一种基于压缩感知的三维导体目标电磁散射问题的快速求解方法

提出了一种将压缩感知和特征基函数结合的方法来计算三维导体目标的雷达散射截面.利用压缩感知理论,将随机选择的矩量法阻抗矩阵作为测量矩阵,将激励电压视为测量值,然后再用恢复算法可实现二维或二维半目标感应电流的求解.对于三维导体目标,使用Rao-Wilton-Glisson基函数表示的感应电流在常用的离散余弦变换基、小波基等稀疏基上不稀疏.为此,本文将计算出的目标特征基函数作为稀疏基,用广义正交匹配追踪算法作为恢复算法来加速恢复过程,并应用到三维导体目标的雷达散射截面计算中.数值结果证明了本文方法的准确性与高效性.

Compressed sensing based fast method of solving the electromagnetic scattering problems for threedimensional conductor targets

The method of moments is one of the most commonly used algorithms for analyzing the electromagnetic scattering problems of conductor targets. However, it is difficult to solve the matrix equation when analyzing the electromagnetic scattering problem of the electric large target. In recent years, the theory of the compressed sensing was introduced into the method of moments to improve the computation efficiency. The random selected impedance matrix is used as a measurement matrix, and the excitation voltage is used as a measurement value when using compressed sensing theory. The recovery algorithm is used to solve the induced current of target. The method can avoid the inverse problem of matrix equation and improve the computational efficiency of the method of moments, but it can be applied only to 2-dimensional or 2.5-dimensional target. The application of compressed sensing needs to know the sparse basis of the current in advance, but the induced current of three-dimensional target which is expressed by an Rao-Wilton-Glisson basis function is not sparse on the commonly used sparse basis, such as discrete cosine transform basis and discrete wavelet basis. To solve this problem, a method of combining compressed sensing with characteristic basis functions is proposed to analyze the electromagnetic scattering problem of three-dimensional conductor target in this paper. The characteristic basis function method is an improved method of moments. The target is divided into several subdomains, the main characteristic basis functions are comprised of current bases arising from the self-interactions within the subdomain, and the secondary characteristic basis functions are obtained from the mutual coupling effects of the rest of the subdomains. Then a reduction matrix is constructed to reduce the order of matrix equation, and the current can be expressed by the characteristic basis function and its weighting coefficient. In the method presented in this paper, the weighting coefficient is considered as a sparse vector to be solved when the characteristic basis function is used as sparse basis. The number of weighting coefficients is less than the number of unknown ones, so it can be obtained from the compressed sensing recovery algorithm. At the same time, the generalized orthogonal matching pursuit algorithm is used as the recovery algorithm to speed up the recovery process. Finally, the proposed method is used to calculate the radar cross sections of a PEC sphere, nine discrete PEC targets and a simple missile model. The numerical results validate the accuracy and efficiency of the method.