实值闭式求根快速阵列测向算法

Fast array direction finding algorithm based on real-valued closed-form rooting

摘要:

谱峰搜索类多重信号分类MUSIC(multiple signal classification,MUSIC)算法作为测向算法中的经典算法,由于具有良好的参数估计性能,因此被广泛使用.但由于庞大的计算量,提高了测向系统的复杂度以及研发成本.相比之下,利用多项式求根获取目标信源方位信息的求根MUSIC(root multiple signal classification,root-MUSIC)算法降低了测向的计算复杂度.但由于root-MUSIC算法涉及复系数多项式求根运算,因此其计算量依然很大.为进一步有效降低算法的计算量,本文基于空间谱函数的极值处导数为零这一性质,提出一种基于实系数多项式闭式求根的快速阵列测向算法.所提算法利用坐标映射关系,在新的坐标系u域内构造一个与传统z域root-MUSIC算法同阶次的实系数求根多项式.同时,由于多项式的根关于实轴对称,利用Bairstow算法进一步将该实系数多项式分解为若干个二次多项式,最后利用一元二次方程求根公式直接给出对目标信源方位信息的估计结果.理论分析和仿真实验表明:新算法相比于传统root-MUSIC算法极大降低了计算量,提高了测向速度,同时保持了相同的估计精度.

Abstract:

Multiple signal classification (MUSIC) algorithm by peak searching is a classical algorithm in direction finding algorithm, which has been widely used because of its good parameter estimation performance, while it needs huge amounts of calculation, which increases the complexity of the direction finding system and the development cost. In contrast, root-MUSIC algorithm that utilizes polynomial rooting to obtain the target source direction information can reduce the computational complexity of the direction finding. However, root-MUSIC algorithm involves complex-valued coefficient polynomial rooting operation, and its complexity is still high. To further effectively reduce complexity, a novel fast array direction finding algorithm based on the real-valued coefficient polynomial closed root finding was proposed. By utilizing coordinate mapping technique as well as the fact that the derivatives with respect to the extreme values of the MUSIC spectrum equal to zero, a new polynomial in the domain with the same order as root-MUSIC in the domain was constructed. Since roots of the polynomial were found symmetric about the real axis, the new polynomial could be further decomposed into several quadratic polynomials by exploiting Bairstow’s method. Consequently, the target source direction information could be estimated by finding the roots of those quadratic polynomials with closed forms. Theoretical analysis and numerical simulation results show that the calculation complexity of the proposed method was significantly reduced compared with the standard root-MUSIC, and the direction finding speed was improved as the estimate accuracy remained the same.