Kim Ghangho, Kim Chongwon, Kee Changdon
School of Mechanical and Aerospace Engineering and SNU-IAMD Seoul National University, 1 Gwanak-ro Gwanak-gu, Seoul 151-744, Korea.
Sensors (Basel). 2015 Apr 1;15(4):7878-97. doi: 10.3390/s150407878.
A practical algorithm is proposed for determining the orbit of a geostationary orbit (GEO) satellite using single-epoch measurements from a Global Positioning System (GPS) receiver under the sparse visibility of the GPS satellites. The algorithm uses three components of a state vector to determine the satellite's state, even when it is impossible to apply the classical single-point solutions (SPS). Through consideration of the characteristics of the GEO orbital elements and GPS measurements, the components of the state vector are reduced to three. However, the algorithm remains sufficiently accurate for a GEO satellite. The developed algorithm was tested on simulated measurements from two or three GPS satellites, and the calculated maximum position error was found to be less than approximately 40 km or even several kilometers within the geometric range, even when the classical SPS solution was unattainable. In addition, extended Kalman filter (EKF) tests of a GEO satellite with the estimated initial state were performed to validate the algorithm. In the EKF, a reliable dynamic model was adapted to reduce the probability of divergence that can be caused by large errors in the initial state.
提出了一种实用算法，用于在全球定位系统（GPS）卫星可见性稀疏的情况下，利用来自GPS接收机的单历元测量值确定地球静止轨道（GEO）卫星的轨道。即使在无法应用经典单点定位（SPS）的情况下，该算法也使用状态向量的三个分量来确定卫星的状态。通过考虑GEO轨道要素和GPS测量的特性，状态向量的分量减少到三个。然而，该算法对GEO卫星仍具有足够的精度。所开发的算法在两颗或三颗GPS卫星的模拟测量值上进行了测试，发现即使在无法获得经典SPS解的情况下，计算出的最大位置误差在几何范围内也小于约40公里，甚至只有几公里。此外，还对具有估计初始状态的GEO卫星进行了扩展卡尔曼滤波器（EKF）测试，以验证该算法。在EKF中，采用了可靠的动力学模型来降低因初始状态的大误差而导致发散的概率。
