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一种估计多信号频率的快速子空间方法
郭红丹
0
((永城职业学院 电子信息工程系,河南 永城 476600))
摘要:
多重信号分类(Multiple Signal Classification,MUSIC)法在估计多信号频率时需要对采样数据序列的自相关矩阵进行特征值分解,并准确划分出信号和噪声子空间,使得其计算量比较大。利用自相关矩阵的Toeplitz特性快速计算其逆矩阵,通过计算逆矩阵的多次幂来逼近噪声子空间,避免了MUSIC法的特征值分解和估计信号个数的过程。在谱峰搜索环节,采用先粗估计频率值再在小区间进行精细搜索的策略,能够避免搜索无用的频率范围。计算量比较分析以及与理论克拉美罗界(Cramer-Rao Bound,CRB)的对比验证结果表明,快速方法性能与MUSIC法相当,能够较好地逼近CRB,且计算量更小,适合实时性要求高的应用场合。
关键词:  频率估计  MUSIC法  噪声子空间
DOI:
基金项目:河南省教育厅重点科研项目(14B880032);河南省教育厅人文社会科学研究项目(2020-ZDJH-392)
A fast subspace method for estimating multisignal frequency
GUO Hongdan
((Department of Electronic and Information Engineering,Yongcheng Vocational College,Yongcheng 476600,China))
Abstract:
Multiple signal classification(MUSIC) method needs to decompose the eigenvalue of the autocorrelation matrix of the sampled data sequence and accurately divide the signal and noise subspace,which makes the computation of the MUSIC method larger.The inverse matrix is quickly calculated by the Toeplitz characteristic of the autocorrelation matrix,and the noise subspace is approximated by calculating the multiple power of the inverse matrix,thus avoiding the process of the eigenvalue decomposition of the MUSIC method and estimation process of the number of signals.In the process of spectral peak search,using fast Fourier transform(FFT) to roughly estimate the frequency value and then search accurately in a small frequency range can avoid searching the useless frequency range.The comparison of computational complexity and the comparison with the theoretical Cramer-Rao Bound(CRB) show that the performance of the new method is equivalent to that of the MUSIC method,and it can approximate the CRB accurately,the amount of calculation is smaller,so it is suitable for applications with high real-time requirements.
Key words:  frequency estimation  MUSIC method  noise subspace
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