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@ARTICLE{2026AdSpR..77.3889Z,
       author = {{Zapevalin}, P.~R. and {Zharov}, V.~E.},
        title = "{Numerical differentiation approaches for kinematic orbit solutions}",
      journal = {Advances in Space Research},
     keywords = {Numerical differentiation, Orbit determination, Kinematic orbit, Space vehicles, 85─04},
         year = 2026,
        month = feb,
       volume = {77},
       number = {3},
        pages = {3889-3905},
     abstract = "{This paper investigates numerical differentiation methods for obtaining
        velocities and accelerations from kinematic low-Earth orbits
        using simulated data and data from the GOCE and GRACE-FO
        missions with reduced-dynamic orbits as a reference. Kinematic
        orbits are crucial for independent gravity field modeling in the
        long-wavelength part of the spectrum free from a priori gravity
        assumptions, but they lack direct velocity and acceleration
        data, requiring numerical differentiation of the orbit data. We
        compare central difference approximation, Extended
        Differentiation and Savitzky-Golay filtering, chosen based on
        previous literature, and integrate low-pass filters (FIR, IIR)
        to reduce noise amplification. Power spectral density analysis
        and error metrics for GOCE and GRACE-FO show that despite slight
        differences in these missions, SGF and low-pass filtering
        generally yield the best accuracy in determining kinematic
        velocity. These studies can be used to construct new gravity
        field maps and can also be considered for future geodetic
        applications.}",
          doi = {10.1016/j.asr.2025.11.059},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2026AdSpR..77.3889Z},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}