基于简化差分插值滤波的编队卫星相对导航

Relative Navigation for Spacecraft Formation Based on Simplified Divided Difference Filter

将一种基于Stirling内插公式的非线性差分插值滤波(Divided Difference Filter-DDF)算法的简化形式(Simplified Divided Difference Filter-SDDF)应用到编队卫星相对导航中.该算法通过对非线性系统方程进行多项式展开并取有限差分插值项进行近似.数值仿真结果表明:该算法相对于EKF(Extended Kalman Filter)算法有明显的优势,有较高的滤波精度、更快的收敛速度和较好的稳定性,其中相对位置估计相比EKF提高79%、相对速度提高52%,对编队卫星相对导航具有一定应用价值.

A simplified version of the nonlinear divided difference filter （DDF） algorithm based on Stirling＇ s interpolation formula called simplified divided difference filter （SDDF） was applied to relative navigation for spacecraft formation, using a limited divided difference items of the Taylor＇s expansions as an approximation to the real nonlinear system equations. Numerical simulation results indicate that the SDDF filter algorithm has the obvious advantages than that of the EKF, including the higher navigation precision, fas ter convergence and better stability; the accuracy improvement of the SDDF compared with the EKF are 79% and 52% for relative position and velocity. This algorithm can be applied to relative navigation for spacecraft formation flying and is worthy of application.