基于粒子群算法的极短弧定轨

Particle Swarm Optimization for Initial Orbit Determination with Too-Short-Arc

针对经典的初轨计算方法在极短弧定轨中不适用的情况,建立了一种基于粒子群算法的极短弧(TooShort-Arc,TSA)定轨的计算方法。该方法将问题转化为两个三变量的分层优化问题,采用(a,e,M)作为优选变量,在保持问题维数较低的同时,实现了计算结果和观测资料的解耦。由于实测资料处理中的野值剔除方法不适用于粒子群算法,所以,采用稳健估计法,通过在适值函数中使用最小中值二乘准则,实现了稳健的极短弧计算方法。同时,应用MATLAB计算软件,选用缺省参数实现该算法,以进行数据验证。基于实测数据的数值验证表明,方法对于近圆轨道目标30s以下的弧段仍可以获得有效的结果,10s弧段误差仅为16km。此精度满足后续处理的需要,且方法稳健,具有很高的崩溃点。

A new method of Initial Orbit Determination （IOD） for too-short-arc （TSA） using PSO （Particle Swarm Optimization） is established as the traditional methods are not applicable. In the method, IOD is reduced to a two-stage hierar-chical optimization problem containing three variables for each stage so that （a, e, M） is regarded as a variable of the optimization. Moreover, optimization brings about decoupling from observation data when the number of dimensions of the problem keeps low. Because of the difference of computing processes between PSO and the classical method, methods for outliers editing are not applicable. To get a robust estimate for PSO, a robust estimation method is used t;y adopting least median square in the fitness function. The algorithm is programmed with MATLAB using default values. Numerical experiments based on real measurements show that for near circular orbit, the method provides valid initial values for 30 s arc length and even shorter, and the error of 10 s arc is only 16 km. The accuracy meets the requirements of post-processing. Meanwhile, the algorithm is robust and has a high breakdown point.