scholarly journals General relativistic effects acting on the orbits of Galileo satellites

2021 ◽  
Vol 133 (4) ◽  
Author(s):  
K. Sośnica ◽  
G. Bury ◽  
R. Zajdel ◽  
K. Kazmierski ◽  
J. Ventura-Traveset ◽  
...  
Keyword(s):  
General Relativity ◽  
Orbit Determination ◽  
Final Height ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
De Sitter ◽  
Circular Orbits ◽  
Precise Orbit ◽  
Artificial Earth Satellites ◽  
Artificial Earth

AbstractThe first pair of satellites belonging to the European Global Navigation Satellite System (GNSS)—Galileo—has been accidentally launched into highly eccentric, instead of circular, orbits. The final height of these two satellites varies between 17,180 and 26,020 km, making these satellites very suitable for the verification of the effects emerging from general relativity. We employ the post-Newtonian parameterization (PPN) for describing the perturbations acting on Keplerian orbit parameters of artificial Earth satellites caused by the Schwarzschild, Lense–Thirring, and de Sitter general relativity effects. The values emerging from PPN numerical simulations are compared with the approximations based on the Gaussian perturbations for the temporal variations of the Keplerian elements of Galileo satellites in nominal, near-circular orbits, as well as in the highly elliptical orbits. We discuss what kinds of perturbations are detectable using the current accuracy of precise orbit determination of artificial Earth satellites, including the expected secular and periodic variations, as well as the constant offsets of Keplerian parameters. We found that not only secular but also periodic variations of orbit parameters caused by general relativity effects exceed the value of 1 cm within 24 h; thus, they should be fully detectable using the current GNSS precise orbit determination methods. Many of the 1-PPN effects are detectable using the Galileo satellite system, but the Lense–Thirring effect is not.

General Relativistic effects acting on GNSS orbits with a focus on Galileo satellites launched into incorrect orbital planes

2021 ◽  
Author(s):  
Krzysztof Sośnica ◽  
Grzegorz Bury ◽  
Radosław Zajdel ◽  
Kamil Kaźmierski ◽  
Javier Ventura-Traveset ◽  
...  
Keyword(s):  
General Relativity ◽  
Orbit Determination ◽  
Precise Orbit Determination ◽  
Major Axis ◽  
Satellite Orbits ◽  
De Sitter ◽  
Semi Major Axis ◽  
Precise Orbit ◽  
Eccentric Orbits ◽  
Galileo Satellite

<p>Three orbital effects emerging from general relativity are typically considered for Earth-orbiting satellites: the Schwarzschild effect, Lense-Thirring effect or frame-dragging, and the de Sitter or geodetic precession effect. For circular orbits and short satellite orbital arcs, the dominating Schwarzschild effect is difficult to determine, because it causes a constant radial acceleration which can be absorbed by a small modification in the gravitational constant GM term or a constant offset in the estimated semi-major axis of a satellite orbit. To separate the effects caused by the Schwarzschild effect from other orbital effects, especially those emerging from orbit modeling issues of non-gravitational accelerations, eccentric satellite orbits should be employed.</p><p>The first pair of satellites belonging to the Galileo satellite system was accidentally launched into non-circular orbits with height variations between from 17,180 km for the perigee to 26,020 km for the apogee. The eccentric orbits introduced new opportunities for the verification of the effects emerging from general relativity when employing the Galileo constellation. Galileo satellites are equipped with two techniques for precise orbit determination: microwave GNSS antennas and SLR retroreflectors which allow for deriving their orbits of superior quality.</p><p>In this study, we discuss effects in GNSS orbits emerging from general relativity. We concentrate on those effects that exceed the value of 1 mm over 1 day, thus are of fundamental importance for precise orbit determination in satellite geodesy and precise high-quality products of the International GNSS Service. We show that the semi-major axis of Galileo satellites in eccentric orbits varies between -29 mm in perigee to -9 mm in apogee due to the Schwarzschild term. For GNSS geostationary satellites with the inclination angle close to zero, the omission of the de Sitter effect may cause an error of the determination of the right ascension of ascending node exceeding the value of 1 meter after 1 day. Finally, we discuss the suitability of using GPS, GLONASS, and Galileo satellite orbits to determine the values of the Post-Newtonian Parameters γ and β and all limitations related to the observability of these parameters at GNSS heights and systematic errors emerging from non-gravitation orbit perturbations.</p>

scholarly journals LEO-Constellation-Augmented BDS Precise Orbit Determination Considering Spaceborne Observational Errors

2021 ◽  
Vol 13 (16) ◽  
pp. 3189
Author(s):  
Min Li ◽  
Tianhe Xu ◽  
Haibo Ge ◽  
Meiqian Guan ◽  
Honglei Yang ◽  
...  
Keyword(s):  
Orbit Determination ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
Satellite Orbits ◽  
Navigation Satellite ◽  
Noise Levels ◽  
Precise Orbit ◽  
Leo Satellites ◽  
Solar Storm ◽  
Observational Errors

The precise orbit determination (POD) accuracy of the Chinese BeiDou Navigation Satellite System (BDS) is still not comparable to that of the Global Positioning System because of the unfavorable geometry of the BDS and the uneven distribution of BDS ground monitoring stations. Fortunately, low Earth orbit (LEO) satellites, serving as fast moving stations, can efficiently improve BDS geometry. Nearly all studies on Global Navigation Satellite System POD enhancement using large LEO constellations are based on simulations and their results are usually overly optimistic. The receivers mounted on a spacecraft or an LEO satellite are usually different from geodetic receivers and the observation conditions in space are more challenging than those on the ground. The noise level of spaceborne observations needs to be carefully calibrated. Moreover, spaceborne observational errors caused by space weather events, i.e., solar geomagnetic storms, are usually ignored. Accordingly, in this study, the actual spaceborne observation noises are first analyzed and then used in subsequent observation simulations. Then, the observation residuals from the actual-processed LEO POD during a solar storm on 8 September 2017 are extracted and added to the simulated spaceborne observations. The effect of the observational errors on the BDS POD augmented with different LEO constellation configurations is analyzed. The results indicate that the noise levels from the Swarm-A, GRACE-A, and Sentinel-3A satellites are different and that the carrier-phase measurement noise ranges from 2 mm to 6 mm. Such different noise levels for LEO spaceborne observations cause considerable differences in the BDS POD solutions. Experiments calculating the augmented BDS POD for different LEO constellations considering spaceborne observational errors extracted from the solar storm indicate that these errors have a significant influence on the accuracy of the BDS POD. The 3D root mean squares of the BDS GEO, IGSO, and MEO satellite orbits are 1.30 m, 1.16 m, and 1.02 m, respectively, with a Walker 2/1/0 LEO constellation, and increase to 1.57 m, 1.72 m, and 1.32 m, respectively, with a Walker 12/3/1 constellation. When the number of LEO satellites increases to 60, the precision of the BDS POD improves significantly to 0.89 m, 0.77 m, and 0.69 m for the GEO, IGSO, and MEO satellites, respectively. While 12 satellites are sufficient to enhance the BDS POD to the sub-decimeter level, up to 60 satellites can effectively reduce the influence of large spaceborne observational errors, i.e., from solar storms.

scholarly journals Precise Orbit Determination for GNSS Maneuvering Satellite with the Constraint of a Predicted Clock

2019 ◽  
Vol 11 (16) ◽  
pp. 1949 ◽  
Author(s):  
Xiaolei Dai ◽  
Yidong Lou ◽  
Zhiqiang Dai ◽  
Caibo Hu ◽  
Yaquan Peng ◽  
...  
Keyword(s):  
Orbit Determination ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
Navigation Satellite ◽  
Precise Orbit ◽  
Gps Satellites ◽  
Global Navigation Satellite ◽  
Cross Track ◽  
Along Track ◽  
Backward Integration

Precise orbit products are essential and a prerequisite for global navigation satellite system (GNSS) applications, which, however, are unavailable or unusable when satellites are undertaking maneuvers. We propose a clock-constrained reverse precise point positioning (RPPP) method to generate the rather precise orbits for GNSS maneuvering satellites. In this method, the precise clock estimates generated by the dynamic precise orbit determination (POD) processing before maneuvering are modeled and predicted to the maneuvering periods and they constrain the RPPP POD during maneuvering. The prediction model is developed according to different clock types, of which the 2-h prediction error is 0.31 ns and 1.07 ns for global positioning system (GPS) Rubidium (Rb) and Cesium (Cs) clocks, and 0.45 ns and 0.60 ns for the Beidou navigation satellite system (BDS) geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO)/Median Earth orbit (MEO) satellite clocks, respectively. The performance of this proposed method is first evaluated using the normal observations without maneuvers. Experiment results show that, without clock-constraint, the average root mean square (RMS) of RPPP orbit solutions in the radial, cross-track and along-track directions is 69.3 cm, 5.4 cm and 5.7 cm for GPS satellites and 153.9 cm, 12.8 cm and 10.0 cm for BDS satellites. When the constraint of predicted satellite clocks is introduced, the average RMS is dramatically reduced in the radial direction by a factor of 7–11, with the value of 9.7 cm and 13.4 cm for GPS and BDS satellites. At last, the proposed method is further tested on the actual GPS and BDS maneuver events. The clock-constrained RPPP POD solution is compared to the forward and backward integration orbits of the dynamic POD solution. The resulting orbit differences are less than 20 cm in all three directions for GPS satellite, and less than 30 cm in the radial and cross-track directions and up to 100 cm in the along-track direction for BDS satellites. From the orbit differences, the maneuver start and end time is detected, which reveals that the maneuver duration of GPS satellites is less than 2 min, and the maneuver events last from 22.5 min to 107 min for different BDS satellites.

scholarly journals Investigating the GALILEO and BeiDou orbit accuracy derived from rapid products

2020 ◽  
Vol 3 (1) ◽  
pp. 316-321
Author(s):  
Sermet Ogutcu ◽  
Salih Alcay ◽  
Omer Faruk Atiz
Keyword(s):  
Orbit Determination ◽  
Precise Orbit Determination ◽  
Solar Radiation Pressure ◽  
Satellite Orbit ◽  
Satellite System ◽  
Precise Orbit ◽  
Yaw Attitude ◽  
Global Navigation Satellite ◽  
Cross Track ◽  
Mean Square Errors

In recent years, the advances of the new Global Navigation Satellite System (GNSS) constellations including, Galileo and BeiDou (BDS), have undergone dramatic changes. Some analysis centers (ACs) produce precise orbit and clock products of Galileo and BeiDou constellations. Currently, three types of Galileo and BeiDou satellite orbit and clock products are available – namely, precise, rapid and ultra-rapid products –. Ultra-rapid and rapid products are generally used for time-constrained applications. Precise orbit determination (POD) of Galileo and BeiDou is much challenging compared with GPS and GLONASS constellations due to the officially undetermined receiver phase center offset (PCO), variations (PCV) of Galileo and BeiDou constellations and, also some other not well-defined factors such as yaw-attitude models and solar radiation pressure. In this study, GALILEO orbit accuracy is investigated using rapid products produced by Center for Orbit Determination in Europe (CODE) GeoForschungsZentrum (GFZ) and Wuhan University (WUHAN), while GFZ and WUHAN rapid products are used for BeiDou constellation only. One month (January) of data in 2020 is used to compute errors of radial, along-track, and cross-track components of Galileo and BeiDou orbit derived by rapid products compared with the CODE final Multi-GNSS Experiment (MGEX) product which is assumed as the reference product. The results show that no significant differences between the products are found for Galileo orbit. For BeiDou orbit, WUHAN rapid product produced the smaller root mean square errors (RMSEs) of orbit components compared with the GFZ rapid product.

scholarly journals Experimental Study on the Precise Orbit Determination of the BeiDou Navigation Satellite System

Sensors ◽  
2013 ◽  
Vol 13 (3) ◽  
pp. 2911-2928 ◽  
Author(s):  
Lina He ◽  
Maorong Ge ◽  
Jiexian Wang ◽  
Jens Wickert ◽  
Harald Schuh
Keyword(s):  
Experimental Study ◽  
Orbit Determination ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
Navigation Satellite ◽  
Beidou Navigation Satellite System ◽  
Precise Orbit

scholarly journals Precise Orbit Determination for BeiDou GEO/IGSO Satellites during Orbit Maneuvering with Pseudo-Stochastic Pulses

2019 ◽  
Vol 11 (21) ◽  
pp. 2587
Author(s):  
Qin ◽  
Huang ◽  
Zhang ◽  
Wang ◽  
Yan ◽  
...  
Keyword(s):  
Orbit Determination ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
Assessment System ◽  
Asia Pacific ◽  
Earth Orbit ◽  
Observation Data ◽  
Navigation Satellite ◽  
Precise Orbit ◽  
Global Navigation Satellite

In order to provide better service for the Asia-Pacific region, the BeiDou navigation satellite system (BDS) is designed as a constellation containing medium earth orbit (MEO), geostationary earth orbit (GEO), and inclined geosynchronous orbit (IGSO). However, the multi-orbit configuration brings great challenges for orbit determination. When orbit maneuvering, the orbital elements of the maneuvered satellites from broadcast ephemeris are unusable for several hours, which makes it difficult to estimate the initial orbit in the process of precise orbit determination. In addition, the maneuvered force information is unknown, which brings systematic orbit integral errors. In order to avoid these errors, observation data are removed from the iterative adjustment. For the above reasons, the precise orbit products of maneuvered satellites are missing from IGS (international GNSS (Global Navigation Satellite System) service) and iGMAS (international GNSS monitoring and assessment system). This study proposes a method to determine the precise orbits of maneuvered satellites for BeiDou GEO and IGSO. The initial orbits of maneuvered satellites could be backward forecasted according to the precise orbit products. The systematic errors caused by unmodeled maneuvered force are absorbed by estimated pseudo-stochastic pulses. The proposed method for determining the precise orbits of maneuvered satellites is validated by analyzing data of stations from the Multi-GNSS Experiment (MGEX). The results show that the precise orbits of maneuvered satellites can be estimated correctly when orbit maneuvering, which could supplement the precise products from the analysis centers of IGS and iGMAS. It can significantly improve the integrality and continuity of the precise products and subsequently provide better precise products for users.

scholarly journals Precise Orbit Determination for Climate Applications of GNSS Radio Occultation including Uncertainty Estimation

2020 ◽  
Vol 12 (7) ◽  
pp. 1180 ◽  
Author(s):  
Josef Innerkofler ◽  
Gottfried Kirchengast ◽  
Marc Schwärz ◽  
Christian Pock ◽  
Adrian Jäggi ◽  
...  
Keyword(s):  
Orbit Determination ◽  
Radio Occultation ◽  
Processing System ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
Uncertainty Estimation ◽  
Low Earth Orbit ◽  
Remote Sensing Technique ◽  
Precise Orbit ◽  
Uncertainty Estimates

Global Navigation Satellite System (GNSS) Radio Occultation (RO) is a highly valuable remote sensing technique for probing the Earth’s atmosphere, due to its global coverage, high accuracy, long-term stability, and essentially all-weather capability. In order to ensure the highest quality of essential climate variables (ECVs), derived from GNSS signal tracking by RO satellites in low Earth orbit (LEO), the orbit positions and velocities of the GNSS transmitter and LEO receiver satellites need to be determined with high and proven accuracy and reliability. Wegener Center’s new Reference Occultation Processing System (rOPS) hence aims to integrate uncertainty estimation at all stages of the processing. Here we present a novel setup for precise orbit determination (POD) within the rOPS, which routinely and in parallel performs the LEO POD with the two independent software packages Bernese GNSS software (v5.2) and NAPEOS (v3.3.1), employing two different GNSS orbit data products. This POD setup enables mutual consistency checks of the calculated orbit solutions and is used for position and velocity uncertainty estimation, including estimated systematic and random uncertainties. For LEOs enabling laser tracking we involve position uncertainty estimates from satellite laser ranging. Furthermore, we intercompare the LEO orbit solutions with solutions from other leading orbit processing centers for cross-validation. We carefully analyze multi-month, multi-satellite POD result statistics and find a strong overall consistency of estimates within LEO orbit uncertainty target specifications of 5 cm in position and 0.05 mm/s in velocity for the CHAMP, GRACE-A, and Metop-A/B missions. In 92% of the days investigated over two representative 3-month periods (July to September in 2008 and 2013) these POD uncertainty targets, which enable highly accurate climate-quality RO processing, are satisfied. The moderately higher uncertainty estimates found for the remaining 8% of days (∼5–15 cm) result in increased uncertainties of RO-retrieved ECVs. This allows identification of RO profiles of somewhat reduced quality, a potential benefit for adequate further use in climate monitoring and research.

scholarly journals Precise Orbit Determination of the China Seismo-Electromagnetic Satellite (CSES) Using Onboard GPS and BDS Observations

2020 ◽  
Vol 12 (19) ◽  
pp. 3234
Author(s):  
Yun Qing ◽  
Jian Lin ◽  
Yang Liu ◽  
Xiaolei Dai ◽  
Yidong Lou ◽  
...  
Keyword(s):  
Orbit Determination ◽  
Precise Orbit Determination ◽  
Satellite System ◽  
Gps Tracking ◽  
Dual Frequency ◽  
Precise Orbit ◽  
Gps Satellites ◽  
Geo Satellites ◽  
Antenna Phase Center ◽  
Global Navigation Satellite

The Global Navigation Satellite System (GNSS) occultation receiver onboard the China Seismo-Electromagnetic Satellite (CSES) can provide dual-frequency observations for both GPS and BDS-2 satellites. In this study, the data quality and orbit determination performance of the CSES are assessed. Severe data loss of about 30% is observed in GPS P2/L2 data, resulting in only 11% of epochs possessing six to eight useful GPS satellites. Due to fewer channels being allocated for BDS signals, less than 5% of epochs have more than three useful BDS satellites. Precise orbit determination (POD) of CSES is firstly carried out using GPS data. The results indicate that the orbit overlap differences improved from 3.65 cm to 2.8 cm in 3D root mean square (RMS) by antenna phase center correction. CSES orbits are then derived from the BDS only, and combined GPS and BDS data. BDS-based POD indicates that adding BDS geostationary Earth orbit (GEO) satellites could dramatically degrade the orbit accuracy. When excluding BDS GEO satellites, the orbit overlap differences of BDS-based and combined POD are 23.68 cm and 2.73 cm in 3D, respectively, while the differences compared with GPS-based POD are 14.83 cm and 1.05 cm, respectively. The results suggest that the obtained orbit can satisfy centimeter-level requirements. Given that large GPS tracking losses occurred and few channels are allocated for BDS signals, it is expected that POD performance can be further improved by increasing the number of dual-frequency observations.

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