## 3 Progress in Atmospheric Density Inversion for Low Earth Orbit Satellites
### Advances in Accelerometer Inversion  
[PERSON] utilized data from the CHAMP satellite's orbit and accelerometer to invert thermospheric density for the first time, proposing an innovative atmospheric density model that became a crucial foundation for subsequent research endeavors [39]. In 2005, he analyzed two years of accelerometer data and CNES/GRGS data from CHAMP satellites to correct for the effects of bias and scale factors during accelerometer calibration and to obtain an accurate dynamic solution for the orbit and calibration parameters, and further quantified the density pattern errors on the grid spatial scales using density data measured by CHAMP accelerometers from 2001 to 2006 [40]. The impact of a severe solar storm occurring between 29 October and 1 November 2003, on thermal atmospheric conditions was illustrated through atmospheric density measurements taken at an altitude of 410 km using the STAR accelerometer by [PERSON] [41]. This investigation was subsequently complemented by comparing CHAMP density measurements with predictions derived from the Nrlmsise00 empirical density model; such comparisons revealed several deficiencies within that model. Furthermore, it has been demonstrated that accelerometer-derived data are susceptible to various influencing factors including spatial and temporal variations as well as fluctuations in solar activity. Consequently, there exist inherent spatial and temporal limitations associated with atmospheric density measurements obtained via accelerometers [26,41].  
Researchers evaluated the GRACE observations and found that the acceleration measurements had better performance in the along-track direction and slightly worse performance in the cross-track direction that could not reach the pre-launch predicted accuracy, so the de-mixing process was improved to obtain more accurate GRACE data [18]. A new radiation pressure model was developed after correcting for temperature bias in theacceleration data calibration and corrected for accelerometer data with measurement errors carried by the GRACE-FO satellite, which continued the GRACE mission, and confirmed the absence of intermittent bias between the switch from GRACE to GRACE-FO by the consistency of observations in different regions with independent estimates of the mass change [19, 20, 42, 43]. There are many anomalies in the Swarm accelerometer data, and [PERSON] et al. used high-quality GPS data to derive the nongravitational accelerations acting on the Swarm satellite. The estimated nongravitational accelerations were used to correct and enhance the accelerometer observations of Swarm-C to improve atmospheric density accuracy [44].  
Over the past two decades, accelerometers on board the CHAMP, GRACE, GOCE, and Swarm satellites have provided high-resolution thermospheric density data that have improved our understanding of atmospheric dynamics and coupling processes in the thermosphere-ionosphere region. Find detailed information on the launch time, altitude, data products, etc. of these satellites from Table 2. Many other researchers and scholars have utilized the high-precision orbital data provided by satellites such as COSMIC, APOD, SAC-C, and GRACE-FO to perform atmospheric density inversion and compared the inversion results with their own carried atmospheric density sounders or empirical models to confirm the reliability of the results [45, 46, 47, 48, 49, 50].