基于自适应卡尔曼滤波的简化地磁定轨

Simplified geomagnetic orbit determination based on adaptive Kalman filter

地磁定轨对追求低成本、高功能密度比的微小卫星具有较重要的价值,但是目前地磁定轨尚存在计算量大、易受各类误差影响导致精度过低等不足。在分析轨道动力学方程误差量级的基础上,建立了简化的状态转移矩阵,根据地磁模型分析了地磁强度随着阶次变高,梯度显著变小的特点,提出了高阶截断的简化地磁测量方程;将复杂的磁强计测量误差近似建模成随机游走形式,用多项式对磁强计误差估计值进行实时拟合去噪,并辨识出磁强计误差的变化特征作为自适应卡尔曼滤波器的调节依据,提高了弱可观测地磁定轨的性能。数学仿真证明了简化地磁定轨模型的有效性,自适应滤波器能够更精确地实现定轨计算,定位精度约为6 km,测速精度约为4 m/s。

Geomagnetic orbit determination is important for small satellites to realize low cost and high power/density ratio, but it has disadvantages such as large amount of calculation and insufficient precision due to various error sources. In this paper, a simplified state transition matrix is established based on the analysis of the orbital dynamics equation. In view that the geomagnetic gradient decreases significantly with higher order geomagnetic model, a simplified measurement equation with higher-order truncation is put forward. The complex magnetometer error is approximately modeled as random walk, and then a polynomial fitting method is employed to de-noise the magnetometer error estimate in real-time. The performance of the weak observable geomagnetic orbit determination is improved by an adaptive Kalman filter regulated by the magnetometer error variation characteristics which is identified from the de-noised estimate. Mathematical simulations verify the validity of the simplified geomagnetic orbit determination model, and the adaptive filter can more accurately achieve orbit calculation, in which the location and speed precisions are about 6 km and 4 m/s, respectively.