基于前后向子分段和频移补偿的频率与相位联合估计器

PDF(1094 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (16) : 207-211.

论文

黄翔东, 靳旭康, 白瑞朋

作者信息 +

Forward and Backward Sub-segmenting Frequency-Phase Joint Estimator base on Frequency Shift Compensation

Xiang-Dong Huang Xu-Kang Jin Rui-Peng Bai

Author information +

文章历史 +

摘要

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：第一，对前、后向子分段FFT谱峰相位值做平均，获得中心样点的瞬时相位估计；第二，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。

Abstract

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 FFT bins of the forward sub-segment and the backward sub-segment yields an estimate of the middle sample’s instantaneous phase; On the other hand, frequency shift and compensation is 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 theoretic 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.

导出引用

黄翔东, 靳旭康, 白瑞朋 . 基于前后向子分段和频移补偿的频率与相位联合估计器[J]. 振动与冲击, 2017, 36(16): 207-211

Xiang-Dong Huang Xu-Kang Jin Rui-Peng Bai. Forward and Backward Sub-segmenting Frequency-Phase Joint Estimator base on Frequency Shift Compensation[J]. Journal of Vibration and Shock, 2017, 36(16): 207-211

参考文献

[1] 青海银，张援农，周晨，等. 基于MST雷达垂直风速的大气温度剖面反演[J]. 物理学报, 2014, 63(9): 094301-1-094301-7.
QING Hai-yin, ZHANG Yuan-nong, ZHOU Chen, et al. Atmospheric temperature profiles estimated by the vertical wind speed observed by MST radar [J]. Acta Physica Sinica, 2014, 63(9): 94301-094301.
[2] Zhang Y D, Amin M G, Himed B. Joint DOD/DOA estimation in MIMO radar exploiting time-frequency signal representations [J]. EURASIP Journal on Advances in Signal Processing, 2012, 2012(1): 1-10.
[3] 李传江，张自强，费敏锐，等. 微速差双转子系统不平衡信号提取方法[J]. 振动与冲击, 2013, 32(14): 29-33.
LI Chuan-jiang, ZHANG Zi-qiang, FEI Min-rui, et al. Extraction method for unbalanced signal in a dual-rotor system with little rotating speed difference [J]. Journal of Vibration and Shock, 2013, 32(14): 29-33.
[4] Zibar D, De Carvalho L H H, Estaran J, et al. Joint iterative carrier synchronization and signal detection employing expectation maximization [J]. Journal of Lightwave Technology 2014, 32(8): 1608-15.
[5] Singh M, Khadkikar V, Chandra A, et al. Grid interconnection of renewable energy sources at the distribution level with power-quality improvement features[J]. IEEE Transactions on Power Delivery, 2011, 26(1): 307 - 15.
[6] Wang L, Jiang Q, Hong L, et al. A novel phase-locked loop based on frequency detector and initial phase angle detector [J]. IEEE Transactions on Power Electronics, 2013, 28(10): 4538-49.
[7] 杨殿阁, 罗禹贡, 李兵, 等. 基于时域多普勒修正的运动声全息识别方法 [J]. 物理学报, 2010, 59(7): 4738-47.
YANG Dian-ge, LUO Yu-gong, LI Bing, et al. Acoustic holography method for measuring moving sound source with correction for Doppler effect in time-domain [J]. Acta Physica Sinica, 2010, 59(7): 4738-47.
[8] 梁美彦, 张存林. 相位补偿算法对提高太赫兹雷达距离像分辨率的研究[J]. 物理学报, 2014, 63(14): 148701-05.
LIANG Mei-yan, ZHANG Cun-lin. Improvement in the range resolution of THz radar using phase compensation algorithm [J]. Acta Physica Sinica, 2014, 63(14): 148701-05.
[9] Rife D, Boorstyn R. Single tone parameter estimation from discrete-time observations[J]. IEEE Transactions on Information Theory, 1974, 20(5): 591-8.
[10] Candan C. Analysis and further improvement of fine resolution frequency estimation method from three DFT Samples[J]. IEEE Signal Processing Letters, 2013, 20(9): 913-6.
[11] Aboutanios E, Mulgrew B. Iterative frequency estimation by interpolation on Fourier coefficients[J]. IEEE Transactions on Signal Processing, 2005, 53(4): 1237-42.
[12] Macleod M D. Fast nearly ML estimation of the parameters of real or complex single tones or resolved multiple tones[J]. IEEE Transactions on Signal Processing, 1998, 46(1): 141-8.
[13] 王凤鹏，邹万芳，尹真，等. 希尔伯特变换实时全息干涉条纹相位提取 [J]. 光电工程, 2009, 36(4): 92-6.
WANG Feng-peng, ZOU Wan-fang, YI Zhen, et al. Phase extracting for real-time holographic interferometry fringe pattern based on hilbert transform [J]. Opto-Electronic Engineering, 2009, 36(4): 92-6.
[14] 沈廷鳌，涂亚庆，李明，等. 基于相关原理的相位差测量改进算法及应用 [J]. 振动与冲击, 2014, 33(21): 177-182.
SHEN Ting-ao, TU Ya-qing, LI Ming, et al. An improved method for phase difference measurement based on correlation theory [J]. Journal of Vibration and Shock, 2014, 33(21): 177-182.
[15] 丁康, 钟舜聪. 通用的离散频谱相位差校正方法[J]. 电子学报, 2003, 31(1): 142-145.
DING Kang, ZHONG Shun-cong. A universal phase diference correcting methods on discrete spectrum [J]. Acta Electronic Sinica, 2003, 31(1): 142-5.
[16] 毛育文, 涂亚庆, 肖玮, 等. 离散密集频谱细化分析与校正方法研究进展[J]. 振动与冲击, 2012, 31(21): 112-119.
MAO Yu-wen, TU Ya-qing, XIAO Wei, et al. Advances and trends of study on discrete intensive frequency spectrum zooming analysis and correction methodology [J]. Journal of Vibration and Shock, 2012, 31(21): 112-9.
[17] 齐国清, 贾欣乐. 插值 FFT 估计正弦信号频率的精度分析[J]. 电子学报, 2004, 32(4): 625-9.
QI Guo-qing, JIA Xin-le. Accuracy analysis of frequency estimation of sinusoid based on interpolated FFT [J]. Acta Electronic Sinica, 2004, 32(4): 625-9.
[18] Novotny M, Slepicka D, Sedlacek M. Uncertainty analysis of the RMS value and phase in the frequency domain by noncoherent sampling [J]. IEEE Transactions on Instrumentation and Measurement, 2007, 56(3): 983-989.
[19] 黄翔东, 王兆华. 基于全相位频谱分析的相位差频谱校正法[J]. 电子与信息学报, 2008, 30(2): 293-297.
HUANG Xiang-dong,WANG Zhao-hua. Phase difference correcting sepctrum method based on all-phase spectrum analysis [J]. Journal of Electronics and Information Technology, 2008, 30(2): 293-7.
[20] 黄翔东, 王博, 杜宇彬, 等. 全相位 FFT 测相方差及其 Cramer-Rao 下限[J]. 数据采集与处理, 2013, 28(2): 161-165.
HUANG Xiang-dong, WANG Bo, DU Yu-bin, et al. Variance of all-phase FFT measuring phases and its Cramer-Rao lower bound [J]. Journal of Acquisition and Processing, 2013, 28(2): 161-5.
[21] 黄翔东, 孟天伟, 丁道贤, 等. 前后向子分段相位差频率估计法[J]. 物理学报, 2014, 63(21): 204304-1-214304-7.
HUANG Xiang-dong, MENG Tian-wei, DING Dao-xian, et al. A novel phase difference frequency estimator based on forward and backward sub-segmenting [J]. Acta Physica Sinica, 2014, 63(21): 204304-1-14304-7.