低信噪比信号的检测与参数估计方法研究
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摘要
超宽带雷达是一种新体制雷达,它的信号带宽很宽,具有高距离分辨率,在雷达探测、精确定位、目标成像、目标识别技术中得到广泛应用。如何在低信噪比下检测宽带信号,并进行参数估计,具有重要的意义。本文针对雷达信号中出现最多的信号形式—线性调频信号,在低信噪比的条件下的检测和参数估计进行了分析与仿真和研究。
本文的主要工作如下:
1、超宽带LFM是非平稳信号,传统的傅里叶分析方和理论已经不能完全表述信号的性质。利用典型的时频分析方法,包括短时傅里叶变换(STFT)、Wigner-Ville分布(WVD)以及在此基础上的Hough-Wigner分布对信号进行了分析。并提出了一种修正的Hough-Wigner方法,实现对强信号和弱信号的一次检测。
2、经验模态分解(EMD: Empirical mode decomposition)方法能把时间序列信号分解成有限数目的本征模态函数(IMF: Intrinsic mode function)。本文利用EMD方法把线性调频信号从混合信号中分解出来,完成对线性调频信号的检测。针对EMD自身的端点效应,提出了改进办法,获得了更好的分解效果。
3、信噪比对信号的检测有很大的影响,在低信噪比下要完成对信号的检测,具有一定的难度,而在高信噪比的条件下,则很容易。本文利用小波变换对线性调频信号进行消噪,以此来提高信噪比。针对线性调频信号自身特点,提出了在频域进行消噪的新方法,获得了很好的消噪效果。
4、通过相位差分法、时频分析等不同的方法对信号的瞬时频率进行估计,并将各种方法进行分析比较。根据解线调方法对线性调频信号进行参数估计的运算量少但精度不高,而最大似然方法估算精度高但运算量大的特点,提出了将两种方法相结合的参数估算方法,获得了很好的效果。
Ultra-wideband radar is a new type of radar system, and it has high range resolution because of its wide bandwidth. Thus, it has been used for target identification, precise position, target imaging and discrimination. How to detect the UVB radar signal and estimate the signal parameters in low signal to noise ratio condition is very important. The main concerned signals are Linear Frequency Modulated (LFM) signal.
The main work can be summarized as:
1. Ultra-wideband LFM is non-stationary signals and the conventional Fourier analysis can’t describe their character completely. We make use of the typical time-frequency analysis which includes STFT, WVD and Hough_Wigner to analyze the LFM. After that, we proposed a mending Hough_Wigner to detect the strong signals and weak signal at the same time.
2. Time series signals can be decomposed to IMFs(Intrinsic mode function) by EMD(Empirical mode decomposition). This paper makes use of EMD algorithm to decompose the mix signals and get the LFM signals. We proposed a new method to eliminate the end effect and got a better decomposition.
3. Signal to noise ratio has strong affection for the signal detection. We can detect the signal in high signal to noise ratio easily but difficultly in low signal to noise ratio. This paper made use of wavelet transform to denoise signals for increase the signal to noise ratio. We proposed a new denosing method which denoise signals in frequency time in stead of time domain and got a better result.
4. We had a comparison between the phase difference method and time-frequency presentation which can be used for estimating the instantaneous frequency. The dechirp method for estimating the parameter had less computation and lower precision ; the maximum likelihood method had more computation and higher precision ;as a result ,we can estimate the instantaneous frequency by making use of the two method’s advantages.
本文的主要工作如下:
1、超宽带LFM是非平稳信号,传统的傅里叶分析方和理论已经不能完全表述信号的性质。利用典型的时频分析方法,包括短时傅里叶变换(STFT)、Wigner-Ville分布(WVD)以及在此基础上的Hough-Wigner分布对信号进行了分析。并提出了一种修正的Hough-Wigner方法,实现对强信号和弱信号的一次检测。
2、经验模态分解(EMD: Empirical mode decomposition)方法能把时间序列信号分解成有限数目的本征模态函数(IMF: Intrinsic mode function)。本文利用EMD方法把线性调频信号从混合信号中分解出来,完成对线性调频信号的检测。针对EMD自身的端点效应,提出了改进办法,获得了更好的分解效果。
3、信噪比对信号的检测有很大的影响,在低信噪比下要完成对信号的检测,具有一定的难度,而在高信噪比的条件下,则很容易。本文利用小波变换对线性调频信号进行消噪,以此来提高信噪比。针对线性调频信号自身特点,提出了在频域进行消噪的新方法,获得了很好的消噪效果。
4、通过相位差分法、时频分析等不同的方法对信号的瞬时频率进行估计,并将各种方法进行分析比较。根据解线调方法对线性调频信号进行参数估计的运算量少但精度不高,而最大似然方法估算精度高但运算量大的特点,提出了将两种方法相结合的参数估算方法,获得了很好的效果。
Ultra-wideband radar is a new type of radar system, and it has high range resolution because of its wide bandwidth. Thus, it has been used for target identification, precise position, target imaging and discrimination. How to detect the UVB radar signal and estimate the signal parameters in low signal to noise ratio condition is very important. The main concerned signals are Linear Frequency Modulated (LFM) signal.
The main work can be summarized as:
1. Ultra-wideband LFM is non-stationary signals and the conventional Fourier analysis can’t describe their character completely. We make use of the typical time-frequency analysis which includes STFT, WVD and Hough_Wigner to analyze the LFM. After that, we proposed a mending Hough_Wigner to detect the strong signals and weak signal at the same time.
2. Time series signals can be decomposed to IMFs(Intrinsic mode function) by EMD(Empirical mode decomposition). This paper makes use of EMD algorithm to decompose the mix signals and get the LFM signals. We proposed a new method to eliminate the end effect and got a better decomposition.
3. Signal to noise ratio has strong affection for the signal detection. We can detect the signal in high signal to noise ratio easily but difficultly in low signal to noise ratio. This paper made use of wavelet transform to denoise signals for increase the signal to noise ratio. We proposed a new denosing method which denoise signals in frequency time in stead of time domain and got a better result.
4. We had a comparison between the phase difference method and time-frequency presentation which can be used for estimating the instantaneous frequency. The dechirp method for estimating the parameter had less computation and lower precision ; the maximum likelihood method had more computation and higher precision ;as a result ,we can estimate the instantaneous frequency by making use of the two method’s advantages.
引文
[1]王意青,张明友.雷达原理,成都:电子科技大学出版社,1993
[2]林象平,雷达对抗原理.西安:西北电讯工程学院出版社,1985.1-20
[3]Henry K.,Kwork,Douglas L,Jones.Improved Instantaneous Frequency Estimation Using an Adaptive Short_Time Fourier Transform. .IEEE trans on signal processing,2000,48(10);296-2972
[4]Adbelghani.Short_Time Fourier Transform analysis of the phonocardiogram.signal. ICSP2000,844-847
[5] Henry K. Kwok,Douglas L.Jones.Improved Instantaneous Frequency Estimation Using an Adaptive Short-Time Fourier Transform.IEEE trans. on signal processing, 2000, 48( 10);2964-2972
[6]Adbelghani.Short-Time Fourier Transform analysis of the phonocardiogram signal. ICSP2000 ,844-847
[7]F. Peyrin, R. A. Prost.A unified definition for the discrete-time, discrete-frequency and discrete-time/frequency Wigner distribution. IEEE Trans. on Acoustic, Speech and Signal Processing, 1986, 34(4): 858~867
[8]张贤达,保铮.非平稳信号分析与处理.北京: 国防工业出版社,1999.7 35-47
[9]Cohen L. A primer on Time-frequency analysis. In: New Method in Time-Frequency Analysis,Sydney Austrlia:Longman cheshie,1992
[10]Cohen L,Posch T E. Generlized ambiguity function.Proc.IEEE ICASSP-85, 1985: 1033- 1036
[11]Cohen L,Posch T E.Positive time-frequency functions.IEEE trans. Acoust, Speech, signal proceesing,1985,33:31-38
[12]Cohen L. Generalized phase-space distribution functions. J. Math,Phy., 1966 , 56(7): 781-786
[13]崔锦泰.小波分析导论.西安:西安交通大学出版社,1995.1
[14]L. B. Almeida.The fractional Fourier transform and time-frequency representation. IEEE Trans. Signal Processing.1994,42(10): 3084- 3091
[15]H. M. Ozaktas. Digital computation of the fractional Fourier transform..IEEE Trans. Signal Processing, 1996,44(9): 2141–2150
[16]Ji Hong-Bing.Fractional Fourier transform based target number detection.ICSP2000, 1896-1898.
[17]P. Soo-Chang, Y. Min-Hung. Fractional time-frequency distributions. ISCAS’97, 4: 2673~2676
[18]T. Alieva, A. M. Barbe. Fractional Fourier and Radon-Wigner transform of periodic signals. Signal Processing, 1998, 69(2): 183~190
[19]杨炯明,秦树人.基于变窗移傅里叶变换实现旋转机械振动信号转速谱阵的算法研究.中国机械工程,Vol 17 No.5 ,.2006.3
[20]李艳,肖怀铁,付强.Radon_Wigner 变换改进算法在多目标分辨及参数估计中的应用.电光与控制,Vol 13 No.3 ,.2006.6
[21]徐毅,阮成礼,魏茂刚.一种性能优越的二次时频分布.电子科技大学学报,Vol 34 No.5 ,2005.10
[22]曾勇虎,王雪松,肖顺平.基于瞬态极化时频分布及奇异值特征提取的雷达目标识别.电子学报,Vol 33 No.3 ,2005.10
[23]江力,李长云.基于经验模分解的小波阈值滤波方法研究.信号处理,Vol 21,No.6,2005.11
[24]Yingxiang Li,Min Yi ,Xianci Xiao. Recursive filtering Radon-ambiguity transform algorithm for multi-LFM signals detection IEEE 2002
[25]朱振波,何明浩.强背景噪声环境下的线性调频信号检测.现代雷达,Vol.26 ,No.3,2004
[26]刘爱芳,朱晓华,陆锦辉,等.基于 Radon_Ambiguity 变换的多分量 LFM 信号检测与参数估计.南京理工大学学报,Vol.28 ,No.4,2004
[27]N E Huang ,Z Shen ,S R Long ,et al.The empirical mode decomposition and Hilbert spectrum for non-linear and non-stationary time series analysis[J].Proc Roy Soc Lond A,1998,454:903-995
[28]Boashash, B.Estimating and interpreting the instantaneous frequency of a signal.Part I Fundamentals. Proc. IEEE, 80, 520-538,1992
[29]OLIVEIRA P M, BARROSO V.Instantaneous frequency of multicomponent signals [J].IEEE Signal Processing Lett,1999,6(4):81-83.
[30]OLIVEIRA P M, BARROSO V.Definitions of instantaneous frequency under physicalconstraints [J].JFranklinInst,2000,337:303-316.
[31]Norden E. Huang, Zheng Shen, Steven R. long, et al.The Empirical Mode Decomposition and The Hilbert Spectrum for Nonlinear Non-stationary Time Series Analysis.Proc. R. Soc. London Ser. A 454:903-95 1998.
[32]杨建文,贾民平.希尔伯特_黄谱的端点效应分析及处理方法研究.振动工程学报,Vol.19,No.2,2006.6
[33]许宝杰,张建民,徐小力,等.抑制EMD端点效应方法的研究.北京理工大学学报,Vol.26,No.3,2006.3
[34] 邓拥军,王伟,钱成春 .EMD 方法及 Hilbert 变换中边界问题的处理 . 科学通报,Vol.46,No.3,2001.2
[35] 程军圣,于德介,杨宇 .Hilbert_Huang 变换端点效应问题的探讨 . 振动与冲击,Vol.24,No.6,2005
[36]Patrick Flandrin,Gabriel Rilling ,Paulo Goncalves.Empirical mode decomposition as a filter bank.IEEE signal processing Letters,2004,11(2):112-114
[37]Alyson K.Fletcher ,Kannan, Ramchandran,et al.Wavelet denoising by recursive cycle spinning.IEEE 2002:873-876
[38]Mingyan Jiang ,Dongfeng Yuan,Zheng Jiang ,Miaomiao Wei.Determination of wavelet denoising threshold by PSO and GA.2005 IEEE International Symposium on Microwave ,Antenna , Propagation and EMC Technologies for Wireless Communications Proceedings :1426-1429
[39]Farid Ykhlef, M.arezki , A.Guessoum,et al.A wavelet denoising method to improve detection with ultrasonic signal.2004 IEEE International Conference on Industrial Technology:1422-1425
[40]Ralph Hippenstiel ,Spiros Mantis.Wavelet denoising of signals based on the fourth order moment.IEEE 2001 International Symposium on signal processing and its Complications.363-366
[41]Donoho D L.Denoising by soft-Thresholding[J]. IEEE Trans Inform Theory,1995,41:613-627
[42]Donoho DL,Johnstone I M.Ideal Spatial Adaptation Via Wavelet Shrinkage [J].Biometrika,1994,81:425-455.
[43] 丰彦,高国荣.小波阈值消噪算法中分解层数的自适应确定.武汉大学学报,Vol.51,No.52,2005.12
[44]R.R coifman ,M.V.Wickerhauser.Entropy_based algorithms for the best selection.IEEE Trans Inform Theory 1992 38(2):713-718
[45]Supratim Saha,Steven Kay.A noniterative maximum likelihood parameter estimator of superimposed chirp signals.IEEE 2001
[46]Vincent C.Vannicola,Michael C.Wicks.Ambiguity function analysis for the chirp diverse waveform (CDW).IEEE 2001 International Radar Conference:666-671
[47]袁俊泉,孙敏琪,孙晓昶.基于 Wigner_Hough 变换的 LFM 信号参数估计方法.航天电子对抗,2004(6)
[48]尉宇,孙德宝,吴江洪,等.基于 WHT 的多分量 LFM 参数估计与分离.系统工程与电子技术,Vol 25,No.12,2003
[49]Supratim Saha,Steven M.Kay.Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling,IEEE Transaction on signal processing.Vol 50,No.2,2002 .2
[2]林象平,雷达对抗原理.西安:西北电讯工程学院出版社,1985.1-20
[3]Henry K.,Kwork,Douglas L,Jones.Improved Instantaneous Frequency Estimation Using an Adaptive Short_Time Fourier Transform. .IEEE trans on signal processing,2000,48(10);296-2972
[4]Adbelghani.Short_Time Fourier Transform analysis of the phonocardiogram.signal. ICSP2000,844-847
[5] Henry K. Kwok,Douglas L.Jones.Improved Instantaneous Frequency Estimation Using an Adaptive Short-Time Fourier Transform.IEEE trans. on signal processing, 2000, 48( 10);2964-2972
[6]Adbelghani.Short-Time Fourier Transform analysis of the phonocardiogram signal. ICSP2000 ,844-847
[7]F. Peyrin, R. A. Prost.A unified definition for the discrete-time, discrete-frequency and discrete-time/frequency Wigner distribution. IEEE Trans. on Acoustic, Speech and Signal Processing, 1986, 34(4): 858~867
[8]张贤达,保铮.非平稳信号分析与处理.北京: 国防工业出版社,1999.7 35-47
[9]Cohen L. A primer on Time-frequency analysis. In: New Method in Time-Frequency Analysis,Sydney Austrlia:Longman cheshie,1992
[10]Cohen L,Posch T E. Generlized ambiguity function.Proc.IEEE ICASSP-85, 1985: 1033- 1036
[11]Cohen L,Posch T E.Positive time-frequency functions.IEEE trans. Acoust, Speech, signal proceesing,1985,33:31-38
[12]Cohen L. Generalized phase-space distribution functions. J. Math,Phy., 1966 , 56(7): 781-786
[13]崔锦泰.小波分析导论.西安:西安交通大学出版社,1995.1
[14]L. B. Almeida.The fractional Fourier transform and time-frequency representation. IEEE Trans. Signal Processing.1994,42(10): 3084- 3091
[15]H. M. Ozaktas. Digital computation of the fractional Fourier transform..IEEE Trans. Signal Processing, 1996,44(9): 2141–2150
[16]Ji Hong-Bing.Fractional Fourier transform based target number detection.ICSP2000, 1896-1898.
[17]P. Soo-Chang, Y. Min-Hung. Fractional time-frequency distributions. ISCAS’97, 4: 2673~2676
[18]T. Alieva, A. M. Barbe. Fractional Fourier and Radon-Wigner transform of periodic signals. Signal Processing, 1998, 69(2): 183~190
[19]杨炯明,秦树人.基于变窗移傅里叶变换实现旋转机械振动信号转速谱阵的算法研究.中国机械工程,Vol 17 No.5 ,.2006.3
[20]李艳,肖怀铁,付强.Radon_Wigner 变换改进算法在多目标分辨及参数估计中的应用.电光与控制,Vol 13 No.3 ,.2006.6
[21]徐毅,阮成礼,魏茂刚.一种性能优越的二次时频分布.电子科技大学学报,Vol 34 No.5 ,2005.10
[22]曾勇虎,王雪松,肖顺平.基于瞬态极化时频分布及奇异值特征提取的雷达目标识别.电子学报,Vol 33 No.3 ,2005.10
[23]江力,李长云.基于经验模分解的小波阈值滤波方法研究.信号处理,Vol 21,No.6,2005.11
[24]Yingxiang Li,Min Yi ,Xianci Xiao. Recursive filtering Radon-ambiguity transform algorithm for multi-LFM signals detection IEEE 2002
[25]朱振波,何明浩.强背景噪声环境下的线性调频信号检测.现代雷达,Vol.26 ,No.3,2004
[26]刘爱芳,朱晓华,陆锦辉,等.基于 Radon_Ambiguity 变换的多分量 LFM 信号检测与参数估计.南京理工大学学报,Vol.28 ,No.4,2004
[27]N E Huang ,Z Shen ,S R Long ,et al.The empirical mode decomposition and Hilbert spectrum for non-linear and non-stationary time series analysis[J].Proc Roy Soc Lond A,1998,454:903-995
[28]Boashash, B.Estimating and interpreting the instantaneous frequency of a signal.Part I Fundamentals. Proc. IEEE, 80, 520-538,1992
[29]OLIVEIRA P M, BARROSO V.Instantaneous frequency of multicomponent signals [J].IEEE Signal Processing Lett,1999,6(4):81-83.
[30]OLIVEIRA P M, BARROSO V.Definitions of instantaneous frequency under physicalconstraints [J].JFranklinInst,2000,337:303-316.
[31]Norden E. Huang, Zheng Shen, Steven R. long, et al.The Empirical Mode Decomposition and The Hilbert Spectrum for Nonlinear Non-stationary Time Series Analysis.Proc. R. Soc. London Ser. A 454:903-95 1998.
[32]杨建文,贾民平.希尔伯特_黄谱的端点效应分析及处理方法研究.振动工程学报,Vol.19,No.2,2006.6
[33]许宝杰,张建民,徐小力,等.抑制EMD端点效应方法的研究.北京理工大学学报,Vol.26,No.3,2006.3
[34] 邓拥军,王伟,钱成春 .EMD 方法及 Hilbert 变换中边界问题的处理 . 科学通报,Vol.46,No.3,2001.2
[35] 程军圣,于德介,杨宇 .Hilbert_Huang 变换端点效应问题的探讨 . 振动与冲击,Vol.24,No.6,2005
[36]Patrick Flandrin,Gabriel Rilling ,Paulo Goncalves.Empirical mode decomposition as a filter bank.IEEE signal processing Letters,2004,11(2):112-114
[37]Alyson K.Fletcher ,Kannan, Ramchandran,et al.Wavelet denoising by recursive cycle spinning.IEEE 2002:873-876
[38]Mingyan Jiang ,Dongfeng Yuan,Zheng Jiang ,Miaomiao Wei.Determination of wavelet denoising threshold by PSO and GA.2005 IEEE International Symposium on Microwave ,Antenna , Propagation and EMC Technologies for Wireless Communications Proceedings :1426-1429
[39]Farid Ykhlef, M.arezki , A.Guessoum,et al.A wavelet denoising method to improve detection with ultrasonic signal.2004 IEEE International Conference on Industrial Technology:1422-1425
[40]Ralph Hippenstiel ,Spiros Mantis.Wavelet denoising of signals based on the fourth order moment.IEEE 2001 International Symposium on signal processing and its Complications.363-366
[41]Donoho D L.Denoising by soft-Thresholding[J]. IEEE Trans Inform Theory,1995,41:613-627
[42]Donoho DL,Johnstone I M.Ideal Spatial Adaptation Via Wavelet Shrinkage [J].Biometrika,1994,81:425-455.
[43] 丰彦,高国荣.小波阈值消噪算法中分解层数的自适应确定.武汉大学学报,Vol.51,No.52,2005.12
[44]R.R coifman ,M.V.Wickerhauser.Entropy_based algorithms for the best selection.IEEE Trans Inform Theory 1992 38(2):713-718
[45]Supratim Saha,Steven Kay.A noniterative maximum likelihood parameter estimator of superimposed chirp signals.IEEE 2001
[46]Vincent C.Vannicola,Michael C.Wicks.Ambiguity function analysis for the chirp diverse waveform (CDW).IEEE 2001 International Radar Conference:666-671
[47]袁俊泉,孙敏琪,孙晓昶.基于 Wigner_Hough 变换的 LFM 信号参数估计方法.航天电子对抗,2004(6)
[48]尉宇,孙德宝,吴江洪,等.基于 WHT 的多分量 LFM 参数估计与分离.系统工程与电子技术,Vol 25,No.12,2003
[49]Supratim Saha,Steven M.Kay.Maximum likelihood parameter estimation of superimposed chirps using Monte Carlo importance sampling,IEEE Transaction on signal processing.Vol 50,No.2,2002 .2