基于滑窗数据和过零检测的正弦频率估计新方法
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摘要
过零检测法计算量小、实现方便,在正弦信号频率估计中有着广泛应用,但是在频率估计时易受随机噪声影响。为降低随机噪声对频率估计性能的影响,提出一种基于滑窗数据和过零检测的正弦频率估计新方法。首先,利用观测数据构造出多组滑窗数据,并应用过零检测法,获得多组频率预估计结果;然后通过门限处理剔除掉预估计结果中的频率野值点;最后将频率均值作为最终的估计结果。详细讨论了数据长度、滑动次数、相邻2次滑动的点数、采样频率等因素对频率估计的影响,结果表明新方法能够改善正弦信号的频率估计性能,数值仿真和实测数据均验证了其有效性。
Although the zero crossing detection algorithm is being applied widely in frequency estimation of a single sinusoid for its low computation and for the convenience of realization,the zero crossing method is easily effected by the stochastic noise in the frequency estimation performance. In order to solve this problem, a new method is presented based on moving window data and zero crossing detection. Firstly, the multi-groups moving window data are obtained from the observation data; Secondly, the pre-estimated frequency values are obtained by using the zero crossing detection algorithm in multi-groups moving window data; Then, the outliers of frequency values are removed by threshold processing. Finally, the average value is confirmed as an estimated result. A series of frequency estimation factors are discussed in detail, such as data length, slipping times, adjoining sliding point number and sampling frequency. The result shows that the proposed method can improve the performance of frequency estimation. And the new method is feasible.
Although the zero crossing detection algorithm is being applied widely in frequency estimation of a single sinusoid for its low computation and for the convenience of realization,the zero crossing method is easily effected by the stochastic noise in the frequency estimation performance. In order to solve this problem, a new method is presented based on moving window data and zero crossing detection. Firstly, the multi-groups moving window data are obtained from the observation data; Secondly, the pre-estimated frequency values are obtained by using the zero crossing detection algorithm in multi-groups moving window data; Then, the outliers of frequency values are removed by threshold processing. Finally, the average value is confirmed as an estimated result. A series of frequency estimation factors are discussed in detail, such as data length, slipping times, adjoining sliding point number and sampling frequency. The result shows that the proposed method can improve the performance of frequency estimation. And the new method is feasible.
引文
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[16] 李夏,郭英,张坤峰,等.基于频移修正的线性方程频率估计算法[J].探测与控制学报,2015,37(4):66-71.LI X,GUO Y,ZHANG K F,et al.Modified Linear Equation Frequency Estimator Based on Frequency Shift[J].Journal of Detection & Control,2015,37(4):66-71.(in Chinese)
[17] 高瑞令,吴晓富,颜俊,等.改进的DFT正弦信号频率估计[J].信号处理,2014,30(9):1071-1077.GAO R L,WU X F,YAN J,et al.A Modified DFT-based Frequency Estimator for Sinusoidal Signals[J].Journal of Signal Processing,2014,30(9):1071-1077.(in Chinese)
[18] 殷波.正弦信号频率估计算法研究[D].哈尔滨:哈尔滨工程大学,2015.YIN B.Research on the Algorithm of Sinusoidal Frequency Estimation[D].Harbin:Harbin Engineering University,2015.(in Chinese)
[19] 张殿伦.舰船声学测速技术研究[D].哈尔滨:哈尔滨工程大学,2001.ZHANG D L.Research on Ship Acoustic Velocity Measurement Technology[D].Harbin:Harbin Engineering University,2001.(in Chinese)
[20] STEVEN M K.统计信号处理基础—估计与检测理论[M].罗鹏飞等,译.北京:电子工业出版社,2011.STEVEN M K.Fundamentals of Statistical Processing-Estimation and Detection Theory[M].Translated by LUO P F,et al.Beijing:Publishing House of Electronics Industry,2011.(in Chinese)
[2] LIU W,PIAO S C,GUO J Y,et al.Frequency Domain Polarization Weighted ESPRIT Method for Bearing Angle[J].Journal of Systems Engineering and Electronics,2014(5):769-775.
[3] STOCIA P,ERIKSSON A.MUSIC Estimation of Real-valued Sine-Wave Frequencies [J].Signal Processing,1995,42(2):139-146.
[4] FRIEDMAN V.A Zero Crossing Algorithm for the Estimation of the Frequency of a Single Sinusoid in White Noise [J].IEEE Trans SP,1994,42(6):1565-1569.
[5] PEI S C,TSENG C C.Adaptive IIR Notch Filter Based on Least Mean P-power Error Criterion [J].IEEE Trans Circuits Syst,1993,40(8):525-529.
[6] TEDESCO F,CASAVOLA A,FEDELE G.Unbiased Estimation of Sinusoidal Signal Parameters via Discrete-Time Frequency-Locked-Loop Filters[J].IEEE Transactions on Automatic Control,2017,62(3):1484-1490.
[7] FAN L,QI G.A New Synthetic Frequency Estimation Method of Sinusoid Based on Interpolated FFT[C]//Fifth International Conference on Instrumentation and Measurement,Computer,Communication and Control,Qinhuangdao,2015:1725-1729.
[8] ABOUTANIOS E.Estimating the Parameters of Sinusoids and Decaying Sinusoids in Noise[J].IEEE Instrumentation & Measurement Magazine,2011,14(2):8-14.
[9] PUNCHALARD R,WARDKEIN P.Linear Prediction Based Adaptive Algorithm for a Complex Sinusoidal Frequency Estimation[J].AEU-International Journal of Electronics and Communications,2013,67(6):521-527.
[10] 张世平,赵永平.一种改进的自适应格型陷波算法及其收敛性分析[J].电子学报,2004,32(2):338-341.ZHANG S P,ZHAO Y P.A Modified Adaptive Algorithm of Lattice Notch Filter and Its Convergence Analysis[J].Acta Electronica Sinica,2004,32(2):338-341.(in Chinese)
[11] 韩仲祥,夏靖波,王元一,等.高斯白噪声中单频复正弦信号频率估计新方法[J].空军工程大学学报(自然科学版),2003,4(3):68-71.HAN Z X,XIA J B,WANG Y Y,et al.A New Method for Frequency Estimation of Single Complex Sinusoid in White Gaussian Noise[J].Journal of Air Force Engineering University:Natural Science Edition,2003,4(3):68-71.(in Chinese)
[12] 柏果,程郁凡,唐万斌,等.利用DFT和迭代校正的正弦信号频率估计算法[J].信号处理,2017,33(12):1536-1541.BAI G,CHENG Y F,TANG W B,et al.A Frequency Estimation Algorithm of Sinusoidal Signal Capable of DFT and Iterative Correction[J].Journal of Signal Processing,2017,33(12):1536-1541.(in Chinese)
[13] 张威,李松,刘进忙,等.基于频差修正的余弦信号频率估计算法[J].传感器与微系统,2017,36(9):121-124.ZHANG W,LI S,LIU J M,et al.Frequency Estimation Algorithm for Cosine Signal Using Frequency-Offset Correction[J].Transducer and Microsystem Technologies,2017,36(9):121-124.(in Chinese)
[14] 谭钏章,李宏伟,樊昌周,等.基于LE和IIN算法的正弦信号频率估计算法[J].探测与控制学报,2017,39(4):119-123.TAN C Z,LI H W,FAN C Z,et al.Frequency Estimator of Sinusoid Signal Based on LE and IIN Algorithm[J].Journal of Detection & Control,2017,39(4):119-123.(in Chinese)
[15] 孙宏军,王小威.基于幅值-相角判据的修正Rife正弦波频率估计算法[J].天津大学学报(自然科学与工程技术版),2018,51(8):810-816.SUN H J,WANG X W.Modified Rife Algorithm for Frequency Estimation of Sinusoid Wave Based on Amplitude and Phase Criterion[J].Journal of Tianjin University:Science and Technology,2018,51(8):810-816.(in Cchinese)
[16] 李夏,郭英,张坤峰,等.基于频移修正的线性方程频率估计算法[J].探测与控制学报,2015,37(4):66-71.LI X,GUO Y,ZHANG K F,et al.Modified Linear Equation Frequency Estimator Based on Frequency Shift[J].Journal of Detection & Control,2015,37(4):66-71.(in Chinese)
[17] 高瑞令,吴晓富,颜俊,等.改进的DFT正弦信号频率估计[J].信号处理,2014,30(9):1071-1077.GAO R L,WU X F,YAN J,et al.A Modified DFT-based Frequency Estimator for Sinusoidal Signals[J].Journal of Signal Processing,2014,30(9):1071-1077.(in Chinese)
[18] 殷波.正弦信号频率估计算法研究[D].哈尔滨:哈尔滨工程大学,2015.YIN B.Research on the Algorithm of Sinusoidal Frequency Estimation[D].Harbin:Harbin Engineering University,2015.(in Chinese)
[19] 张殿伦.舰船声学测速技术研究[D].哈尔滨:哈尔滨工程大学,2001.ZHANG D L.Research on Ship Acoustic Velocity Measurement Technology[D].Harbin:Harbin Engineering University,2001.(in Chinese)
[20] STEVEN M K.统计信号处理基础—估计与检测理论[M].罗鹏飞等,译.北京:电子工业出版社,2011.STEVEN M K.Fundamentals of Statistical Processing-Estimation and Detection Theory[M].Translated by LUO P F,et al.Beijing:Publishing House of Electronics Industry,2011.(in Chinese)