO. In order to be compatible with GNSS-RO requirements, the clocks of the onboard receivers that are estimated through the precise orbit determination (POD) should have short-term stabilities. This is essential to correctly time tag the excess phase observations used in the derivation of the GNSS-RO UTLS atmospheric profiles. In this study, the stabilities of estimated clocks of a set of CubeSats launched for GNSS-RO in the Spire Global constellation are rigorously analysed and evaluated in comparison to the ultra-stable oscillators (USOs) onboard the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-2) satellites. Methods for improving their clock stabilities are proposed and tested. The results (i) show improvement of the estimated clocks at the level of several microseconds, which increases their short-term stabilities, (ii) indicate that the quality of the frequency oscillator plays a dominant role in CubeSats’ clock instabilities, and (iii) show that CubeSats’ derived UTLS (i.e., tropopause) atmospheric profiles are comparable to those of COSMIC-2 products and in situ radiosonde observations, which provided external validation products. Different comparisons confirm that CubeSats, even those with unstable onboard clocks, provide high-quality RO profiles, comparable to those of COSMIC-2. The proposed remedies in POD and the advancements of the COTS components, such as chip-scale atomic clocks and better onboard processing units, also present a brighter future for real-time applications that require precise orbits and stable clocks. Full article
(This article belongs to the Special Issue LEO-Augmented PNT Service)
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17 pages, 7756 KiB  
Article
Multi-GNSS Combined Orbit and Clock Solutions at iGMAS
by Wei Zhou, Hongliang Cai, Guo Chen, Wenhai Jiao, Qianqian He and Yuguo Yang
Sensors 2022, 22(2), 457; https://doi.org/10.3390/s22020457 - 8 Jan 2022
Cited by 18 | Viewed by 3242
Abstract
Global navigation services from the quad-constellation of GPS, GLONASS, BDS, and Galileo are now available. The international GNSS monitoring and assessment system (iGMAS) aims to evaluate the navigation performance of the current quad systems under a unified framework. In order to assess impact [...] Read more.
Global navigation services from the quad-constellation of GPS, GLONASS, BDS, and Galileo are now available. The international GNSS monitoring and assessment system (iGMAS) aims to evaluate the navigation performance of the current quad systems under a unified framework. In order to assess impact of orbit and clock errors on the positioning accuracy, the user range error (URE) is always taken as a metric by comparison with the precise products. Compared with the solutions from a single analysis center, the combined solutions derived from multiple analysis centers are characterized with robustness and reliability and preferred to be used as references to assess the performance of broadcast ephemerides. In this paper, the combination method of iGMAS orbit and clock products is described, and the performance of the combined solutions is evaluated by various means. There are different internal precisions of the combined orbit and clock for different constellations, which indicates that consistent weights should be assigned for individual constellations and analysis centers included in the combination. For BDS-3, Galileo, and GLONASS combined orbits of iGMAS, the root-mean-square error (RMSE) of 5 cm is achieved by satellite laser ranging (SLR) observations. Meanwhile, the SLR residuals are characterized with a linear pattern with respect to the position of the sun, which indicates that the solar radiation pressure (SRP) model adopted in precise orbit determination needs further improvement. The consistency between combined orbit and clock of quad-constellation is validated by precise point positioning (PPP), and the accuracies of simulated kinematic tests are 1.4, 1.2, and 2.9 cm for east, north, and up components, respectively. Full article
(This article belongs to the Collection Multi-GNSS Precise Positioning and Applications)
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17 pages, 4829 KiB  
Article
Precise Orbit Determination and Maneuver Assessment for TH-2 Satellites Using Spaceborne GPS and BDS2 Observations
by Houzhe Zhang, Defeng Gu, Bing Ju, Kai Shao, Bin Yi, Xiaojun Duan and Zhiyong Huang
Remote Sens. 2021, 13(24), 5002; https://doi.org/10.3390/rs13245002 - 9 Dec 2021
Cited by 10 | Viewed by 2542
Abstract
The TH-2 satellite system, including the TH-2A and TH-2B, is the first distributed interferometric synthetic aperture radar (InSAR) satellite system in China. During the in-orbit operation, the TH-2A satellite should perform three maneuvers per day to keep the formation flying geometry. We estimate [...] Read more.
The TH-2 satellite system, including the TH-2A and TH-2B, is the first distributed interferometric synthetic aperture radar (InSAR) satellite system in China. During the in-orbit operation, the TH-2A satellite should perform three maneuvers per day to keep the formation flying geometry. We estimate those maneuvers in the precise orbit determination (POD) by the GPS and BDS2 measurements on board, respectively. The residuals of the POD show that the effects caused by orbital maneuvers can be well eliminated for both the GPS and BDS2 data. The precision of the BDS2-based POD is better than 8.0 cm in the three-dimensional direction (3D) compared with the orbit derived from the GPS observations. Such a precision level of the satellite orbit satisfies the InSAR mission requirement of the TH-2. In addition, the relative error of velocity changes is employed to evaluate the maneuver estimations by the POD using the regional navigation system of BDS2. The results show that the relative error of velocity changes between the GPS- and BDS2-based POD is less than 7.0%, which indicates that the maneuver performance extracted from the regional BDS2 data is as good as that extracted from the global GPS data. In the GNSS fused processing, we found that the independent receiver clock offsets should be taken into account, since the time tag corrections for the GPS and BDS2 observations collected on the TH-2 spaceborne receivers were different. The precision of the GPS and BDS2 (GC) combined single point positioning (SPP) can be improved by 12–14% compared with the GPS-only solution when the position dilution of precision (PDOP) of GPS exceeds three. The overlap comparisons of the GC combined orbits show that the internal orbit precision of the TH-2 satellites is better than 0.7 cm. However, the improvement of the GC combined POD result is only 3–4% with respect to the GPS-only solution, which is limited to the precision of the precise orbit and clock products of BDS2 at the present stage. Full article
(This article belongs to the Section Satellite Missions for Earth and Planetary Exploration)
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15 pages, 83382 KiB  
Technical Note
Performance of Multi-GNSS Real-Time UTC(NTSC) Time and Frequency Transfer Service Using Carrier Phase Observations
by Pengfei Zhang, Rui Tu, Xiaochun Lu, Lihong Fan and Rui Zhang
Remote Sens. 2021, 13(20), 4184; https://doi.org/10.3390/rs13204184 - 19 Oct 2021
Viewed by 2145
Abstract
The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and [...] Read more.
The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and clock determinations has enabled GNSS time and frequency transfer using the CP technique to be performed in real-time mode, without any issues associated with latency. In this contribution, we preliminarily built the prototype system of real-time multi-GNSS time and frequency transfer service in National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS), which undertakes the task to generate, maintains and transmits the national standard of time and frequency UTC(NTSC). The comprehensive assessment of the availability and quality of the service system were provided. First, we assessed the multi-GNSS state space representation (SSR) correction generated in real-time multi-GNSS prototype system by combining broadcast ephemeris through a comparison with the GeoForschungsZentrum (GFZ) final products. The statistical results showed that the orbit precision in three directions was smaller than 6 cm for global positioning system (GPS) and smaller than approximately 10 cm for BeiDou satellite system (BDS). The root mean square (RMS) values of clock differences for GPS were approximately 2.74 and 6.74 ns for the GEO constellation of BDS, 3.24 ns for IGSO, and 1.39 ns for MEO. The addition, the GLObal NAvigation Satellite System (GLONASS) and Galileo satellite navigation system (Galileo) were 4.34 and 1.32 ns, respectively. In order to assess the performance of real-time multi-GNSS time and frequency transfer in a prototype system, the four real-time time transfer links, which used UTC(NTSC) as the reference, were employed to evaluate the performance by comparing with the solution determined using the GFZ final products. The RMS could reach sub-nanosecond accuracy in the two solutions, either in the SSR or GFZ solution, or in GPS, BDS, GLONASS, and Galileo. The frequency stability within 10,000 s was 3.52 × 10−12 for SSR and 3.47 × 10−12 for GFZ and GPS, 3.63 × 10−12 for SSR and 3.53 × 10−12 for GFZ for BDS, 3.57 × 10−12 for SSR and 3.52 × 10−12 for GFZ for GLONASS, and 3.56 × 10−12 for SSR and 3.48 × 10−12 for GFZ for Galileo. Full article
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32 pages, 33008 KiB  
Article
Precise Point Positioning with Almost Fully Deployed BDS-3, BDS-2, GPS, GLONASS, Galileo and QZSS Using Precise Products from Different Analysis Centers
by Xuanping Li and Lin Pan
Remote Sens. 2021, 13(19), 3905; https://doi.org/10.3390/rs13193905 - 29 Sep 2021
Cited by 7 | Viewed by 2980
Abstract
The space segment of all the five satellite systems capable of providing precise position services, namely BeiDou Navigation Satellite System (BDS) (including BDS-3 and BDS-2), Global Positioning System (GPS), GLObal NAvigation Satellite System (GLONASS), Galileo and Quasi-Zenith Satellite System (QZSS), has almost been [...] Read more.
The space segment of all the five satellite systems capable of providing precise position services, namely BeiDou Navigation Satellite System (BDS) (including BDS-3 and BDS-2), Global Positioning System (GPS), GLObal NAvigation Satellite System (GLONASS), Galileo and Quasi-Zenith Satellite System (QZSS), has almost been fully deployed at present, and the number of available satellites is approximately 136. Currently, the precise satellite orbit and clock products from the analysis centers European Space Agency (ESA), GeoForschungsZentrum Potsdam (GFZ) and Wuhan University (WHU) can support all five satellite systems. Thus, it is necessary to investigate the positioning performance of a five-system integrated precise point positioning (PPP) (i.e., GRECJ-PPP) using the precise products from different analysis centers under the current constellation status. It should be noted that this study only focuses on the long-term performance of PPP based on daily observations. The static GRECJ-PPP can provide a convergence time of 5.9–6.9/2.6–3.1/6.3–7.1 min and a positioning accuracy of 0.2–0.3/0.2–0.3/1.0–1.1 cm in east/north/up directions, respectively, while the corresponding kinematic statistics are 6.8–8.6/3.3–4.0/7.8–8.1 min and 1.0–1.1/0.8/2.5–2.6 cm in three directions, respectively. For completeness, although the real-time precise products from the analysis center Centre National d’Etudes Spatiales (CNES) do not incorporate QZSS satellites, the performance of real-time PPP with the other four satellite systems (i.e., GREC-PPP) is also analyzed. The real-time GREC-PPP can achieve a static convergence time of 8.7/5.2/11.2 min, a static positioning accuracy of 0.6/0.8/1.3 cm, a kinematic convergence time of 11.5/6.9/13.0 min, and a kinematic positioning accuracy of 1.7/1.6/3.6 cm in the three directions, respectively. For comparison, the results of single-system and dual-system PPP are also provided. In addition, the consistency of the precise products from different analysis centers is characterized. Full article
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18 pages, 13601 KiB  
Article
Accuracy Evaluation of Ionospheric Delay from Multi-Scale Reference Networks and Its Augmentation to PPP during Low Solar Activity
by Lewen Zhao, Jan Douša and Pavel Václavovic
ISPRS Int. J. Geo-Inf. 2021, 10(8), 516; https://doi.org/10.3390/ijgi10080516 - 30 Jul 2021
Cited by 5 | Viewed by 2345
Abstract
The Precise Point Positioning (PPP) with fast integer ambiguity resolution (PPP-RTK) is feasible only if the solution is augmented with precise ionospheric parameters. The vertical ionospheric delays together with the receiver hardware biases, are estimated simultaneously based on the uncombined PPP model. The [...] Read more.
The Precise Point Positioning (PPP) with fast integer ambiguity resolution (PPP-RTK) is feasible only if the solution is augmented with precise ionospheric parameters. The vertical ionospheric delays together with the receiver hardware biases, are estimated simultaneously based on the uncombined PPP model. The performance of the ionospheric delays was evaluated and applied in the PPP-RTK demonstration during the low solar activity period. The processing was supported by precise products provided by Deutsches GeoForschungsZentrum Potsdam (GFZ) and also by real-time products provided by the National Centre for Space Studies (CNES). Since GFZ provides only precise orbits and clocks, other products needed for ambiguity resolution, such as phase biases, were estimated at the Geodetic Observatory Pecny (GOP). When ambiguity parameters were resolved as integer values in the GPS-only solution, the initial convergence period was reduced from 30 and 20 min to 24 and 13 min when using CNES and GFZ/GOP products, respectively. The accuracy of ionospheric delays derived from the ambiguity fixed PPP, and the CODE global ionosphere map were then assessed. Comparison of ambiguity fixed ionospheric delay obtained at two collocated stations indicated the accuracy of 0.15 TECU for different scenarios with more than 60% improvement compared to the ambiguity float PPP. However, a daily periodic variation can be observed from the multi-day short-baseline ionospheric residuals. The accuracy of the interpolated ionospheric delay from global maps revealed a dependency on the location of the stations, ranging from 1 to 3 TECU. Precise ionospheric delays derived from the EUREF permanent network with an inter-station distance larger than 73 km were selected for ionospheric modeling at the user location. Results indicated that the PPP ambiguity resolution could be achieved within three minutes. After enlarging the inter-station distance to 209 km, ambiguity resolution could also be achieved within several minutes. Full article
(This article belongs to the Special Issue Advances in Localization and Navigation (GIS Ostrava 2021))
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15 pages, 5080 KiB  
Article
Impact of Attitude Model, Phase Wind-Up and Phase Center Variation on Precise Orbit and Clock Offset Determination of GRACE-FO and CentiSpace-1
by Junjun Yuan, Shanshi Zhou, Xiaogong Hu, Long Yang, Jianfeng Cao, Kai Li and Min Liao
Remote Sens. 2021, 13(13), 2636; https://doi.org/10.3390/rs13132636 - 5 Jul 2021
Cited by 12 | Viewed by 3045
Abstract
Currently, low Earth orbit (LEO) satellites are attracting great attention in the navigation enhancement field because of their stronger navigation signal and faster elevation variation than medium Earth orbit (MEO) satellites. To meet the need for real-time and precise positioning, navigation and timing [...] Read more.
Currently, low Earth orbit (LEO) satellites are attracting great attention in the navigation enhancement field because of their stronger navigation signal and faster elevation variation than medium Earth orbit (MEO) satellites. To meet the need for real-time and precise positioning, navigation and timing (PNT) services, the first and most difficult task is correcting errors in the process of precise LEO orbit and clock offset determination as much as possible. Launched in 29 September 2018, the CentiSpace-1 (CS01) satellite is the first experimental satellite of LEO-based navigation enhancement system constellations developed by Beijing Future Navigation Technology Co. Ltd. To analyze the impact of the attitude model, carrier phase wind-up (PWU) and phase center variation (PCV) on precise LEO orbit and clock offset in an LEO-based navigation system that needs extremely high precision, we not only select the CS01 satellite as a testing spacecraft, but also the Gravity Recovery and Climate Experiment Follow-On (GRACE-FO). First, the dual-frequency global positioning system (GPS) data are collected and the data quality is assessed by analyzing the performance of tracking GPS satellites, multipath errors and signal to noise ratio (SNR) variation. The analysis results show that the data quality of GRACE-FO is slightly better than CS01. With residual analysis and overlapping comparison, a further orbit quality improvement is possible when we further correct the errors of the attitude model, PWU and PCV in this paper. The final three-dimensional (3D) root mean square (RMS) of the overlapping orbit for GRACE-FO and CS01 is 2.08 cm and 1.72 cm, respectively. Meanwhile, errors of the attitude model, PWU and PCV can be absorbed partly in the clock offset and these errors can generate one nonnegligible effect, which can reach 0.02~0.05 ns. The experiment results indicate that processing the errors of the attitude model, PWU and PCV carefully can improve the consistency of precise LEO orbit and clock offset and raise the performance of an LEO-based navigation enhancement system. Full article
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23 pages, 5196 KiB  
Article
Comparison of Single-Site Ionospheric Delays Derived from Geometry-Free and Geometry-Based Approaches with an Analysis of Orbit and Clock Error Effects
by Sijing Liu, Qile Zhao, Gang Chen, Zhigang Hu and Nengfang Chao
Atmosphere 2021, 12(6), 703; https://doi.org/10.3390/atmos12060703 - 30 May 2021
Cited by 2 | Viewed by 2314
Abstract
The reparameterization of the geometry-free and geometry-based approaches to derive single-site ionospheric delays using Global Navigation Satellite System (GNSS) measurements is described. Kalman filtering is used to compute the geometry-free and geometry-based ionospheric delays in a forward computation procedure, aiming for a real-time [...] Read more.
The reparameterization of the geometry-free and geometry-based approaches to derive single-site ionospheric delays using Global Navigation Satellite System (GNSS) measurements is described. Kalman filtering is used to compute the geometry-free and geometry-based ionospheric delays in a forward computation procedure, aiming for a real-time application case. The numerical similarity and differences between the geometry-free and geometry-based ionospheric delays are assessed in terms of both formal and experimental errors (precision). The differences between geometry-free and geometry-based ionospheric delays are derived using two types of precise orbit and clock products. The effects of the precise orbit and clock residual errors are analyzed. The correlation coefficients between the L1 and L2 wide-lane ambiguities with the ionospheric delay are derived and analyzed. It is discovered that the geometry-based ionospheric delay is negatively correlated with geometry-based wide-lane ambiguities, while the geometry-free ionospheric delay and wide-lane ambiguities are much less correlated. A simulation analysis indicates that the impacts on geometry-based ionospheric delay estimates are partly coincided with the actual time-variant errors of the used orbit and clock in the line-of-sight direction. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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29 pages, 7472 KiB  
Article
Ultra-Low-Cost Tightly Coupled Triple-Constellation GNSS PPP/MEMS-Based INS Integration for Land Vehicular Applications
by Abdelsatar Elmezayen and Ahmed El-Rabbany
Geomatics 2021, 1(2), 258-286; https://doi.org/10.3390/geomatics1020015 - 27 May 2021
Cited by 10 | Viewed by 4460
Abstract
The rapid rise of ultra-low-cost dual-frequency GNSS chipsets and micro-electronic-mechanical-system (MEMS) inertial sensors makes it possible to develop low-cost navigation systems, which meet the requirements for many applications, including self-driving cars. This study proposes the use of a dual-frequency u-blox F9P GNSS receiver [...] Read more.
The rapid rise of ultra-low-cost dual-frequency GNSS chipsets and micro-electronic-mechanical-system (MEMS) inertial sensors makes it possible to develop low-cost navigation systems, which meet the requirements for many applications, including self-driving cars. This study proposes the use of a dual-frequency u-blox F9P GNSS receiver with xsens MTi670 industrial-grade MEMS IMU to develop an ultra-low-cost tightly coupled (TC) triple-constellation GNSS PPP/INS integrated system for precise land vehicular applications. The performance of the proposed system is assessed through comparison with three different TC GNSS PPP/INS integrated systems. The first system uses the Trimble R9s geodetic-grade receiver with the tactical-grade Stim300 IMU, the second system uses the u-blox F9P receiver with the Stim300 IMU, while the third system uses the Trimble R9s receiver with the xsens MTi670 IMU. An improved robust adaptive Kalman filter is adopted and used in this study due to its ability to reduce the effect of measurement outliers and dynamic model errors on the obtained positioning and attitude accuracy. Real-time precise ephemeris and clock products from the Centre National d’Etudes Spatials (CNES) are used to mitigate the effects of orbital and satellite clock errors. Three land vehicular field trials were carried out to assess the performance of the proposed system under both open-sky and challenging environments. It is shown that the tracking capability of the GNSS receiver is the dominant factor that limits the positioning accuracy, while the IMU grade represents the dominant factor for the attitude accuracy. The proposed TC triple-constellation GNSS PPP/INS integrated system achieves sub-meter-level positioning accuracy in both of the north and up directions, while it achieves meter-level positioning accuracy in the east direction. Sub-meter-level positioning accuracy is achieved when the Stim300 IMU is used with the u-blox F9P GNSS receiver. In contrast, decimeter-level positioning accuracy is consistently achieved through TC GNSS PPP/INS integration when a geodetic-grade GNSS receiver is used, regardless of whether a tactical- or an industrial-grade IMU is used. The root mean square (RMS) errors of the proposed system’s attitude are about 0.878°, 0.804°, and 2.905° for the pitch, roll, and azimuth angles, respectively. The RMS errors of the attitude are significantly improved to reach about 0.034°, 0.038°, and 0.280° for the pitch, roll, and azimuth angles, respectively, when a tactical-grade IMU is used, regardless of whether a geodetic- or low-cost GNSS receiver is used. Full article
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