基于前后向子分段和频移补偿的频率与相位联合估计器

A forward and backward sub-segmenting frequency-phase joint estimator base on frequency shift compensation

频率估计和相位估计是物理学中的两个基本的测量问题。现有的估计器难以对这两个参数实现高精度的联合测量。为实现联合测量,对已有前后向子分段频率估计器做如下两方面改进:(1)对前、后向子分段快速傅里叶变换(Fast Fourier Transform,FFT)谱峰相位值做平均,获得中心样点的瞬时相位估计;(2)引入频移补偿措施,使得前、后向子分段的峰值谱能量更为集中,增强了估计器抵御噪声的能力,同时提升了估计器的频率和相位估计精度。理论分析和仿真实验表明,该联合估计器性能高于原有前后向子分段估计器和全相位FFT/FFT相位差估计器,对于频率偏离情况,其频率估计方差为克拉美-罗限的4/3倍,其相位估计方差可达到克拉美-罗限。

Frequency estimation and phase estimation are two basic measurement problems in physics.However,the existing estimators can hardly achieve high-accuracy joint estimation of these two parameters.To acquire the joint estimation,two aspects of improvement have been made on the original forward and backward sub-segmenting frequency estimator.On one hand,averaging the phase spectra of the peak fast fourier transform(FFT) bins of the forward subsegment and the backward sub-segment yields an estimate of the middle sample's instantaneous phase;on the other hand,frequency shift and compensation was introduced to concentrate the energy of the peak FFT bins of the aforementioned two sub-segments,which enhances the joint estimator's resistance to noise and thus improves the accuracy.Both theoretical analysis and numerical simulation confirm that,the performance of the proposed joint estimator is superior to that of the original forward and backward sub-segmenting estimator and all-phase FFT/FFT phase difference estimator.For frequency offset cases,the frequency estimation variance of the proposed joint estimator is only 4/3 times of the Cramer-Rao lower Bound,and its phase estimation variance can reach the Cramer-Rao lower Bound.