Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids
Efficient and Accurate Detection and Frequency Estimation of Multiple Sinusoids
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DOI：
10.1109/access.2018.2886397
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发表时间：
2019-01-01
期刊：
影响因子：
3.9
通讯作者：
Popovic-Bugarin, Vesna
中科院分区：
文献类型：
--
作者：
Djukanovic, Slobodan;Popovic-Bugarin, Vesna
提出了加性高斯白噪声中复正弦波的检测及其频率估计的方法。它包含两个阶段：1）正弦检测（模型阶数估计）和粗频率估计，2）精细频率估计。所提出的方法在频域中运行，即它使用离散傅里叶变换（DFT）作为主要工具。执行正弦波检测，以便提供固定的误报概率（内曼-皮尔逊准则）。对于粗略和精细频率估计，都使用三点周期图最大化方法。对可变信噪比、正弦曲线之间的可变频率位移以及与频率网格的可变偏移进行仿真。所提出的方法满足频率估计中的 Cramer-Rao 下界，并且除了非常小的位移值之外实际上不依赖于频率位移。就模型阶数估计精度而言，它优于最先进的方法。该方法中最昂贵的操作是 DFT 的计算。因此，就计算复杂度而言，所提出的方法与最有效的多频率估计算法相当。
The method for detection of complex sinusoids in additive white Gaussian noise and estimation of their frequencies is proposed. It contains two stages: 1) sinusoid detection (model order estimation) and coarse frequency estimation, and 2) fine frequency estimation. The proposed method operates in the frequency domain, i.e., it uses the discrete Fourier transform (DFT) as the main tool. Sinusoid detection is performed so that a fixed probability of false alarm is provided (Neymann-Pearson criterion). For both coarse and fine frequency estimations, the three-point periodogram maximization approach is used. Simulations are carried out for variable signal-to-noise ratio, variable frequency displacement between the sinusoids and variable offset from the frequency grid. The proposed method meets the Cramer-Rao lower bound in frequency estimation and practically does not depend on the frequency displacement except for very small displacement values. In terms of model order estimation accuracy, it outperforms the state-of-the-art approaches. The most expensive operation in the method is the calculation of the DFT. Therefore, in terms of calculation complexity, the proposed method is on par with the most efficient algorithms for multiple frequency estimations.