# Atmospheric Density Inversion Based on Swarm-C Satellite Accelerometer
## 3 Results
### Atmospheric Density Inversion Results of Swarm-C Accelerometer  
NASA researchers calculated 31 years of satellite data to obtain the average value of the bounce tract coefficient, which is a very accurate value. However, this method requires a very accurate atmospheric model. The current atmospheric model cannot guarantee accuracy in extreme environments, so obtaining the accurate value of the bounce tract coefficient in extreme environments is impossible. Therefore, in this paper, the Sentman model was used to calculate the real-time atmospheric drag coefficient instead of the average drag coefficient value, giving the later calculated atmospheric density a better real-time and dynamic performance. Since the accelerometer density on Swarm-C has been published by [PERSON] et al. [24] and can be retrieved, we selected the data on 1 January 2016, as a comparison. Since the accelerometer retrieval density obtained from [[http://thermosphere.tudelft.nl/](http://thermosphere.tudelft.nl/)]([http://thermosphere.tudelft.nl/](http://thermosphere.tudelft.nl/)) started at 01:00 on the 1 st of January 2016, we used the data from the same period for comparison. At the same time, we also obtained the provided POD (Precise Orbit Determination) inversion density data, which were also presented in the figure. Figure 10a-c shows the thermospheric atmospheric density time series calculated by the accelerometer inversion method in this paper and the density time series published by [PERSON] et al. Figure 10: _Cont._  
From the time series plot presented in Figure 10, it can be seen that the atmospheric density around the orbit of the Swarm-C satellite on that date, 1 January 2016, has a magnitude of \(10^{-12}\) kg/m\({}^{3}\) and shows a cyclic trend with a fluctuation period of about 1.5 h, which is related to the flight trajectory of the Swarm-C satellite. Figure 10a,b illustrates that we have eliminated part of the high-frequency information in the accelerometer data correction stage; thus, the results of our inversion using the accelerometer are smoother. However, it can be seen from the results that the original characteristics of the data are preserved while correcting. We believe the correction process used is factual and does not discard the value-added properties of the high-frequency information produced by the accelerometer. It can be seen from Figure 10a and c that the density curves presented by the two are consistent in trend. Although there are numerical differences, our method retains the characteristics of the accelerometer, and the calculated density changes are more detailed. In order to have a clearer understanding of the spatial distribution of atmospheric density at a fixed latitude, this article used the GPS precise orbit data of the Swarm-C satellite. After obtaining the time series of the thermospheric atmospheric density, the position coordinates of the Swarm-C satellite in the GPS precise orbit data were found according to the time of each item of the atmospheric density time series. Then, the time as the abscissa axis and the latitude of the satellite coordinate position as the ordinate axis was taken. Figure 11a shows the relationship diagram of the thermospheric atmospheric density changing with time at different latitudes. Since the atmospheric density time series cannot cover all times at all latitudes, it was necessary to perform interpolation on Figure 11a. We  
Figure 10: Atmospheric density time series obtained from Swarm-C satellite accelerometer data. (**a**) Our method; (**b**) accelerometer inversion results; (**c**) POD inversion results. used the ordinary Kriging interpolation algorithm. Furthermore, the interpolated results are shown in Figure 11b. Due to the limited coverage of the satellite orbit, the atmospheric density time series cannot be included at all times and at all latitudes, so the interpolation operation of the results in Figure 11a is required next. Figure 11b shows the latitudinal time distribution of atmospheric density obtained after interpolation on Figure 10b.