## 2 Materials and Methods
### Error Model Analysis  
LEO satellites operate at relatively low altitudes in a complicated orbital environment characterized by multiple perturbative factors, many of which are challenging to accurately model. While the majority of these pressures can be adequately compensated using existing models, certain non-conservative perturbations remain difficult to precisely quantify and require further investigation to improve overall orbit determination accuracy [36]. [PERSON] et al. completed a thorough examination of the perturbative forces operating on an LEO spacecraft at 500-1000 km altitude. The typical magnitudes of these forces are summarized in Table 2[37]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Orbit Determination** & **Description** \\ \hline \multirow{8}{*}{Observation Model} & Observation Value & Non-Differenced Ionosphere-Free \\  & Processing Strategy & Combination \\  & Sampling Interval & 1 s \\  & Integration Step Size & 20 s \\  & Satellite Attitude & Attitude quaternion \\  & GNSS orbit, satellite clock offset & GPS LNAV broadcast ephemeris \\  & Estimation filter & SRIF (Square Root Information Filter) \\  & Estimated parameters & LEO satellite position, velocity, atmospheric \\  & Estimated parameters & deg coefficient, tangential and normal \\  & Earth Orientation Parameters (EOP) & Broadcast ephemeris EOP \\  & Earth Gravity Field & EIGEN-6C ([PERSON] et al., 2014)[31] \\  & Three-Body Perturbation & JPL DE405 ([PERSON] et al., 1992)[32] \\  & Relativistic Effects & IERS 2010 \\  & Solid Tides, Polar Tides & IERS 2010 ([PERSON] et al., 2010)[33] \\  & Atmospheric Drag & DTM94 ([PERSON], 2003)[34] \\  & Solar radiation pressure & Box-Wing Model ([PERSON] et al., 1994)[35] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Satellite Solution Strategy. Effect of Atmospheric Density Models on Orbit Determination Accuracy  
Atmospheric drag perturbation refers to the aerodynamic resistance exerted by the atmosphere on a satellite and is one of the most common perturbation sources for LEO satellites [38; 39; 40]. This can be expressed as:  
\[\overset{\rightarrow}{a}_{\mathit{g}\mathit{g}}=\overset{\rightarrow}{a}_{ \mathit{DB}}+\overset{\rightarrow}{a}_{\mathit{DP}} \tag{3}\]  
In this context, \(a_{\mathit{DB}}\) and \(a_{\mathit{DP}}\) represent the atmospheric drag perturbations on the satellite body and the solar panels, respectively. \(a_{\mathit{DB}}\) can be expressed as:  
\[\overset{\rightarrow}{a}_{\mathit{DB}}=-\frac{1}{2}C_{\mathit{D}}.\rho.( \frac{s}{m})v_{R}\overset{\rightarrow}{v}_{R} \tag{4}\]  
In this equation, \(\frac{s}{m}\) denotes the area-to-mass ratio of the satellite, defined as the ratio of its reference cross-sectional area to its mass, \(\rho\) denotes atmospheric density, and \(\overset{\rightarrow}{v}_{R}\) represents the velocity of atmospheric motion. Satellites use varying installation angles for their solar panels and sun-pointing control systems. As a result, the direction and amount of air drag vary correspondingly. This section describes the method for calculating the atmospheric drag acceleration acting on solar panels in a full sun-pointing control mode, where the panels are constantly pointed toward the Sun. In this design, the atmospheric drag acceleration on the solar panels \(a_{\mathit{DP}}\) is given by:  
\[\overset{\rightarrow}{a}_{\mathit{DP}}=-\frac{1}{2}C_{\mathit{D}}.\rho.( \frac{s_{p}}{m})v_{R}(\overset{\rightarrow}{v}_{R}.\overset{\rightarrow}{ \Delta}_{S})\overset{\rightarrow}{\Delta}_{S} \tag{5}\]  
In this equation, \(C_{\mathit{D}}\) represents the solar panel's air drag coefficient, \(s_{p}\) is the panel area, and \(\overset{\rightarrow}{\Delta}_{S}\) is the unit normal vector of the surface. The atmospheric drag coefficient \(C_{\mathit{D}}\) is difficult to properly calculate due to factors such as satellite surface material, shape, and atmospheric composition.