基于球谐变换的无人机蜂群RCS快速分析算法

为了获取目标的雷达截面积(Radar Cross Section,RCS),传统的方法是采用矩量法(Method of Moment,MOM)或多层快速多极子方法(Multi-level Fast Multipole Algorithm,MLFMA),尽管对目标的RCS计算精确,但其要求计算机的存储量大且计算耗时。而对于由上百成千个小型无人机组成的无人机蜂群而言,若采用上述方法来计算其RCS,计算量巨大,甚至无法计算。针对上述问题,提出了采用球面波展开技术与球谐变换相结合的方法来提升对无人机蜂群RCS的仿真效率,其关键技术是通过改变球谐函数中的求和次序,利用快速傅里叶变换来计算偏心球面上离散点的电场分布。数值实例表明,相比于高精度的MLFMA,所提方法获取蜂群无人机RCS的结果与其吻合良好,但对计算机内存的需求远远小于MLFMA,且随着无人机数量的增加,其计算速度可提升几个数量级。

A Fast RCS Analysis Algorithm for Drone Swarm Based on Spherical Harmonic Transformation

In order to obtain the radar cross section(RCS)of the target,the traditional methods are the moment method(MOM)or the multilevel fast multipole algorithm(MLFMA).Although the methods above are accurate in calculating the RCS of target,they require large amount of memory and time-consuming calculation.For the drone swarm composed of hundreds of thousands of small unmanned aerial vehicles(UAVs),the calculation amount is huge and even impossible by above methods.To solve the problems,a method combining spherical wave expansion technology and spherical harmonic transformation is proposed to improve the simulation efficiency of RCS of the drone swarm.The key point is computing the electric field on an eccentric sphere efficiently by changing the order of the summation of the spherical harmonic functions and then using fast Fourier transform.Numerical examples show that compared with the high-precision MLFMA,the RCS obtained by the method proposed is in good agreement with the result,but the demand for computer memory is far less than that of MLFMA.Moreover,with the increase of the number of UAV,the calculation speed can be improved by several orders of magnitude.