# Improving Low Earth Orbit (LEO) Prediction with Accelerometer Data
## 4 Results of LEO Orbit Prediction
We calculated the differences of the predicted non-gravitational acceleration between ACC_B_K and the corresponding non-gravitational acceleration calculated from estimated biases and the scale factor as well as the differences of predicted non-gravitational acceleration between ACC_B and the corresponding non-gravitational acceleration calculated from estimated biases for a one hour prediction, as shown in Figure 9.  
From Figure 9, we can see that the difference of non-gravitational accelerations in the x direction (orbit along-track direction) and z direction (radial direction) with the ACC_B_K method were much smaller than those of the ACC_B method, which means that the along-track and radial direction precision of the prediction part with ACC_B_K should be better than those of the ACC_B method. For the cross-track direction (y direction of acceleration), the differences between the predicted acceleration and the calculated one with the ACC_B_K method were larger than that of the ACC_B method, which corroborated the worse results of the cross-track direction with the ACC_B_K method. In conclusion, one set of scales and biases for each direction reflected the calibration parameters of the accelerometer for the long term while one set of biases every hour reflected for the short term. For orbit prediction for less than 20 min, the precision of all orbit components with all strategies was better than 10 cm. This means that if the interval of the uplink and downlink was shorter than 20 min, all strategies could be used for real time LEO POD. For orbit prediction for more than 20 min, the best way to realize the real time LEO precise orbit determination is by using accelerometer data with the estimation of one set of scales and biases for each direction. In this way, less than a 5 centimeter level of LEO orbit precision can be achieved for the one hour LEO orbit prediction, which satisfies the demand of a centimeter level requirement mentioned in the Introduction section. Figure 8: User Ranging Error (URE) of a real time LEO orbit for three different strategies. Usually, most precise positioning users care more about the orbit errors for every epoch while not for the averaged ones over one hour. Figure 10 shows RMS values of LEO orbits for three directions of every 10 min over a one hour prediction time period. The great increase of along-track RMS values with the empirical method can be easily found, which is from about 5.0 cm at 10 min to approximately 49.4 cm over one hour. However, the method with accelerometer data with one set of biases and scales for each direction shows a stable RMS of 4.9 cm, 4.0 cm, and 1.2 cm in the along-track, cross-track, and radial directions all the time, respectively. The corresponding URE for every 10 min is shown in Figure 11. The method with accelerometer data with one set of biases and scales for each direction shows the most stable results about 4.6 cm even if the integration time is one hour while the method of empirical and accelerometer data with  
Figure 10: RMS values of LEO orbits for the along-track, cross-track, and radial direction for every 10 min over a one hour period. Figure 9: Differences of predicted non-gravitational acceleration between the ACC_B_K method and the calculated ones as well as the differences of predicted non-gravitational acceleration between the ACC_B method and the calculated ones for a one hour prediction in each direction. “Oneday dif” means the ACC_B_K method and “Onehour dif” means the ACC_B method. one-hour biases for each direction shows an increased trend, from about 4.6 cm at 0-10 min to 31.4 cm and 14.0 cm within 50-60 min. As mentioned above in the \"LEO orbit prediction procedure\", if the orbital elements do not uplink in time, one has to wait until the next uplink, which means a delay of nearly two hours.