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).

对于 POD 产品的精确轨道确定 （POD） 和精确应用，关键问题之一是对作用在卫星上的非守恒力进行建模。自 2017 年正式发布伽利略卫星元数据以来，已经建立了包括箱翼模型和热推力模型在内的分析模型，以吸收大量的太阳辐射压力 （SRP） 和热推力。这些模型是最佳整体建模方法的基础，使用欧洲轨道确定中心 （CODE） 的各种优化经验 CODE 轨道模型 （ECOM） 将分析箱翼模型和热推力模型与剩余非守恒扰动力的参数化相结合。首先，通过纯箱翼模型的光谱分析，证明了 D 方向的二阶信号和 B 方向的一阶信号的重要性，这与目前推荐的 7 参数经验 CODE 轨道模型 2 （ECOM2） 一致。尽管如此，我们仍然发现，当使用 ECOM2 模型时，轨道精度经常发生在深食季节。我们通过频谱分析确认了波动轨道中存在的高频信号重叠差异。考虑到这一点，应将 ECOM2 力模型扩展到更高阶，并进行调整以吸收潜在扰动力的剩余影响。在将 ECOM2 力模型扩展到太阳方向的六阶后，我们证明了四阶和六阶正弦项对深食的重要性。由于高阶周期项，深食轨道重叠差的平均 RMS 值可以从 5.3、10.8 和 23.8 cm 减少到 3.2、3。9 厘米和 9.9 厘米用于在轨验证 （IOV） 卫星，第一代完全作战能力 （FOC-1） 卫星从 5.0、8.6 和 17.7 厘米到 3.0、3.0 和 7.1 厘米，第二代 FOC （FOC-2） 卫星从 5.4、8.6 和 19.0 厘米到 3.6、3.6 和 7.4 厘米，采用径向交叉轨道、 和沿轨道方向。在太阳能电池板轴 （Y） 方向的偏置（Y 偏置）上峰值振幅约为 0.4 nm/s² 的波动被高阶项有效缓解。由于高阶项，在 95.5% 的置信水平下，运动学精确点定位 （PPP） 收敛过程中的垂直定位误差可以从 42.3 cm 改善到 37.1 cm。同时，新引入的高阶参数与地球自转参数 （ERP） 之间存在高达 0.02 的低相关水平。