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

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.