PPP-based Swarm kinematic orbit determination

Abstract. The Swarm mission of the European Space Agency (ESA) offers excellent opportunities to study the ionosphere and to provide temporal gravity field information for the gap between the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO). In order to contribute to these studies, at the Institut für Erdmessung (IfE) Hannover, a software based on precise point positioning (PPP) batch least-squares adjustment is developed for kinematic orbit determination. In this paper, the main achievements are presented. The approach for the detection and repair of cycle slips caused by ionospheric scintillation is introduced, which is based on the Melbourne–Wübbena and ionosphere-free linear combination. The results show that around 95 % of cycle slips can be repaired and the majority of the cycle slips occur on L2. After the analysis and careful preprocessing of the observations, 1-year kinematic orbits of Swarm satellites from September 2015 to August 2016 are computed with the PPP approach. The kinematic orbits are validated with the reduced-dynamic orbits published by the ESA in the Swarm Level 2 products and SLR measurements. The differences between IfE kinematic orbits and ESA reduced-dynamic orbits are at the 1.5, 1.5 and 2.5 cm level in the along-track, cross-track and radial directions, respectively. Remaining systematics are characterized by spectral analyses, showing once-per-revolution period. The external validation with SLR measurements shows RMSEs at the 4 cm level. Finally, fully populated covariance matrices of the kinematic orbits obtained from the least-squares adjustment with 30, 10 and 1 s data rate are discussed. It is shown that for data rates larger than 10 s, the correlation between satellite positions should be taken into account, for example, for the recovery of gravity field from kinematic orbits.

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PPP-based Swarm kinematic orbit determination

10.5194/angeo-2018-52 ◽

2018 ◽

Author(s):

Le Ren ◽

Steffen Schön

Keyword(s):

Gravity Field ◽

Orbit Determination ◽

External Validation ◽

Ionospheric Scintillation ◽

Kinematic Orbit ◽

Cycle Slips ◽

Gravity Field Recovery ◽

Swarm Satellites ◽

Least Squares Adjustment ◽

Reduced Dynamic

Abstract. ESA's Swarm mission offers excellent opportunities to study the ionosphere and to bridge the gap in gravity field recovery between GRACE and GRACE-FO. In order to contribute to these studies, at IfE Hannover, a software based on Precise Point Positioning (PPP) batch least-squares adjustment is developed for kinematic orbit determination. In this paper, the main achievements are presented. The approach for the detection and repair of cycle slips caused by ionospheric scintillation is introduced, which is based on the Melbourne-Wübbena and ionosphere-free linear combination. The results show that around 95 % cycle slips can be repaired and the majority of the cycle slips occur on L2. After the analysis and careful preprocessing of the observations, one year kinematic orbits of Swarm satellites from Sept., 2015 to Aug., 2016 are computed with the PPP approach. The kinematic orbits are validated with the reduced-dynamic orbits published by ESA in Swarm Level 2 products and the SLR measurements. The differences between our kinematic orbits and ESA reduced-dynamic orbits are at the 1.5 cm, 1.5 cm and 2.5 cm level in the along, cross and radial track, respectively. Remaining systematics are characterised by spectral analyses. The external validation with SLR measurements shows rms errors at the 4 cm level. Finally, fully populated covariance matrices of the kinematic orbits obtained from 30 s, 10 s and 1 s data rate are discussed. It is shown that for data rates larger than 10 s, the correlation should be taken into account when using POD coordinates as input for the gravity field recovery.

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Assessing reduced-dynamic parametrizations for GRAIL orbit determination and the recovery of independent lunar gravity field solutions

10.1002/essoar.10504583.1 ◽

2020 ◽

Author(s):

Stefano Bertone ◽

Daniel Arnold ◽

Valère Girardin ◽

Martin Lasser ◽

Ulrich Meyer ◽

...

Keyword(s):

Gravity Field ◽

Orbit Determination ◽

Lunar Gravity ◽

Lunar Gravity Field ◽

Reduced Dynamic

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Assessing reduced‐dynamic parametrizations for GRAIL orbit determination and the recovery of independent lunar gravity field solutions

Earth and Space Science ◽

10.1029/2020ea001454 ◽

2021 ◽

Author(s):

S. Bertone ◽

D. Arnold ◽

V. Girardin ◽

M. Lasser ◽

U. Meyer ◽

...

Keyword(s):

Gravity Field ◽

Orbit Determination ◽

Lunar Gravity ◽

Lunar Gravity Field ◽

Reduced Dynamic

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From Kinematic Orbit Determination to Derivation of Satellite Velocity and Gravity Field

Observation of the Earth System from Space ◽

10.1007/3-540-29522-4_13 ◽

2006 ◽

pp. 177-192 ◽

Cited By ~ 5

Author(s):

Dražen Švehla ◽

Lóránt Földváry

Keyword(s):

Gravity Field ◽

Orbit Determination ◽

Kinematic Orbit ◽

Satellite Velocity

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Kinematic and highly reduced-dynamic LEO orbit determination for gravity field estimation

Dynamic Planet - International Association of Geodesy Symposia ◽

10.1007/978-3-540-49350-1_52 ◽

2008 ◽

pp. 354-361 ◽

Cited By ~ 3

Author(s):

A. Jäggi ◽

G. Beutler ◽

H. Bock ◽

U. Hugentobler

Keyword(s):

Gravity Field ◽

Orbit Determination ◽

Field Estimation ◽

Reduced Dynamic

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Using Least-Squares Residuals to Assess the Stochasticity of Measurements—Example: Terrestrial Laser Scanner and Surface Modeling

Engineering Proceedings ◽

10.3390/engproc2021005059 ◽

2021 ◽

Vol 5 (1) ◽

pp. 59

Author(s):

Gaël Kermarrec ◽

Niklas Schild ◽

Jan Hartmann

Keyword(s):

Least Squares ◽

Laser Scanner ◽

Real Data ◽

Point Clouds ◽

Statistical Testing ◽

Normal Vector ◽

Engineering Structures ◽

3D Point Clouds ◽

Least Squares Adjustment ◽

Correlation Parameters

Terrestrial laser scanners (TLS) capture a large number of 3D points rapidly, with high precision and spatial resolution. These scanners are used for applications as diverse as modeling architectural or engineering structures, but also high-resolution mapping of terrain. The noise of the observations cannot be assumed to be strictly corresponding to white noise: besides being heteroscedastic, correlations between observations are likely to appear due to the high scanning rate. Unfortunately, if the variance can sometimes be modeled based on physical or empirical considerations, the latter are more often neglected. Trustworthy knowledge is, however, mandatory to avoid the overestimation of the precision of the point cloud and, potentially, the non-detection of deformation between scans recorded at different epochs using statistical testing strategies. The TLS point clouds can be approximated with parametric surfaces, such as planes, using the Gauss–Helmert model, or the newly introduced T-splines surfaces. In both cases, the goal is to minimize the squared distance between the observations and the approximated surfaces in order to estimate parameters, such as normal vector or control points. In this contribution, we will show how the residuals of the surface approximation can be used to derive the correlation structure of the noise of the observations. We will estimate the correlation parameters using the Whittle maximum likelihood and use comparable simulations and real data to validate our methodology. Using the least-squares adjustment as a “filter of the geometry” paves the way for the determination of a correlation model for many sensors recording 3D point clouds.

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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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