东北大学学报（自然科学版）

东北大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (4): 457-463.DOI: 10.12068/j.issn.1005-3026.2022.04.001

• 信息与控制 •    下一篇

一种高精度低复杂度的改进Root-MUSIC算法

佘黎煌， 刘平凡， 张石， 许方晗   

  1. (东北大学 计算机科学与工程学院， 辽宁 沈阳110169)
  • 修回日期:2021-02-01 接受日期:2021-02-01 发布日期:2022-05-18
  • 通讯作者: 佘黎煌
  • 作者简介:佘黎煌(1980-)，男，福建莆田人，东北大学讲师，博士； 张石(1963-)，男，辽宁抚顺人，东北大学教授，博士生导师.
  • 基金资助:
    中央高校基本科研业务费专项资金资助项目(N182410001).

An Improved Root-MUSIC Algorithm with High Precision and Low Complexity

SHE Li-huang， LIU Ping-fan， ZHANG Shi， XU Fang-han   

  1. School of Computer Science & Engineering， Northeastern University， Shenyang 110169， China.
  • Revised:2021-02-01 Accepted:2021-02-01 Published:2022-05-18
  • Contact: SHE Li-huang
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摘要： 针对目前多数低复杂度Root-MUSIC算法的精度损失问题，研究并提出了一种具备精度补偿能力的低复杂度Root-MUSIC算法.该算法依据有限快拍数得到的近似数据观测矩阵首行重构具有Toeplitz形态的自相关矩阵，使重构的自相关矩阵具备Hermitian性;对重构的自相关矩阵特征值分解后获得噪声子空间，并将噪声子空间翻转拆分，重构新的求根多项式，进而通过求根方法得到DOA估计值.本文算法通过Toeplitz矩阵重构及求根多项式降阶，不但有效提高了改进Root-MUSIC算法的DOA估计精度，同时改进算法的时间复杂度不高于前人算法;在不同的入射信源及采样快拍数下，本文算法表现出更强的鲁棒性和稳定性.

关键词: Root-MUSIC算法;精度损失;重构Toeplitz矩阵;噪声子空间;翻转拆分;求根多项式降阶;鲁棒性和稳定性

Abstract: Aiming at the precision loss problem of most low-complexity Root-MUSIC algorithms at present， a low-complexity Root-MUSIC algorithm with precision compensation ability is studied and proposed. The algorithm reconstructs the autocorrelation matrix with Toeplitz shape according to the first row of the approximate data observation matrix obtained by finite snapshots， so that the reconstructed autocorrelation matrix has Hermitian property. After decomposing the reconstructed autocorrelation matrix， the noise subspace is obtained， the noise subspace is flipped and split， a new root-finding polynomial is reconstructed， and then the DOA estimated value is obtained by the root-finding method. The algorithm proposed in this paper using Toeplitz matrix reconstruction and root polynomial reduction effectively improves the DOA estimation accuracy of the improved Root-MUSIC algorithm. And the time complexity of the improved algorithm is no higher than that of previous algorithms. Under different incident sources and sampling snapshots， the algorithm proposed in this paper also shows stronger robustness and stability.

Key words: Root-MUSIC algorithm; precision loss; reconstructing Toeplitz matrix; noise subspace; flip and split; root polynomial reduction; robustness and stability

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