前后向子分段相位差频率估计法

为提高直接频率估计法的精度并推导出估计误差方差的闭合表达式,本文提出基于前后向子分段相位差的直接频率估计法. 该方法对样本的前向和后向两个子段做快速傅里叶变换,再提取这两个子段变换后的峰值谱相位差而获得频率估计. 本文证明了该估计器具有无偏性,并推导出其频率估计方差的闭合理论表达式. 仿真实验验证了该闭合表达式的正确性,故本文方法具有更高的测频精度和广泛的应用前景. 关键词： 频率估计 前后向子段 相位差 克拉美罗限

A novel phase difference frequency estimator based on forward and backward sub-segmenting

In engineering applications, many measurements of physical quantities can be converted into the problems of frequency estimation. The current frequency estimators are mainly divided into two categories: iterative approaches and direct approaches. However, iterative approaches are not suitable for rapid physical measurement occasions due to its complicated process. But most of the direct approaches are the biased estimators, which are incapable of providing quantitative estimates of variance expression. To enhance the accuracy of the direct frequency estimator and derive the closed-form theoretic expression of the estimated error variance, this paper proposes a novel phase difference frequency estimator based on the forward and backward sub-segmenting. This estimator implements forward and backward fast Fourier transform (FFT) on the given samples separately, and then extracts the phase difference from the peak FFT bins of these two sub-segments to estimate the frequency. And it is emphasized that the proposed method is an unbiased frequency estimator, whose closed-form theoretic expression of the frequency estimated error variance is also derived. Moreover, simulation not only verifies the correctness of this closed-form expression but also proves that the proposed frequency estimator's mean square error is closer to the Cramer-Rao lower bound than that of apFFT/FFT phase difference estimator and Candan estimator. In conclusion, the proposed estimator has higher accuracy in measuring frequencies and has a wide application prospect.
Keywords： frequency estimation forward and backward sub-segment phase difference CRLB