Abstract
Gravity recovery from kinematic orbits is possible at three levels: (1) coordinates (integral of Fredholm type, i.e. boundary value problem for short arcs), (2) velocity (integrals of motion, e.g. energy balance approach) and (3) accelerations, which are directly connected to the force function by the equation of motion (e.g. acceleration approach). For CHAMP, these three approaches have been applied successfully. With the advent of e.g. GOCE and SWARM, and given the uncertainty of a GRACE follow-on mission, the kinematic orbit analysis methods have gained further relevance. In this paper, the aforementioned approaches are compared by means of simulations. Important issues as the influence of the correlation of kinematic orbit errors and data weighting are investigated. A big advantage of the acceleration approach is its simplicity and speed due to missing integration. As it amplifies noise, the numerical differentiation in approaches 2 and especially 3 are regarded as a bottleneck. However, the noise of kinematic orbits is highly correlated, which reduces the effect of noise amplification, such that approaches 2 and 3 are not affected. Simulations based on white and correlated orbit noise show that both the acceleration approach and the boundary value problem lead to promising results. However, an advantage of the acceleration approach is that the non-diagonal elements can be neglected in data weighting (for a conventional kinematic orbit sampling interval of 30 s) without significant loss of accuracy, which reduces the computational effort significantly.
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Reubelt, T., Sneeuw, N., Grafarend, E.W. (2012). Comparison of Kinematic Orbit Analysis Methods for Gravity Field Recovery. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22078-4_39
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DOI: https://doi.org/10.1007/978-3-642-22078-4_39
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