# Improving Low Earth Orbit (LEO) Prediction with Accelerometer Data
## 3 Analysis of Dynamic Parameters
The corresponding averaged RMS values of all days for three directions are shown in Table 2.  
In general, the RMS values are smallest for all directions when empirical force models are used. These empirical models can efficiently absorb the unmodeled part of the non-gravitational forces. The averaged RMS values for all days were 12.1 mm, 6.2 mm, and 6.8 mm for along-track, cross-track, and radial direction, respectively. For radial direction, the RMS values of the two strategies using accelerometer data were nearly the same as using the empirical force models with about 6.8 mm, while the RMS values of cross-track direction were larger than that of empirical method, which were 14.3 mm and 11.9 mm for the ACC_B_K method and ACC_B method. This is mainly caused by the sensitivity of the accelerometer [42]. The more sensitive axes point in the flight and radial directions, the less sensitive axis points in the cross-track direction [26]. The precision of the sensitive axes is specified to be \(10^{-10}\) m/s\({}^{2}\) and that of the less sensitive axis \(10^{-9}\) m/s\({}^{2}\)[27]. The RMS values of the along-track direction for the strategy of estimating the accelerometer bias every one hour and empirical forces were almost the same at about 12.0 mm while the strategy of estimating the accelerometer bias and scale for one day were worse than those two strategies with 23.3 mm. Such a difference may be caused by the number of estimated parameters. The number of estimated dynamic parameters of the three strategies is 6 (B\({}_{X}\), B\({}_{Y}\), B\({}_{Z}\), K\({}_{X}\), K\({}_{Y}\), and K\({}_{Z}\)), 72 (B\({}_{X}\), B\({}_{Y}\), and B\({}_{Z}\) every one hour for 24 h, 24 x 3 = 72), and 80 (Ca, Sa, Ce, Sc, and a scale factor every one cycle per revolution for 24 h, 24/1.5 \(\times\) 5 = 80), \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Along-Track (mm)** & **Cross-Track (mm)** & **Radial (mm)** \\ \hline ACC\_B\_K & 23.3 & 14.3 & 6.8 \\ ACC\_B & 11.8 & 11.9 & 6.1 \\ EMP & 12.1 & 6.2 & 6.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Averaged RMS values on all days for three directions with three strategies. Figure 3: Averaged Root Mean Square (RMS) values for along-track, cross-track, and radial directions with the three strategies. respectively. In the least square estimator, the more parameters, the smaller the fitted residuals if all parameters are estimable. The initial conditions and dynamic parameters estimated from the POD process are then used for the LEO orbit prediction. It is of great importance to analyze dynamic parameters since they will have a direct effect on the orbit precision for orbit prediction. If only one set dynamic parameters is estimated for one arc, then these estimated parameters are used for LEO orbit prediction, such as strategy 1 (ACC_B_K). If there are more than one set of dynamic parameters estimated like strategy 2 (ACC_B) and 3 (EMP), one has to firstly investigate the characteristics of the dynamic parameters and then decide the way to predict the LEO orbit. Figure 4 shows the accelerometer bias parameters for strategy 2. The behavior of three biases was different for the three directions. By linear fitting, we could find that biases in the y direction show a clear smooth trend in the year. It changed about 10,450 nm/s\({}^{2}\) in the year. For the x direction, there was also a small trend, which was about -9 nm/s\({}^{2}\) in 2007. Biases in the z direction keep quite stable, which was only 1.3 nm/s\({}^{2}\) in the year. Due to this increased or decreased trend of the biases, it may not be appropriate using the last set of accelerometer calibration parameters to conduct the real time orbit prediction and linear fitting and an extrapolation should be used when doing the orbit integration for real time LEO orbits.