Reduced dynamic orbit determination using GPS code and carrier measurements

Montenbruck, Oliver; Helleputte, Tom van; Kroes, R.; Gill, Eberhard

doi:10.1016/j.ast.2005.01.003

Cited by 182 publications

(112 citation statements)

References 9 publications

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“…The basic mathematical formulas for the aforementioned numerical methods are described here while an extended description is given by Montenbruck and Gill (2000), Xu (2008b) and Beutler (2005).…”

Section: Orbit Integratorsmentioning

confidence: 99%

“…This can be performed by analytical methods (Brouwer 1959;Kozai 1959;Wnuk 1999) or numerical integration methods (Seeber 2003;Montenbruck and Gill 2000). The analytical approach leads to a closed formula for the solution.…”

Section: Orbit Integratorsmentioning

confidence: 99%

“…According to these criteria, optimum values are needed in order to achieve a precise solution in a practical amount of computational time. The selection of these values is an objective to be investigated for each individual problem of orbit determination (Montenbruck and Gill 2000).…”

Section: Orbit Integratorsmentioning

confidence: 99%

“…low earth orbit (LEO), medium earth orbit (MEO), as they are strongly affected by the orbit dynamics. Thus, quality control of the numerical methods is required for each individual orbit analysis (Montenbruck and Gill 2000) prior to the operational use in the procedure of orbit determination products. A variety of tests for the comparison of numerical integrators through orbit analysis can be found in Hull et al (1972), Fox (1984), Montenbruck (1992), Somodi and Földvary (2011).…”

Section: Introductionmentioning

confidence: 99%

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Assessment of numerical integration methods in the context of low Earth orbits and inter-satellite observation analysis

Papanikolaou

Tsoulis

2016

Acta Geod Geophys

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The integration of differential equations is a fundamental tool in the problem of orbit determination. In the present study, we focus on the accuracy assessment of numerical integrators in what refers to the categories of single-step and multistep methods. The investigation is performed in the frame of current satellite gravity missions i.e. Gravity Recovery and Climate Experiment (GRACE) and Gravity Field and steady-state Ocean Circulation Explorer (GOCE). Precise orbit determination is required at the level of a few cm in order to satisfy the primary missions' scope which is the rigorous modelling of the Earth's gravity field. Therefore, the orbit integration errors are critical for these low earth orbiters. As the result of different schemes of numerical integration is strongly affected by the forces acting on the satellites, various validation tests are performed for their accuracy assessment. The performance of the numerical methods is tested in the analysis of Keplerian orbits as well as in real dynamic orbit determination of GRACE and GOCE satellites by taking into account their sophisticated observation techniques and orbit design. Numerical investigation is performed in a wide range of the fundamental integrators' parameters i.e. the integration step and the order of the multistep methods.

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Section: Orbit Integratorsmentioning

confidence: 99%

Section: Orbit Integratorsmentioning

confidence: 99%

Section: Orbit Integratorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Assessment of numerical integration methods in the context of low Earth orbits and inter-satellite observation analysis

Papanikolaou

Tsoulis

2016

Acta Geod Geophys

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“…However, precise modeling of all forces acting on each spacecraft is a very complicated process, and it still contains modeling errors. To reduce orbit errors caused by the mismodeling of spacecraft forces, the deterministic dynamics model of the spacecraft is complemented by empirical forces which are estimated by least-squares estimation or Kalman filtering with measurement geometric information [24,25]. However, a precise dynamic model is still required to produce a satisfactory orbit.…”

Section: Modeling a Dynamical Systemmentioning

confidence: 99%

Estimating the non-linear dynamics of free-flying objects

Kim

Billard

2012

Robotics and Autonomous Systems

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a b s t r a c tThis paper develops a model-free method to estimate the dynamics of free-flying objects. We take a realistic perspective to the problem and investigate tracking accurately and very rapidly the trajectory and orientation of an object so as to catch it in flight. We consider the dynamics of complex objects where the grasping point is not located at the center of mass.To achieve this, a density estimate of the translational and rotational velocity is built based on the trajectories of various examples. We contrast the performance of six non-linear regression methods (Support Vector Regression (SVR) with Radial Basis Function (RBF) kernel, SVR with polynomial kernel, Gaussian Mixture Regression (GMR), Echo State Network (ESN), Genetic Programming (GP) and Locally Weighted Projection Regression (LWPR)) in terms of precision of recall, computational cost and sensitivity to choice of hyper-parameters. We validate the approach for real-time motion tracking of 5 daily life objects with complex dynamics (a ball, a fully-filled bottle, a half-filled bottle, a hammer and a pingpong racket). To enable real-time tracking, the estimated model of the object's dynamics is coupled with an Extended Kalman Filter for robustness against noisy sensing.

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