# Improving Low Earth Orbit (LEO) Prediction with Accelerometer Data
## 4 Results of LEO Orbit Prediction  
After conducting LEO POD, the initial conditions as well as the dynamic parameters can be uplinked to the corresponding LEO satellites. Then the processor on LEO satellites can do orbit prediction/propagation for real time applications. We used one hour for orbit prediction as mentioned before. One issue should be clarified here. If we used the EMP method in which empirical force models are applied, the orbit prediction could also be conducted at the analysis center in advance since no real time onboard observations are required whereas for the ACC_B_K and ACC_B method, it must be conducted onboard because real time accelerometer data must be used. The initial conditions and the dynamic parameters have great impact on the precision of LEO orbit. For the EMP method, the last set of empirical coefficients were chosen for real time orbit integration as usual and for the ACC_B_K method there was only one set of calibrations parameters for each direction including scales and biases for the orbit integration. For the ACC_B method, we used a linear fitting for the previous 24-h arc since an obvious trend could be found in these biases, and then extrapolated the biases according to the integration time. The differences between PSO and predicted orbits were calculated for the orbit evaluation and their User Ranging Error (URE) were also calculated and compared. URE provides the average range error in the line-of-sight direction at a global scale. Its computation is related to the maximum satellite coverage on the Earth's surface. The coverage depends on the angular range of the satellite, which is the angle of the emission cone with respect to the boresight direction. With the angular range of LEO satellites at the altitude of 500 km being about 68.02\({}^{\circ}\), the URE can be approximately determined as [8; 9; 43]:  
\[\mathrm{URE}=\sqrt{0.205(\mathrm{RMS_{R}})^{2}+0.397\big{(}(\mathrm{RMS_{A}}) ^{2}+(\mathrm{RMS_{C}})^{2}\big{)}} \tag{3}\]  
Figure 7 shows the averaged RMS values of a one hour predicted orbit in three directions with the three strategies. The corresponding averaged RMS values of all days for each direction with different strategies are shown at the top left of each panel. It is easy to find out that the ACC_B_K strategy shows the best results, especially for along-track direction at 4.8 cm while the ACC_B and EMP strategies were at 15.6 cm and 31.5 cm. For the radial direction, the RMS values were 1.7 cm, 3.7 cm, and 8.6 cm for the ACC_B_K, ACC_B, and EMP strategy, respectively. The RMS value of cross-track direction for the ACC_B_K strategy was 4.3 cm, which was  
Figure 7: Averaged RMS values for the three directions with three strategies for an orbit prediction of one hour. worse than the other two strategies with 1.6 cm and 1.7 cm. As Figure 8 shows, the averaged URE values for the three strategies were 4.4 cm, 10.1 cm, and 20.3 cm, respectively. It is easy to understand that predicted LEO orbit precision by using accelerometer data were better than that of using empirical force models since accelerometer data could better reflect the non-gravitational forces than that of the empirical force models. We found that with the method of strategy 1 (ACC_B_K), the predicted LEO orbit precision shows a better result in the along and radial directions than with strategy 2 (ACC_B), though the calculation part (orbit determination part) of ACC_B_K of the along-track and radial directions was worse than those of ACC_B.