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.