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Integer Ambiguity Resolution (IAR) can significantly improve the accuracy of GNSS Precise Orbit Determination (POD). Traditionally, the IAR in POD is achieved at the Double Differenced (DD) level. In this contribution, we develop an Un-Differenced (UD) IAR method for Global Positioning System (GPS)+ BeiDou Navigation Satellite System (BDS) + Galileo navigation satellite system (Galileo)+ Global'naya Navigatsionnaya Sputnikovaya Sistema (GLONASS) quad-system POD by calibrating UD ambiguities in the raw carrier phase and generating the so-called carrier range. Based on this method, we generate the UD ambiguity-fixed orbit and clock products for the Wuhan Innovation Application Center (IAC) of the International GNSS Monitoring and Assessment System (iGMAS). One-year observations in 2020 from 150 stations are employed to investigate performance of orbit and clock products. Notably, the UD Ambiguity Resolution (AR) yields more resolved integer ambiguities than the traditional DD AR, scaling up to 9%, attributable to its avoidance of station baseline formation. Benefiting from the removal of ambiguity parameters, the computational efficiency of parameter estimation undergoes a substantial 70% improvement. Compared with the float solution, the orbit consistencies of UD AR solution achieve the accuracy of 1.9, 5.2, 2.8, 2.1, and 2.7 cm for GPS, BeiDou-2 Navigation Satellite System (BDS-2), BeiDou-3 Navigation Satellite System (BDS-3), Galileo, and GLONASS satellites respectively, reflecting enhancements of 40%, 24%, 54%, 34%, and 42%. Moreover, the standard deviations of Satellite Laser Ranging (SLR) residuals are spanning 2.5–3.5 cm, underscoring a comparable accuracy to the DD AR solution, with discrepancies below 5%. A notable advantage of UD AR lies in its capability to produce the Integer Recovered Clock (IRC), facilitating Precise Point Positioning (PPP) AR without requiring additional Uncalibrated Phase Delay (UPD) products. To assess the performance of quad-system kinematic PPP based on IRC, a network comprising 120 stations is utilized. In comparison to the float solution, the IRC-based PPP AR accelerates convergence time by 31% and enhance positioning accuracy in the east component by 54%. [ABSTRACT FROM AUTHOR]

In recent years, the large Low Earth Orbit (LEO) constellations have become a hot topic due to their great potential to improve the Global Navigation Satellite Systems (GNSS) positioning performance. One of the important focus is how to obtain the accurate and reliable orbits for these constellations with dozens of LEO satellites. The GNSS-based Precise Orbit Determination (POD) will be exclusively performed to achieve this goal, where the Integer Ambiguity Resolution (IAR) plays a key role in acquiring high-quality orbits. In this study, we present a comprehensive analysis of the benefit of the single-receiver IAR in LEO POD and discuss its implication for the future LEO constellations. We perform ambiguity-fixed LEO POD for four typical missions, including Gravity Recovery and Climate Experiment (GRACE) Follow-On (GRACE-FO), Swarm, Jason-3 and Sentinel-3, using the Uncalibrated Phase Delay (UPD) products generated by our GREAT (GNSS+ REsearch, Application and Teaching) software. The results show that the ambiguity fixing processing can significantly improve the accuracy of LEO orbits. There are negligible differences between our UPD-based ambiguity-fixed orbits and those based on the Observable Signal Bias (OSB) and Integer Recovery Clock (IRC) products, indicating the good-quality of UPD products we generated. Compared to the float solution, the fixed solution presents a better consistency with the external precise science orbits and the largest accuracy improvement of 5 mm is achieved for GRACE-FO satellites. Meanwhile, the benefit can be observed in laser ranging residuals as well, with a Standard Deviation (STD) reduction of 3–4 mm on average for the fixed solutions. Apart from the absolute orbits, the relative accuracy of the space baseline is also improved by 20–30% in the fixed solutions. The result demonstrates the superior performance of the ambiguity-fixed LEO POD, which appears as a particularly promising technique for POD of future LEO constellations. [ABSTRACT FROM AUTHOR]

In recent years, numerous low earth orbit (LEO) satellites have been launched for different scientific tasks such as the Earth's magnetic field, gravity recovering and ocean altimetry. The LEO satellites can cover the ocean area and are less affected by atmospheric delays and multipath errors, which provides new opportunities for calibrating the phase biases of the Global Navigation Satellite System (GNSS). In this contribution, we propose an alternative approach for uncalibrated phase delay (UPD) estimation by making full use of onboard observations of LEO satellites. Stable wide-lane (WL) and narrow-lane (NL) UPDs can be obtained from spaceborne GNSS observations and agree well with the UPD products derived from 106 IGS stations. To further verify the feasibility of the proposed method for UPD estimation, zero-difference (ZD) ambiguity resolution (AR) for precise point positioning (PPP) and LEO precise orbit determination (POD) are implemented. After applying the LEO-based UPDs, the averaged convergence time for PPP AR can be reduced to 15.2 min, with an improvement of 24% compared to float solutions. As for LEO AR, the fixing rates of WL and NL ambiguities exceed 98 and 92%, respectively. The accuracies of ambiguity-fixed orbits are validated by comparing with external satellite laser ranging (SLR) and K-band ranging (KBR) observations. Compared to float solutions, the standard deviations (STDs) of SLR residuals can be reduced by 8 ~ 43%, and the KBR residuals of 3.75 mm can be achieved for fixed solutions using LEO-based UPDs, with an improvement of 60%. Although the current UPD results derived from LEO satellites are slightly worse than those of ground-based UPD, it is anticipated that the performance of LEO-based UPD can be further improved in the near future with the rapidly increasing number of LEO satellites and the continuous refinements of the POD method. [ABSTRACT FROM AUTHOR]

During 2016–2018, satellite metadata/information including antenna parameters, attitude laws and physical characteristics such as mass, dimensions and optical properties were released for Galileo and QZSS (except for the QZS-1 optical coefficients). These metadata are critical for improving the accuracy of precise orbit and clock determination. In this contribution, we evaluate the benefits of these new metadata to orbit and clock in three aspects: the phase center offsets and variations (PCO and PCV), the yaw-attitude model and solar radiation pressure (SRP) model. The updating of Galileo PCO and PCV corrections, from the values estimated by Deutsches Zentrum für Luft- und Raumfahrt and Deutsches GeoForschungsZentrum to the chamber calibrations disclosed by new metadata, has only a slight influence on Galileo orbits, with overlap differences within only 1 mm. By modeling the yaw attitude of Galileo satellites and QZS-2 spacecraft (SVN J002) according to new published attitude laws, the residuals of ionosphere-free carrier-phase combinations can be obviously decreased in yaw maneuver seasons. With the new attitude models, the 3D overlap RMS in eclipse seasons can be decreased from 12.3 cm, 14.7 cm, 16.8 cm and 34.7 cm to 11.7 cm, 13.4 cm, 15.8 cm and 32.9 cm for Galileo In-Orbit Validation (IOV), Full Operational Capability (FOC), FOC in elliptical orbits (FOCe) and QZS-2 satellites, respectively. By applying the a priori box-wing SRP model with new satellite dimensions and optical coefficients, the 3D overlap RMS are 5.3 cm, 6.2 cm, 5.3 cm and 16.6 cm for Galileo IOV, FOCe, FOC and QZS-2 satellites, with improvements of 11.0%, 14.7%, 14.0% and 13.8% when compared with the updated Extended CODE Orbit Model (ECOM2). The satellite laser ranging (SLR) validation reveals that the a priori box-wing model has smaller mean biases of − 0.4 cm, − 0.4 cm and 0.6 cm for Galileo FOCe, FOC and QZS-2 satellites, while a slightly larger mean bias of − 1.0 cm is observed for Galileo IOV satellites. Moreover, the SLR residual dependencies of Galileo IOV and FOC satellites on the elongation angle almost vanish when the a priori box-wing SRP model is applied. As for satellite clocks, a visible bump appears in the Modified Allan deviation at integration time of 20,000 s for Galileo Passive Hydrogen Maser with ECOM2, while it almost vanishes when the a priori box-wing SRP model and new metadata are applied. The standard deviations of clock overlap can also be significantly reduced by using new metadata. [ABSTRACT FROM AUTHOR]

In this contribution, we focus on the precise orbit determination (POD) for BDS3 experimental satellites with the international GNSS Monitoring and Assessment System (iGMAS) and Multi-GNSS Experiment (MGEX) tracking networks. The datasets of DOY (day of year) 001-230 in 2017 are analyzed with different processing strategies. By comparing receiver clock biases and receiver B1I-B3I DCBs, it is confirmed that there is no obvious systematic bias between experimental BDS3 and BDS2 in the common B1I and B3I signals, which indicates that experimental BDS3 and BDS2 can be treated as one system when performing combined POD. With iGMAS-only BDS3 stations, the 24-h overlap RMS of BDS3+BDS2+GPS combined POD is 24.3, 16.1 and 8.4 cm in along-track, cross-track and radial components, which is better than BDS3-only POD by 80-90% and better than BDS3+BDS2 combined POD by about 10%. With more stations (totally 20 stations from both iGMAS and MGEX) and the proper ambiguity resolution strategy (GEO ambiguities are float and BDS3 ambiguities are fixed), the performance of BDS3 POD can be further improved to 14.6, 7.9 and 3.7 cm, respectively, in along-track, cross-track and radial components, which is comparable to the performance of BDS2 POD. The 230-day SLR validations of C32, C33 and C34 show that the mean differences of -3.48, 7.81 and 8.19 cm can be achieved, while the STD is 13.35, 13.46 and 13.11 cm, respectively. Furthermore, the 230-day overlap comparisons reveal that C31 most likely still uses an orbit-normal mode and exhibits similar orbit modeling problems in orbit-normal periods as found in most of the BDS2 satellites. [ABSTRACT FROM AUTHOR]

The rapid growing number of earth observation missions and commercial low-earth-orbit (LEO) constellation plans have provided a strong motivation to get accurate LEO satellite position and velocity information in real time. This paper is devoted to improve the real-time kinematic LEO orbits through fixing the zero-differenced (ZD) ambiguities of onboard Global Navigation Satellite System (GNSS) phase observations. In the proposed method, the real-time uncalibrated phase delays (UPDs) are estimated epoch-by-epoch via a global-distributed network to support the ZD ambiguity resolution (AR) for LEO satellites. By separating the UPDs, the ambiguities of onboard ZD GPS phase measurements recover their integer nature. Then, wide-lane (WL) and narrow-lane (NL) AR are performed epoch-by-epoch and the real-time ambiguity–fixed orbits are thus obtained. To validate the proposed method, a real-time kinematic precise orbit determination (POD), for both Sentinel-3A and Swarm-A satellites, was carried out with ambiguity–fixed and ambiguity–float solutions, respectively. The ambiguity fixing results indicate that, for both Sentinel-3A and Swarm-A, over 90% ZD ambiguities could be properly fixed with the time to first fix (TTFF) around 25–30 min. For the assessment of LEO orbits, the differences with post-processed reduced dynamic orbits and satellite laser ranging (SLR) residuals are investigated. Compared with the ambiguity–float solution, the 3D orbit difference root mean square (RMS) values reduce from 7.15 to 5.23 cm for Sentinel-3A, and from 5.29 to 4.01 cm for Swarm-A with the help of ZD AR. The SLR residuals also show notable improvements for an ambiguity–fixed solution; the standard deviation values of Sentinel-3A and Swarm-A are 4.01 and 2.78 cm, with improvements of over 20% compared with the ambiguity–float solution. In addition, the phase residuals of ambiguity–fixed solution are 0.5–1.0 mm larger than those of the ambiguity–float solution; the possible reason is that the ambiguity fixing separate integer ambiguities from unmodeled errors used to be absorbed in float ambiguities. [ABSTRACT FROM AUTHOR]

• An efficient parallel approach for multi-GNSS real-time precise orbit determination is proposed. • The proposed method improves computational efficiency by 70% compared with the traditional method. • Quad-system real-time POD with 90 stations can be completed within 5 s. Real-time Global Navigation Satellite System (GNSS) precise orbits are essential prerequisites for real-time GNSS-based applications. However, the high computational demands of filter-based real-time multi-GNSS POD methods present a significant challenge for practical utilization. This study introduces an efficient parallel approach for quad-constellation GNSS real-time POD using the square root information filter (SRIF). In the proposed approach, parallel QR factorization algorithms are implemented to expedite parameter estimation based on SRIF, while parallel processing model is designed for real-time POD to enhance its computational efficiency. Validation experiments show that the computation time for measurement and time update in SRIF can be reduced by 78.5% and 80.5%, respectively, compared to the traditional serial approach. Additionally, parallel computing improves the computational efficiency of GNSS processing algorithms in real-time POD by approximately 70%. The proposed approach enables the completion of quad-system real-time POD solutions with 90 stations within 5 s, representing an impressive 73.0% reduction. [ABSTRACT FROM AUTHOR]

The Japanese Quasi-Zenith Satellite System (QZSS) has become a four-satellite constellationin 2017, including three Inclined Geosynchronous Orbit (IGSO) satellites and oneGeostationary Earth Orbit (GEO) satellite. In this study, refined solar radiationpressure (SRP) models are proposed for QZSS IGSO and GEO satellites, by taking theL-band antenna and the communication antenna into consideration, respectively. Theperformances of the new proposed models in precise orbit and clock determination areevaluated in comparison with the Empirical CODE Orbit Model (ECOM), extendedECOM (ECOM2) as well as the a priori SRP model based on generic box-wingassumption. Each IGSO satellite has a large L-band antenna cover on the PZ (Earth direction) plane.The shape of the antenna can be assumed as the combination of a circular cylinder and acircular truncated cone. Therefore, the "box-wing-hat" acceleration can be calculated andused as the a priori values to augment ECOM model. With the a priori box-wing-hat model,the stability of estimated SRP parameters can be significantly improved when compared toECOM, ECOM2 and the a priori box-wing model. As of QZSS satellite laser ranging (SLR)residuals, the a priori box-wing-hat model achieves the smallest STD values of 5.6 cm, 5.5cm and 5.3 cm for QZS-1, QZS-2 and QZS-4, respectively, compared with theother three SRP models. The a priori box-wing-hat model also reduces the SLRresidual dependencies on the orbital angle as well as the Sun elongation angle.Furthermore, the a priori box-wing-hat model has the smallest 3-dimensional 24-horbit overlapping RMS of 12.4 cm, with improvements of 80.6 %, 24.7 % and19.6 % when compared with ECOM, ECOM2 and the a priori box-wing model,respectively. Similarly, box-wing-hat model can also improve the clock accuracy by55.8 %, 34.9 % and 1.2 % compared with ECOM, ECOM2 and box-wing model,respectively. The GEO satellite QZS-3 carries a large communication antenna (CA) on the +X panel,pointing to the Earth direction. Since the area of the CA (9.1 m2) is even larger than the +Zand –Z panels, an acceleration of almost the same magnitude could be generated when theCA is illuminated. Besides, it is worth noting that there will be times when the shadow of theCA will be projected on the +X panel, hence the change of illuminated area of +X panelshould be taken into consideration. By modeling the two contributions above, theSLR residuals can be slightly reduced compared with the other three SRP models. [ABSTRACT FROM AUTHOR]