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中文摘要：
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。
英文摘要：
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.
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