基于分数阶共变的有色谐波信号频谱估计

Spectrum Estimation of Colored Harmonic Signal Based on Fractional Order Covariation

在alpha稳定分布噪声下,传统的谐波信号的频谱估计方法会失去其韧性。本文简要分析了分数阶共变矩阵的结构,在此基础上提出了基于分数阶统计量的谐波信号的频谱估计新方法:基于分数阶共变的Pisarenko谐波分解(FOC-PHD)算法和多信号分类法(FOC-MUSIC)算法。这种方法将信号频谱估计的范围从二阶矩扩大到p阶矩(1<p<α≤2)。通过对给定的alpha稳定分布噪声中正弦信号的估计与分辨进行仿真,详细比较了传统的谐波信号频谱估计和FOC-PHD、FOC-MUSIC频谱估计算法的性能,仿真结果表明,本文提出的方法明显优于传统的频谱估计算法,具有良好的韧性。

Under the alpha stable distribution noise , the convential harmonic signal spectrum estimate algorithm would lose its capability. This paper briefly analyzes the frame of fractional order covariation, proposes some new methods for frequency estimation under alpha-stable noise conditions： Fractional Order Covariation Pisarenko harmonic decomposition （FOC-PHD） and Fractional Order Covariation Multiple Signal Classification （FOC-MUSIC）. This method extends the range from 2 to p （l〈p〈a~_2）. By estimating the sinusoidal signals embedded in the a stable noise, the convential harmonic signal spectrum estimate algorithm and FOC-PHD, FOC-MUSIC algorithm are compared in detail. Simulation results show that the new methods are robust, and their resolution capability and probability of resolution are better than conventional algorithm.