# Impacts of Arc Length and ECOM Solar Radiation Pressure Models on BDS-3 Orbit Prediction
## 2 Orbit Prediction Method and Data Collection
### Data Collection and Dynamic Model  
The final orbit products released by the Center for Orbit Determination in Europe (CODE) are used for BDS-3 orbit prediction research studies, and the data's length ranges from 1 July 2021 to 30 September 2021. The final precise ephemeris is not only used as observed orbits but also as reference orbits for evaluating the accuracy of BDS-3-predicted orbits. Table 1 summarizes the precise orbit-prediction strategies in the experiment, including the dynamical models and integration method. It is noteworthy that in order to reduce the influence of Earth orientation parameter (EOP) errors on the predicted orbit, this study uses the final EOP released by the IERS Earth orientation center. Moreover, the same empirical force parameters, integration methods, and integration step sizes are used in this experiment.  
As can be seen on the website of the precise orbit-determination strategies adopted by the major analysis centers of IGS (see [[https://files.igs.org/pub/center/analysis/](https://files.igs.org/pub/center/analysis/)]([https://files.igs.org/pub/center/analysis/](https://files.igs.org/pub/center/analysis/)), accessed on 17 January 2022), most analysis centers use nine-parameter ECOM or its simplified version to determine precise orbits [28]. Therefore, ECOM and its simplified version were used in our BDS-3 orbit prediction strategy to assess its accuracy in orbit prediction. The ECOM SRP model adopts the form of constant components in addition to periodic terms. Three sets of parameters were used to absorb the influence of solar radiation pressure [29]. The ECOM SRP model formulas are as follows:  
\[\begin{array}{l}\stackrel{{\rightarrow}}{{\mathrm{a}}}={\rm a }_{\rm srp,D}\cdot\stackrel{{\rightarrow}}{{\mathrm{e}}}+{\rm a }_{\rm srp,Y}\cdot\stackrel{{\rightarrow}}{{\mathrm{e}}}+{\rm a }_{\rm srp,B}\cdot\stackrel{{\rightarrow}}{{\mathrm{e}}}_{\rm B} \\ {\rm a}_{\rm srp,D}={\rm D}_{0}+{\rm D}_{\rm Cu}\cos{\rm u}+{\rm D}_{\rm Su}\sin{ \rm u}\\ {\rm a}_{\rm srp,Y}={\rm Y}_{0}+{\rm Y}_{\rm Cu}\cos{\rm u}+{\rm Y}_{\rm Su} \sin{\rm u}\\ {\rm a}_{\rm srp,B}={\rm B}_{0}+{\rm B}_{\rm Cu}\cos{\rm u}+{\rm B}_{\rm Su} \sin{\rm u}\\ \end{array} \tag{4}\]  
where \(\stackrel{{\rightarrow}}{{\mathrm{a}}}\) represents the acceleration of SRP, \({\rm a}_{\rm srp,D}\), \({\rm a}_{\rm srp,Y}\), \({\rm a}_{\rm srp,B}\) are the SRP accelerations of the D-axis, Y-axis, and B-axis, respectively, \({\rm u}\) is the argument of the ascending node, and \({\rm D}_{0}\), \({\rm D}_{\rm Cu}\), \({\rm D}_{\rm Su}\), \({\rm Y}_{0}\), \({\rm Y}_{\rm Cu}\), \({\rm Y}_{\rm Su}\), \({\rm B}_{0}\), \({\rm B}_{\rm Cu}\), and \({\rm B}_{\rm Su}\) are constant parameters, which are estimated in the orbit's determination process. In the following, when these nine parameters are used for parameter estimations, we call this strategy the ECOM9 SRP model. [PERSON] et al. (1999) introduced a simplified ECOM SRP model containing only 5 parameters (\({\rm D}_{0},\ {\rm B}_{0},\ {\rm Y}_{0},\ {\rm B}_{\rm Cu}\), and \({\rm B}_{\rm Su}\)) [30], which is called the ECOM5 SRP model. The experimental results confirm that when the ECOM SRP model with 7 parameters (\({\rm D}_{0},\ {\rm D}_{\rm Cu},\ {\rm D}_{\rm Su},\ {\rm Y}_{0},\ {\rm B}_{0},\ {\rm B}_{\rm Cu}\), and \({\rm B}_{\rm Su}\)) is used, the orbit's overlap accuracy with resepct to BDS-2's precise orbit determination can be greatly improved [31], which is called the ECOM7 SRP model in the following.