Modeling the neutral density in the upper atmosphere is a major challenge as it involves a comprehensive understanding of the complex coupling between the thermosphere and its environment. In addition, this system is strongly driven by solar activity, which is hardly predictable. This complexity limits the ability of thermospheric models to accurately estimate thermospheric characteristics, such as the neutral density. With the rapidly increasing number of satellites in orbit and the recent progress in tracking their trajectories, new techniques are being implemented to derive density estimates based on trajectory perturbations. However, most of these methods require the integration of complex and costly orbit determination algorithms, which greatly limit their applicability at a public level. The approach presented here provides density estimates along a spacecraft trajectory and only requires the implementation of an orbit propagator. More specifically, it corrects density predictions made by the NRLMSIS00e thermosphere model by optimizing the orbit fitting of modeled trajectories with observations under different thermospheric density conditions. The algorithm is applied to the Cyclone Global Navigation Satellite System and Swarm-B spacecraft trajectories during a period of varying geomagnetic activity. The study puts in evidence a bias in NRLMSIS00e estimates during moderate solar activity, corrected by the algorithm. In addition, the approach provides a better characterization of the rapid density enhancement resulting from a geomagnetic storm. Overall, the correlation with the Level 2 data is improved by 15% and the normalized root mean square error decreased by a factor ~2.3, compared to the estimations with NRLMSIS00e.

对高层大气中的中性密度进行建模是一项重大挑战，因为它涉及对热层与其环境之间复杂耦合的全面理解。此外，该系统受到太阳活动的强烈驱动，这很难预测。这种复杂性限制了热层模型准确估计热层特性（例如中性密度）的能力。随着在轨卫星数量的迅速增加以及最近在跟踪其轨迹方面取得的进展，正在实施新技术以基于轨迹扰动推导出密度估计。然而，这些方法中的大多数需要集成复杂且昂贵的定轨算法，这极大地限制了它们在公共层面的适用性。这里介绍的方法提供沿航天器轨迹的密度估计，并且只需要实施轨道传播器。更具体地说，它通过在不同热层密度条件下通过观测优化模拟轨迹的轨道拟合来校正 NRLMSIS00e 热层模型所做的密度预测。该算法适用于 Cyclone 全球导航卫星系统和 Swarm-B 航天器在地磁活动变化期间的轨迹。该研究证明了在中等太阳活动期间 NRLMSIS00e 估计值存在偏差，并通过算法进行了修正。此外，该方法提供了由地磁暴引起的快速密度增强的更好表征。全面的，