Extending higher-order model for non-conservative perturbing forces acting on Galileo satellites during eclipse periods

For precise orbit determination (POD) and precise applications with POD products, one of the critical issues is the modeling of non-conservative forces acting on satellites. Since the official publication of Galileo satellite metadata in 2017, analytical models including the box-wing model and thermal thrust models have been established to absorb a substantial amount of solar radiation pressure (SRP) and thermal thrust. These models serve as the foundation for the best overall modeling approach, combining the analytical box-wing model and thermal thrust model with parameterization of the remaining non-conservative perturbing forces using various optimized Empirical CODE Orbit Models (ECOMs) of the Center for Orbit Determination in Europe (CODE). Firstly, we have demonstrated the significance of the second-order signals in the D direction and the first-order signals in the B direction through spectral analyses of the pure box-wing model, which are consistent with the currently recommended 7-parameter Empirical CODE Orbit Model 2 (ECOM2). In spite of this, we still found that degradation in orbit accuracy frequently occurs during deep eclipse seasons when using the ECOM2 model. We confirm a high-frequency signal existing in the fluctuating orbit overlap differences through the spectral analysis. Considering this, the ECOM2 force model should be extended to higher order and adapted to absorb the remaining effects of potential perturbing forces. After extending the ECOM2 force model to the sixth order in the Sun direction, we demonstrated the significance of fourth- and sixth-order sine terms for deep eclipses. Due to the higher-order periodic terms, the averaged RMS values of orbit overlap difference over deep eclipses can be reduced from 5.3, 10.8, and 23.8 cm to 3.2, 3.9, and 9.9 cm for in-orbit validation (IOV) satellites, from 5.0, 8.6, and 17.7 cm to 3.0, 3.0, and 7.1 cm for the first generation of full operational capability (FOC-1) satellites, and from 5.4, 8.6, and 19.0 cm to 3.6, 3.6, and 7.4 cm for the second generation of FOC (FOC-2) satellites, in the radial, cross-track, and along-track directions, respectively. Fluctuations with a peak amplitude of approximately 0.4 nm/s² in the bias in the solar panel axis (Y) direction (Y-bias) are effectively mitigated by the higher-order terms. Due to the higher-order terms, the vertical positioning errors during kinematic precise point positioning (PPP) convergence can be improved from 42.3 to 37.1 cm at the 95.5% confidence level. Meanwhile, a low correlation level of up to 0.02 is found between the newly introduced higher-order parameters and earth rotation parameters (ERPs).