椭圆轨道航天器相对导航的多项式插值滤波算法

Polynomial Interpolation Filtering for Relative Navigation of Spacecraft on Elliptical Orbit

针对运行于椭圆轨道的航天器的相对自主导航问题,建立了惯性坐标系下的近距离相对运动方程,方程中没有圆轨道的假设,相对Clohessy-Wiltshire(C-W)方程具有更广的应用范围。将二阶多项式插值(Divided Difference 2,DD2)滤波应用于相对导航算法中,和扩展卡尔曼滤波(Extended Kalman Filter,EKF)相比,前者不需要对状态方程组进行微分处理,且对非线性函数统计特性近似到二阶程度。数值仿真比较了DD2滤波和EKF两种算法的性能,验证了利用惯性坐标系下的近距离相对运动方程实现相对导航的可行性,并分析了主动航天器的轨道和姿态确定误差对相对导航精度的影响。

According to Kepler orbit motion, the short distance relative dynamics equations of spacecrafts were obtained in the inertial frame. Compared with Clohessy-Wiltshire （C-W） equations, these equations were adaptable to the spacecrafts on the elliptical orbit because of no restriction for eccentricity. To avoid the Taylor linearization, the divided difference 2 （DD2） filtering used polynomial interpolation to parameterize the first two moments of a probability distribution. For the determination of the spacecrafts relative position and relative velocity, the DD2 filtering was more accurate and easier to implement than the extended Kalman filtering（EKF）. The simulation results validate the availability of the relative navigation algorithm based on DD2 filtering.