Global Navigation Satellite System (GNSS) can be applied for the navigation of the high-orbit satellites. The system observability will change due to the changes in the visible satellite numbers and the spatial geometry between the navigation satellites and the users in the navigation system. The influence of the observability changing is not considered in the traditional navigation filter algorithm. In this paper, an optimized navigation filter method based on observability analysis is proposed. Firstly, a novel criterion for the relative observable degree is proposed for each observation component by making use of observation data from previous and posterior time simultaneously. Secondly, according to the relationship between observability and navigation filter accuracy, a novel optimized navigation filter method is constructed by introducing an adjusting factor based on the relative observable degree. Through the comparative simulations with the traditional Extended Kalman Filter (EKF), the optimized navigation filter method can reduce the estimation error of position and velocity by about 36% and 44% respectively. Therefore, the superiority of the proposed filter optimization algorithm is verified.

中文翻译：

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基于GNSS的高轨道卫星导航系统可观测性分析及导航滤波器的优化

全球导航卫星系统（GNSS）可以用于高轨道卫星的导航。系统的可观察性将由于可见卫星数和导航卫星与导航系统用户之间的空间几何形状的变化而改变。在传统的导航滤波算法中没有考虑可观察性变化的影响。提出了一种基于可观察性分析的优化导航滤波方法。首先，通过同时利用来自前后时间的观测数据，提出了针对每个观测分量的相对可观测度的新判据。其次，根据可观察性与导航过滤精度之间的关系，通过引入基于相对可观测度的调整因子，构造了一种新颖的优化导航滤波方法。通过与传统扩展卡尔曼滤波器（EKF）的比较仿真，优化的导航滤波器方法可以将位置和速度的估计误差分别减少约36％和44％。因此，证明了所提出的滤波器优化算法的优越性。