Publications related to the GRACE Missions (no abstracts)

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Deriving Thermospheric Density from GNSS POD: An Orthogonal Polynomial Differentiation Approach for Accelerometer–Free LEO Satellites–A High–Fidelity Simulation Study

Yao, Liang, Zhang, Yasheng, Tao, Xuefeng, Zhang, Zhongtao, Zhao, Shuailong, and Jiang, Yawen, 2026. Deriving Thermospheric Density from GNSS POD: An Orthogonal Polynomial Differentiation Approach for Accelerometer–Free LEO Satellites–A High–Fidelity Simulation Study. Aerospace, 13(8):682, doi:10.3390/aerospace13080682.

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@ARTICLE{2026Aeros..13..682Y,
       author = {{Yao}, Liang and {Zhang}, Yasheng and {Tao}, Xuefeng and {Zhang}, Zhongtao and {Zhao}, Shuailong and {Jiang}, Yawen},
        title = "{Deriving Thermospheric Density from GNSS POD: An Orthogonal Polynomial Differentiation Approach for Accelerometer-Free LEO Satellites-A High-Fidelity Simulation Study}",
      journal = {Aerospace},
     keywords = {GNSS POD observations, thermospheric mass density, orthogonal polynomial, LEO satellite, space weather, autonomous navigation},
         year = 2026,
        month = jul,
       volume = {13},
       number = {8},
          eid = {682},
        pages = {682},
     abstract = "{Accurate thermospheric mass density is crucial for precision orbit
        determination, trajectory prediction, and collision warning in
        the increasingly congested Low Earth Orbit (LEO) region.
        Traditional high-precision instantaneous inversion methods rely
        on dedicated onboard accelerometers (e.g., CHAMP and GRACE
        satellites), which are costly, scarce, and unable to meet the
        expansive monitoring needs of modern mega-constellations. In
        recent years, orbit data inversion methods based on high-
        precision orbit determination data have been extensively
        studied. Among them, the interpolation--differentiation method,
        although capable of retrieving instantaneous atmospheric
        density, severely amplifies position errors and measurement
        noise, significantly limiting retrieval accuracy. To address
        this gap, this study proposes a novel atmospheric density
        retrieval scheme for accelerometer-free LEO satellites,
        introducing an orthogonal polynomial (Legendre and Chebyshev)
        sliding-window fitting approach. The proposed method is
        evaluated using high-precision simulated orbit data. Under
        instantaneous inversion conditions, the Legendre method yields
        an average relative error (MRE) of 16.55\%, a normalized root
        mean square deviation (NRMSD) of 12.80\%, and a correlation
        coefficient R of 0.9370. To further evaluate its potential in
        climatological modeling, this paper also proposes a local solar
        time (LST) bin-averaging method to assess atmospheric inversion
        accuracy. Under this LST averaging approach, the inversion
        performance achieves an MRE of 6.83\% and a correlation
        coefficient R exceeding 0.98. This demonstrates the feasibility
        of the inversion method for analyzing diurnal effects on
        atmospheric field evolution.}",
          doi = {10.3390/aerospace13080682},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2026Aeros..13..682Y},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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