基于无奇点根数的空间相对导航插值滤波算法

Interpolation Filtering for Relative Navigation in Space Based on Non-Singularity Orbit Elements

为了提高椭圆轨道航天器的相对导航精度,将基于Stirling公式的多项式插值滤波方法(DDF2)引入导航算法,降低了传统的卡尔曼滤波方法中泰勒级数展开线性化造成的误差,有效提高了相对导航滤波精度;算法将无奇点根数引入系统状态方程作为状态变量,推导了相对无奇点根数到相对位置和相对速度的转换公式,避免了开普勒轨道根数容易产生的奇异性问题。同传统的C-W方程相比,本方法无需假设航天器是正圆轨道,更加适用于考虑地球J2项摄动的情况。以星间相对距离和角度作为观测量,数值仿真比较了UKF算法和多项式插值滤波方法的性能,仿真结果表明,采用同样的sigma点选取策略,且运算复杂度相当的条件下,本方法具有更高的精度和稳定性。

In order to improve the relative navigation accuracy of spacecrafts with elliptical orbit, the polynomial interpolation based on Stirling formula is applied to decrease the model error caused by Taylor expansion linearization in traditional Kalman filter, thus improving relative navigation accuracy effectively. The non-singularity orbit elements are applied as the state variables in the state equation, the transform formulas between relative non-singularity orbit elements and relative position（velocity） between spacecrafts are also derived, so that the singular points are avoided in the Kepler＇ s elements. Compared with the traditional C-W formula, the non-singularity formula is more suitable without any restriction of eccentricity. Taking the relative distance, azimuth and elevation between spacecrafts as measurement vectors, validity of UKF and polynomial interpolation is compared by using the same principal of sigma-point selecting method and approximate computational load, the polynomial interpolation is proved to be more accurate and stable by using the numerical simulation results.