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

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.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.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 &#947; and &#946; and all limitations related to the observability of these parameters at GNSS heights and systematic errors emerging from non-gravitation orbit perturbations.

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General relativistic effects acting on the orbits of Galileo satellites

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/s10569-021-10014-y ◽

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.

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

Remote Sensing ◽

10.3390/rs13163189 ◽

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.

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Potential of VLBI observations to satellites for precise orbit determination

10.5194/egusphere-egu21-12458 ◽

2021 ◽

Author(s):

Nicat Mammadaliyev ◽

Patrick Schreiner ◽

Susanne Glaser ◽

Karl Hans Neumayer ◽

Rolf Koenig ◽

...

Keyword(s):

Orbit Determination ◽

Precise Orbit Determination ◽

Satellite Observations ◽

Satellite Orbits ◽

Error Sources ◽

Interferometric Technique ◽

Precise Orbit ◽

Vlbi Observations ◽

Low Earth Orbits ◽

Earth Orbits

Besides the natural extra-galactic radio sources, observing an artificial Earth-orbiting radio source with the Very Long Baseline Interferometry (VLBI) permits to extend the geodetic and geodynamic applications of this highly accurate interferometric technique. Furthermore, combining aforementioned observations provides a promising method to determine the satellite orbit and delivers the new type of observations such as group delay and delay rate which might be employed to validate the orbit independent of other space geodetic techniques.In this research, the potential of the interferometric satellite tracking for the Precise Orbit Determination (POD) has been explored based on simulated observations for different scenarios with various VLBI networks, satellite orbits (eccentric low Earth orbits or circular medium Earth orbits) and error sources. POD of the Earth-orbiting satellites is studied on the basis of daily VLBI sessions where satellite observations are scheduled together with the quasar observation for regionally or globally distributed legacy as well as next generation VLBI station networks. In order to simulate VLBI to satellite observations, the influence of the most prominent random error sources in VLBI as well as mismodelling of different force models acting on the satellite are utilized. This study indicates that POD is feasible with VLBI observations and the accuracy mainly depends on the observation geometry.

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GPS, GLONASS, and Galileo orbit geometry variations caused by general relativity focusing on Galileo in eccentric orbits

GPS Solutions ◽

10.1007/s10291-021-01192-1 ◽

2021 ◽

Vol 26 (1) ◽

Author(s):

Krzysztof Sośnica ◽

Grzegorz Bury ◽

Radosław Zajdel ◽

Javier Ventura-Traveset ◽

Luis Mendes

Keyword(s):

General Relativity ◽

Semimajor Axis ◽

Satellite Orbit ◽

Earth Satellite ◽

Satellite Orbits ◽

De Sitter ◽

Size And Shape ◽

Eccentric Orbits ◽

Spacetime Curvature ◽

Orbit Geometry

AbstractThree main effects from general relativity (GR) may change the geometry and orientation of artificial earth satellite orbits, i.e., the Schwarzschild, Lense–Thirring, and De Sitter effects. So far, the verification of GR effects was mainly based on the observations of changes in the orientation of satellite orbital planes. We directly observe changes of the satellite orbit geometry caused by GR represented by the semimajor axis and eccentricity. We measure the variations of orbit size and shape of GPS, GLONASS, and Galileo satellites in circular and eccentric orbits and compare the results to the theoretical effects using three years of real GNSS data. We derive a solution that assumes the GR to be true, and a second solution, in which the post-Newtonian parameters are estimated, thus, allowing satellites to find their best spacetime curvature. For eccentric Galileo, GR changes the orbital shape and size in perigee in such a way that the orbit becomes smaller but more circular. In the apogee, the semimajor axis decreases but eccentricity increases, and thus, the orbit becomes more eccentric. Hence, the orbital size variabilities for eccentric orbits are greatly compensated by the orbital shape changes, and thus the total effect of satellite height change is much smaller than the effects for the size and shape of the orbit, individually. The mean semimajor axis offset based on all GPS, GLONASS, and Galileo satellites is − 17.41 ± 2.90 mm, which gives a relative error of 0.36% with respect to the theoretical value.

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Precise Orbit Determination of Combined GNSS and LEO Constellations with Regional Ground Stations

Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017) ◽

10.33012/2017.15329 ◽

2017 ◽

Author(s):

Bofeng Li ◽

Liangwei Nie ◽

Haibo Ge ◽

Maorong Ge ◽

Ling Yang

Keyword(s):

Orbit Determination ◽

Precise Orbit Determination ◽

Precise Orbit

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A Second-Order Time-Difference Position Constrained Reduced-Dynamic Technique for the Precise Orbit Determination of LEOs Using GPS

Remote Sensing ◽

10.3390/rs13153033 ◽

2021 ◽

Vol 13 (15) ◽

pp. 3033

Author(s):

Hui Wei ◽

Jiancheng Li ◽

Xinyu Xu ◽

Shoujian Zhang ◽

Kaifa Kuang

Keyword(s):

Orbit Determination ◽

Dynamic Models ◽

Precise Orbit Determination ◽

Second Order ◽

Time Difference ◽

Error Sources ◽

Precise Orbit ◽

Unmodeled Dynamic ◽

Reduced Dynamic

In this paper, we propose a new reduced-dynamic (RD) method by introducing the second-order time-difference position (STP) as additional pseudo-observations (named the RD_STP method) for the precise orbit determination (POD) of low Earth orbiters (LEOs) from GPS observations. Theoretical and numerical analyses show that the accuracies of integrating the STPs of LEOs at 30 s intervals are better than 0.01 m when the forces (<10−5 ms−2) acting on the LEOs are ignored. Therefore, only using the Earth’s gravity model is good enough for the proposed RD_STP method. All unmodeled dynamic models (e.g., luni-solar gravitation, tide forces) are treated as the error sources of the STP pseudo-observation. In addition, there are no pseudo-stochastic orbit parameters to be estimated in the RD_STP method. Finally, we use the RD_STP method to process 15 days of GPS data from the GOCE mission. The results show that the accuracy of the RD_STP solution is more accurate and smoother than the kinematic solution in nearly polar and equatorial regions, and consistent with the RD solution. The 3D RMS of the differences between the RD_STP and RD solutions is 1.93 cm for 1 s sampling. This indicates that the proposed method has a performance comparable to the RD method, and could be an alternative for the POD of LEOs.

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Assessment of single-difference and track-to-track ambiguity resolution in LEO precise orbit determination

GPS Solutions ◽

10.1007/s10291-021-01103-4 ◽

2021 ◽

Vol 25 (2) ◽

Author(s):

Xingyu Zhou ◽

Hua Chen ◽

Wenlan Fan ◽

Xiaohui Zhou ◽

Qusen Chen ◽

...

Keyword(s):

Ambiguity Resolution ◽

Orbit Determination ◽

Precise Orbit Determination ◽

Precise Orbit ◽

Single Difference

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Comparisons of CODE and CNES/CLS GPS satellite bias products and applications in Sentinel-3 satellite precise orbit determination

GPS Solutions ◽

10.1007/s10291-021-01164-5 ◽

2021 ◽

Vol 25 (4) ◽

Author(s):

Bingbing Duan ◽

Urs Hugentobler

Keyword(s):

Linear Combination ◽

Orbit Determination ◽

Fractional Part ◽

Precise Orbit Determination ◽

Satellite Orbit ◽

Satellite Orbits ◽

Satellite Clock ◽

Analysis Center ◽

Wide Lane ◽

Total Difference

AbstractTo resolve undifferenced GNSS phase ambiguities, dedicated satellite products are needed, such as satellite orbits, clock offsets and biases. The International GNSS Service CNES/CLS analysis center provides satellite (HMW) Hatch-Melbourne-Wübbena bias and dedicated satellite clock products (including satellite phase bias), while the CODE analysis center provides satellite OSB (observable-specific-bias) and integer clock products. The CNES/CLS GPS satellite HMW bias products are determined by the Hatch-Melbourne-Wübbena (HMW) linear combination and aggregate both code (C1W, C2W) and phase (L1W, L2W) biases. By forming the HMW linear combination of CODE OSB corrections on the same signals, we compare CODE satellite HMW biases to those from CNES/CLS. The fractional part of GPS satellite HMW biases from both analysis centers are very close to each other, with a mean Root-Mean-Square (RMS) of differences of 0.01 wide-lane cycles. A direct comparison of satellite narrow-lane biases is not easily possible since satellite narrow-lane biases are correlated with satellite orbit and clock products, as well as with integer wide-lane ambiguities. Moreover, CNES/CLS provides no satellite narrow-lane biases but incorporates them into satellite clock offsets. Therefore, we compute differences of GPS satellite orbits, clock offsets, integer wide-lane ambiguities and narrow-lane biases (only for CODE products) between CODE and CNES/CLS products. The total difference of these terms for each satellite represents the difference of the narrow-lane bias by subtracting certain integer narrow-lane cycles. We call this total difference “narrow-lane” bias difference. We find that 3% of the narrow-lane biases from these two analysis centers during the experimental time period have differences larger than 0.05 narrow-lane cycles. In fact, this is mainly caused by one Block IIA satellite since satellite clock offsets of the IIA satellite cannot be well determined during eclipsing seasons. To show the application of both types of GPS products, we apply them for Sentinel-3 satellite orbit determination. The wide-lane fixing rates using both products are more than 98%, while the narrow-lane fixing rates are more than 95%. Ambiguity-fixed Sentinel-3 satellite orbits show clear improvement over float solutions. RMS of 6-h orbit overlaps improves by about a factor of two. Also, we observe similar improvements by comparing our Sentinel-3 orbit solutions to the external combined products. Standard deviation value of Satellite Laser Ranging residuals is reduced by more than 10% for Sentinel-3A and more than 15% for Sentinel-3B satellite by fixing ambiguities to integer values.

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A More Reliable Orbit Initialization Method for LEO Precise Orbit Determination Using GNSS

Remote Sensing ◽

10.3390/rs12213646 ◽

2020 ◽

Vol 12 (21) ◽

pp. 3646

Author(s):

Xuewen Gong ◽

Jizhang Sang ◽

Fuhong Wang ◽

Xingxing Li

Keyword(s):

Parameter Estimation ◽

Orbit Determination ◽

High Reliability ◽

Precise Orbit Determination ◽

Direct Approach ◽

Design Matrix ◽

Reference Orbit ◽

Stability Analyses ◽

Precise Orbit ◽

Orbit Parameter

Precise orbit determination (POD) using GNSS has been rapidly developed and is the mainstream technology for the navigation of low Earth orbit (LEO) satellites. The initialization of orbit parameters is a key prerequisite for LEO POD processing. For a LEO satellite equipped with a GNSS receiver, sufficient discrete kinematic positions can be obtained easily by processing space-borne GNSS data, and its orbit parameters can thus be estimated directly in iterative manner. This method of direct iterative estimation is called as the direct approach, which is generally considered highly reliable, but in practical applications it has risk of failure. Stability analyses demonstrate that the direct approach is sensitive to oversized errors in the starting velocity vector at the reference time, which may lead to large errors in design matrix because the reference orbit may be significantly distorted, and eventually cause the divergence of the orbit parameter estimation. In view of this, a more reliable method, termed the progressive approach, is presented in this paper. Instead of estimating the orbit parameters directly, it first fits the discrete kinematic positions to a reference ephemeris in the form of the GNSS broadcast ephemeris, which construct a reference orbit that is smooth and close to the true orbit. Based on the reference orbit, the starting orbit parameters are computed in sufficient accuracy, and then the final orbit parameters are estimated with a high accuracy by using discrete kinematic positions as measurements. The stability analyses show that the design matrix errors are reduced in the progressive approach, which would assure more robust orbit parameter estimation than the direct estimation approach. Various orbit initialization experiments are performed on the KOMPSAT-5 and FY3C satellites. The results have fully verified the high reliability of the proposed progressive approach.

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