水声信号处理中的盲解卷积技术研究
|
摘要
多径效应是影响水下被动声纳系统检测性能的重要因素。针对该问题,论文对水声信号源分离中的盲解卷积技术进行了研究。结合已有的盲信号处理研究成果,以线性卷积混合模型为对象,分别针对时间域算法、变换域算法以及源信号数目未知条件下的盲解卷积算法等问题进行研究。提出了几类适用于水声工程领域的盲源分离方法,论文的计算机仿真及实测水声数据分析处理,取得了良好的结果,验证了本文方法的可行性和有效性。论文的主要研究内容包括：
(1)基于舰船辐射噪声实测数据,分析了水声信号的非高斯分布特性,为盲信号处理技术用于水声信号源分离,提供了先验知识积累。针对舰船辐射噪声的非平稳特征,研究了循环频率估计和经验模态分解两种非平稳信号处理方法,用于提取螺旋桨噪声中的低频线谱,为后续章节中的实测数据盲源分离实验所获得的源估计信号作进一步分析,奠定了理论基础。
(2)研究了两种基于二阶统计量的水声多途信道时域盲解卷积算法。针对盲源分离中存在的幅度模糊问题,提出了一种应用参考信号估计信道参数,利用自适应逆滤波分离源估计信号的盲源恢复算法。该方法可同时获得源信号的时序结构与幅度信息,这对声纳信号处理是很有帮助的；为改善长时延下时域算法计算量过大问题,提出了一种时域与频域相结合的盲解卷积算法,在频域中进行自适应滤波器权向量的更新,在时域中完成信号波形的分离。
(3)分析和研究了变换域中的水声信号盲分离问题。针对实际中源信号间存在的相干分量会造成盲源分离性能下降的情况,提出了一种基于小波包变换子带分解的盲解卷积算法,通过最小化源信号间的互信息来降低源信号间的依赖性。算法可分别在时间域或小波域内进行未知源的分离。
(4)分析和研究了源信号数目未知,且系统为欠定条件下的稀疏源盲分离算法的整体思路。基于短时傅里叶变换,提出了一种接收传感器数目和空间分布任意情况下的利用二分提取的欠定稀疏源盲分离算法。最后设计了实际中盲源分离的总体框架,并用于舰船辐射噪声实测数据的盲源分离实验中。
Multipath effect impacts passive SONAR detection performance seriously. To solve this problem, this dissertation explored multi-channel blind deconvolution (MBD) techniques for underwater acoustic signals separation. Combined with existing research work, we studied three kinds of algorithm with the linear convolutive mixture model, which are concerned with theories in time-domain, frequency-domain and the case of source numbers unknown. Several algorithms, which are applicable to underwater acoustic engineering for multi-channel phenomenon, were proposed. Simulation and measured underwater acoustic data processing results show the good performance. The main contents of this paper are as follows:
(1) Based on the real data of warship radiated noise, non-gaussianity of the underwater acoustic signal was analyzed. It provided prior knowledge for the underwater acoustic source signals separation using blind signal processing (BSP). Then, aimed at the non-stationarity of warship radiated noise, two kinds of nonstationary signal processing methods, i.e. cycle frequency evaluation and empirical modal decomposition, were studied to extract low frequency line spectrum of propeller noise. It established theoretical basis for the following work of thoroughly analyzing the evaluated source signals from the real measured data via blind source separation.
(2) Based on two-order moment, two kinds of acoustic multi-channel blind deconvolution algorithms were proposed in time domain. Aimed at the obscure amplitude during blind source separation (BSS), a new blind source signal restoration algorithm was proposed, which evaluated channel parameters through reference signals, and separ..ted source signals through inverse adaptive filtering. It could obtain both source signals'time structure and amplitude information, which is helpful to SONAR signal processing. Then, to improve large computation of BSS with huge delay in time domain, a fast multi-channel blind deconvolution algorithm was proposed. It updated weight vectors in frequency domain and separated the source signals in temporal domain.
(3) MBD algorithm was investigated in transform domain. Owing to the actual source signals'mutual dependency, the performance of BSS algorithms descended heavily. So, a new algorithm, which used wavelet packets transformation for sub-band decomposition, was proposed to process statistically dependent sources. By minimizing the source signals'mutual information, the dependency of the source signals was reduced. The algorithm can be carried out both in temporal domain and wavelet domain.
(4) After investigating the whole tenor of underdetermined sparse source separation technique when the source numbers unknown, a novel blind source separation algorithm was proposed, which utilized binary mask (BM) method, and extended the unrestricted receiving sensors both in dimension and the condition of spatial distribution, based on short-time Fourier transformation. In the end, a general framework for BSS problem was set up and applied in actual underwater acoustic signal processing for warship radiated noise seperation.
(1)基于舰船辐射噪声实测数据,分析了水声信号的非高斯分布特性,为盲信号处理技术用于水声信号源分离,提供了先验知识积累。针对舰船辐射噪声的非平稳特征,研究了循环频率估计和经验模态分解两种非平稳信号处理方法,用于提取螺旋桨噪声中的低频线谱,为后续章节中的实测数据盲源分离实验所获得的源估计信号作进一步分析,奠定了理论基础。
(2)研究了两种基于二阶统计量的水声多途信道时域盲解卷积算法。针对盲源分离中存在的幅度模糊问题,提出了一种应用参考信号估计信道参数,利用自适应逆滤波分离源估计信号的盲源恢复算法。该方法可同时获得源信号的时序结构与幅度信息,这对声纳信号处理是很有帮助的；为改善长时延下时域算法计算量过大问题,提出了一种时域与频域相结合的盲解卷积算法,在频域中进行自适应滤波器权向量的更新,在时域中完成信号波形的分离。
(3)分析和研究了变换域中的水声信号盲分离问题。针对实际中源信号间存在的相干分量会造成盲源分离性能下降的情况,提出了一种基于小波包变换子带分解的盲解卷积算法,通过最小化源信号间的互信息来降低源信号间的依赖性。算法可分别在时间域或小波域内进行未知源的分离。
(4)分析和研究了源信号数目未知,且系统为欠定条件下的稀疏源盲分离算法的整体思路。基于短时傅里叶变换,提出了一种接收传感器数目和空间分布任意情况下的利用二分提取的欠定稀疏源盲分离算法。最后设计了实际中盲源分离的总体框架,并用于舰船辐射噪声实测数据的盲源分离实验中。
Multipath effect impacts passive SONAR detection performance seriously. To solve this problem, this dissertation explored multi-channel blind deconvolution (MBD) techniques for underwater acoustic signals separation. Combined with existing research work, we studied three kinds of algorithm with the linear convolutive mixture model, which are concerned with theories in time-domain, frequency-domain and the case of source numbers unknown. Several algorithms, which are applicable to underwater acoustic engineering for multi-channel phenomenon, were proposed. Simulation and measured underwater acoustic data processing results show the good performance. The main contents of this paper are as follows:
(1) Based on the real data of warship radiated noise, non-gaussianity of the underwater acoustic signal was analyzed. It provided prior knowledge for the underwater acoustic source signals separation using blind signal processing (BSP). Then, aimed at the non-stationarity of warship radiated noise, two kinds of nonstationary signal processing methods, i.e. cycle frequency evaluation and empirical modal decomposition, were studied to extract low frequency line spectrum of propeller noise. It established theoretical basis for the following work of thoroughly analyzing the evaluated source signals from the real measured data via blind source separation.
(2) Based on two-order moment, two kinds of acoustic multi-channel blind deconvolution algorithms were proposed in time domain. Aimed at the obscure amplitude during blind source separation (BSS), a new blind source signal restoration algorithm was proposed, which evaluated channel parameters through reference signals, and separ..ted source signals through inverse adaptive filtering. It could obtain both source signals'time structure and amplitude information, which is helpful to SONAR signal processing. Then, to improve large computation of BSS with huge delay in time domain, a fast multi-channel blind deconvolution algorithm was proposed. It updated weight vectors in frequency domain and separated the source signals in temporal domain.
(3) MBD algorithm was investigated in transform domain. Owing to the actual source signals'mutual dependency, the performance of BSS algorithms descended heavily. So, a new algorithm, which used wavelet packets transformation for sub-band decomposition, was proposed to process statistically dependent sources. By minimizing the source signals'mutual information, the dependency of the source signals was reduced. The algorithm can be carried out both in temporal domain and wavelet domain.
(4) After investigating the whole tenor of underdetermined sparse source separation technique when the source numbers unknown, a novel blind source separation algorithm was proposed, which utilized binary mask (BM) method, and extended the unrestricted receiving sensors both in dimension and the condition of spatial distribution, based on short-time Fourier transformation. In the end, a general framework for BSS problem was set up and applied in actual underwater acoustic signal processing for warship radiated noise seperation.
引文
[1]Cichocki A, Amari S-I. Adaptive blind signal and image processing: learning algorithms and applications, Chichester:John Wiley & Sons, Ltd., 2002.
[2]C.Jutten, J.Herault eds., Independent Component Analysis (INCA) versus Principal Component Analysis. Elsevier,1988.
[3]Chung W. Blind Parameter Estimation for Data Acquisition in Digital Communication Systems. Cornell University. Ph. D.,2002.
[4]James C J, Lowe D. Extracting multisource brain activity from a single electromagnetic channel. Artificial Intelligence in Medicine.2003,28 (1): 89-104.
[5]Mei T, Xi J, Yin F, et al. Blind Source Separation Based on Time-Domain Optimization of a Frequency-Domain Independence Criterion. Audio, Speech, and Language Processing, IEEE Transactions on [see also Speech and Audio Processing, IEEE Transactions on].2006,14 (6):2075-2085.
[6]Li W. Algorithms for blind FIR channel estimation and signal restoration. The Hong Kong Polytechnic University. Ph. D.,1999.
[7]Chi C-Y, Chen C-H, Chen C-Y. Blind MAI and ISI Suppression for DS/CDMA Systems Using HOS-Based Inverse Filter Criteria. IEEE Transactions on Signal Processing.2002,50 (6):1368-1381.
[8]Amari S-I, Cichocki A. Adaptive Blind Signal Processing-Neural Network Approaches. Proceedings of the IEEE.1998,86 (10):2026-2048.
[9]王之程,陈宗歧,于渢等.舰船噪声测量与分析,北京：国防工业出版社，2004.
[10]杨德森,战国辰,刘星.低噪声水下目标辐射噪声测量的新方法研究.中国声学学会2001青年学术会议,上海,2001：245-247.
[11]倪晋平.水声信号盲分离技术研究.西北工业大学博士论文,2002.
[12]孔薇,杨杰,周越.一种改进的最大熵方法在船舶辐射噪声盲分离中的应用.上海交通大学学报.2004,38(12)：1962-1965.
[13]姜卫东,陆佶人,张宏滔.基于单个频点的水声信号盲源分离.电子与信息学报.2005,27(04)：532-535.
[14]张安清,邱天爽,章新华.分数低阶矩的信号盲分离方法.通信学报.2006,27(3)：32-36.
[15]肖瑛.基于水声信道的盲均衡算法研究.哈尔滨工程大学博士论文,2006.
[16]袁连喜.线性盲源分离算法的理论与应用研究.哈尔滨工程大学博士论文,2006.
[17]张艳萍,赵俊渭,王尚斌等.基于判决导引的水声信道混合盲均衡算法研究.声学学报.2005,30(5)：442-446.
[18]张安清,章新华.基于信息理论的舰船噪声盲分离算法.系统工程与电子技术.2002,24(1)：38-51.
[19]倪晋平,马远良,孙超等.用独立成份分析算法实现水声信号盲分离.声学学报.2002,27(4)：321-326.
[20]郭业才,何龙庆,韩迎鸽等.盲均衡技术在水声信道均衡中的应用进展.舰船科学技术.2007,29(2)：22-27.
[21]Gomes J, Barras V. Acoustic channel equalization results for the ASIMOV high-speed coherent data link. OVEANS 2000 MTS/IEEE Coference and Exhibition,2002:1437-1442.
[22]Liu H, Xu G. Closed-form blind symbol estimation in digital communications. IEEE Trans. Signal Processing.1995,43 (11): 2714-2723.
[23]王峰,赵俊渭,李桂娟.一种常数模与判决引导相结合的盲均衡算法研究.通信学报.2002,23(6)：105-112.
[24]Halzinakos D, Nikias C L. Blind Decision Feedback Equalization Structure Based on Adaptive CumulantTechnigures. ICCS'89,1989:1278-1282.
[25]Tong L. Blind sequence estimation. IEEE Trans. On Communication.1995, 43:2986-2995.
[26]Shalvi O, Weistein E. Super-exponential methods for blind equalization. IEEE Trans. Information Theory.1993,39 (2):505-519.
[27]肖瑛,刘国枝,李振兴等.遗传优化神经网络的水声信道盲均衡.应用声学.2006,25(6)：340-345.
[28]Kechriotis G, Zervas E. Using recurrent neural network for adaptive communication channel equalization. IEEE Trans. On neural networks. 1994,5:267-278.
[29]王永川,陈自力,刘增田.基于小波分解的时变信道盲辨识.测试技术学报.2005,19(1)：79-82.
[30]韩迎鸽,郭业才,吴造林等.基于正交小波变换的多模盲均衡器设计与算法仿真研究.仪器仪表学报.2008,29(7)：1441-1445.
[31]张安清,邱天爽,章新华.扩展联合对角化法的水声信号盲分离技术.系统工程与电子技术.2003,25(9)：1058-1060.
[32]姜卫东,陆佶人,张宏滔.基于两个邻近频点相关特性的水声信号盲源分离.电子与信息学报.2006,28(9)：1555-1559.
[33]张安清,章新华,邱天爽等.基于线谱点的一种频域盲分离方法.系统工程与电子技术.2006,28(9)：1307-1310.
[34]姜卫东,张宏滔,陆佶人.噪声环境下水声信号瞬时盲源分离方法研究.声学技术.2006,25(3)：182-186.
[35]倪晋平,马远良,张忠兵.一种强干扰下超弱水声信号自适应盲分离的快速算法.声学技术.2002,3：
[36]Jutten C, Herault J. Blind separation of sources, part I. An adaptive algorithm based on neuromimetic architecture. Signal Processing.1991,24 (1):1-10.
[37]Comon P. Independent component analysis, A new concept? Signal Processing.1994,36 (3):287-314.
[38]Hyvarinen A, Karhunen J, Oja E. Independent component analysis, New York:John Wiley & Sons, Inc.,2001.
[39]Comon P, Jutten C, Herault J. Blind separation of sources, part II. Problems statement. Signal Processing.1991,24 (1):11-20.
[40]Sorouchyari E. Blind separation of sources, part III. Stability analysis. Signal Processing.1991,24 (1):21-29.
[41]Cardoso J-F. Source separation using higher order moments. Icassp'89, 1989:2109-2112.
[42]Cardoso J F. Super-symmetrical decomposition of the 4th-order cumulant tensor-blind identification of more sources than sensors. Icassp 91, Vols 1-5.1991:3109-3112.
[43]Tong L, Liu R-W, Soon V C, et al. Indeterminacy and identifiability of blinde identification. IEEE transactions on circuits and systems.1991,38 (5):499-509.
[44]Tong L, Inouye Y, Liu R-W. Waveform-Preserving Blind Estimation of Multiple Independent Sources. IEEE Transactions on Signal Processing. 1993,41 (7):2461-2470.
[45]Tong L, Soon V C, Huang Y. F, et al. AMUSE:a new blind identification algorithm. Circuits and Systems,1990., IEEE International Symposium on,, 1990:1784-1787.
[46]Cao X-R, Liu R-w. General approach to blind source separation. IEEE Transactions on Signal Processing.1996,44 (3):562-571.
[47]Hyvarinen A. A unifying model for blind separation of independent sources. Signal Processing.2005,85:1419-1427.
[48]Cardoso J F, Souloumiac A. Blind beamforming for non-Gaussian signals. lee Proceedings-F Radar and Signal Processing.1993,140 (6):362-370.
[49]Cardoso J F, Moulines E. Minimum contrast estimation with application to array-processing. Icassp-93:1993 Ieee International Conference on Acoustics, Speech, and Signal Processing, Vols 1-5.1993:D384-D387.
[50]Cardoso J F, Laheld B H. Equivariant adaptive source separation. IEEE Transactions on Signal Processing.1996,44 (12):3017-3030.
[51]Amari S, Cardoso J F. Blind source separation-Semiparametric statistical approach. IEEE Transactions on Signal Processing.1997,45 (11): 2692-2700.
[52]Yang H H, Amari S-I. Adaptive on-line learning algorithms for blind separation-maximum entropy and minimum mutal information. Neural Computation.1997,7 (9):1457-1482.
[53]Hyvarinen A. Fast and robust fixed-point algorithms for independent component analysis. Neural Networks, IEEE Transactions on.1999,10 (3): 626-634.
[54]Cichocki A, Unbehauen R, Rummert E. Robust learning algorithm for blind separation of signals. Electronic letters.1994,30 (17):1386-1387.
[55]Cichocki A, Unbehauen R. Robust neural networks with on-line learning for blind identification and blind separation of sources. IEEE transactions on circuits and systems.1996,43 (11):894-906.
[56]Karhunen J, Liuyue W, Vigario R. Nonlinear PCA type approaches for source separation and independent component analysis. Neural Networks, 1995. Proceedings., IEEE International Conference on,1995:995-1000.
[57]Karhunen J, Oja E, Wang L, et al. A class of neural networks for independent component analysis. Neural Networks, IEEE Transactions on. 1997,8 (3):486-504.
[58]Oja E. The nonlinear PCA learning rule in independent component analysis. Neurocomputing.1997,17 (1):25-45.
[59]Hyvarinen A. The Fixed-Point Algorithm and Maximum Likelihood Estimation for Independent Component Analysis. Neural Processing Letters.1999,10(1):1-5.
[60]Matsuoka K, Ohoya M, Kawamoto M. A neural net for blind separation of nonstationary signals. Neural Networks.1995,8 (3):411-419.
[61]Choi S, Cichocki A. Algebraic differential decorrelation for nonstationary source separation. Electronics Letters.2001,37 (23):1414-1415.
[62]Pham D T, Cardoso J F. Blind separation of instantaneous mixtures of nonstationary sources. IEEE Transactions on Signal Processing.2001,49 (9):1837-1848.
[63]Douglas S C, Kung S Y. Kuicnet Algorithms for Blind Deconvolution. IEEE Workshop on Neural Networks for Signal Processing, Cambridge, UK,1998:3-12.
[64]Hyvarinen A, Oja E. A Fast Fixed-Point Algorithm for Independent Component Analysis. Neural Computation.1997,9 (7):1483-1492.
[65]Bingham E, Hyvarinen A. A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals. International Journal of Neural Systems.2000,10 (1):1-8.
[66], Novey M, Adali T. On Extending the Complex FastICA Algorithm to Noncircular Sources. Signal Processing, IEEE Transactions on.2008,56 (5):2148-2154.
[67]Hyvarinen A, Koster U. FastISA:A fast fixed-point algorithm for Independent Subspace Analysis, ESANN'2006 proceedings-European Symposium on Artificial Neural Networks, Bruges, Belgium,2006: 371-376.
[68]Valpola H, Giannakopoulos X, Honkela A, et al. Nonlinear independent component analysis using ensemble learning:Experiments and discussion. Proc. Int. Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000), Helsinki, Finland,2000:351-356.
[69]Taleb A, Jutten C. Source separation in post-nonlinear mixtures. IEEE Transactions on Signal Processing.1999,47 (10):2807-2820.
[70]Jutten C, Taleb A. Source Separation:from Dusk till Dawn. Second International Workshop on Independent Component Analysis and Blind Signal Separation,2000:662-673.
[71]Hyvarinen A, Pajunen P. Nonlinear independent component analysis: Existence and uniqueness results. Neural Networks.1999,12 (3):429-439.
[72]Pajunen P, Hyvarinen A, Karhunen J. Nonlinear blind source separation by self-organizing maps, Proc. Int. Conf. on Neural Information Processing, Hong Kong,1996:1207-1210.
[73]Bishop C M, Svensen M, Williams C K I. GTM:The generative topographic mapping. Neural Computation.1998,10:215-234.
[74]Pajunen P, Karhunen J. A maximum likelihood approach to nonlinear blind source separation. Int. Conf. on Artificial Neural Networks (ICANN’97), Lausanne, Switzerland,1997:541-546.
[75]H.Valpola. Nonlinear independent component analysis using ensemble learning:Theory. Girolami M ed. Proc. Int.Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000), Helsinki, Finland,2000:251-256.
[76]Valpola H, Giannakopoulos X, Honkela A, et al. Nonlinear independent component analysis using ensemble learning:experiments and discussion, Proc. Int. Workshop on Independent Component Analysis and Blind Signal Separation, Helsinki, Finland,2000:351-356.
[77]Lappalainen H, Honkela A. Bayesian nonlinear independent component analysis by multi-layer perceptrons, Advances in Independent Component Analysis, Girolami M. ed., New York:Springer-Verlag,2000:93-121.
[78]Cichocki A, Sabala I, Choi S, et al. Self-adaptive independent component analysis for sub-gaussian and super-gaussian mixtures with unknown number of source signals and additive noise. Int. Symp. on Nonlinear Theory and Applications, Honolulu, HI,1997:731-734.
[79]Cichocki A, Sabala I, Amari S. Intelligent neural networks for blind signal processing with unknown number of sources. Int. Symp. on Engineering of Intelligent Systems, Tenerife, Spain,1998:148-154.
[80]Lathauwer L D, Castaing J, Cardoso J F. Fourth-order cumulant-based blind identification of underdetermined mixtures. IEEE Transactions on Signal Processing.2007,55 (6):2965-2973.
[81]Vielva L, Pereiro Y, Erdogmus D, et al. Inversion Techniques for Underdetermined Bss in an Arbitrary Number of Dimensions.4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA03), Nara, Japan,2003:131-136.
[82]Araki S, Makino S, Sawada H, et al. Underdetermined blind separation of convolutive mixtures of speech with directivity pattern based mask and ICA. Independent Component Analysis and Blind Signal Separation.2004, 3195:898-905.
[83]Luengo D, Santamaria I, Vielva L, et al. Underdetermined blind separation of sparse sources with instantaneous and convolutive mixtures.2003 IEEE Xiii Workshop on Neural Networks for Signal Processing-Nnsp'03.2003: 279-288.
[84]Bofill P, Monte E. Underdetermined convoluted source reconstruction using LP and SOCP, and a neural approximator of the optimizer. Independent Component Analysis and Blind Signal Separation, Proceedings,2006:569-576.
[85]Winter S, Kellermann W, Sawada H, et al. MAP based underdetermined blind source separation of convolutive mixtures by hierarchical clustering and 11-norm minimization. EURASIP J. Adv.2Signal Process.2007:
[86]Bofill P, Zibulevsky M. Blind separation of more sources than mixtures using sparasity of their short-time Fourier transform. International Workshop on ICA and BSS (ICA00), Helsinki, Finland,2000:87-92.
[87]Abed-Meraim K, Nguyen L-W, Belouchrani A. Underdetermined Blind Source Separation for FM-Like Signals, Time Frequency Signal Analysis and Processing, Boashash B, ed., Oxford, UK:ELSEVIER Ltd,2003: 357-368.
[88]Widrow B, Glover J R, McCool J M, et al. Adaptive noise canceling: Principles and applications. IEEE Proceedings.1975,63:1692-1716.
[89]Widrow B, Steams S D. Adaptive Signal Processing, New Jersey: Prentice-Hall, Inc.,1985.
[90]Haykin S. Adaptive Filter Theory.3rd Ed. ed., New Jersey:Prentice-Hall, Inc.,2002.
[91]Godrey R, Rocca F. Zero memory non-linear deconvolution. Geophysical Processing.1981,29:189-228.
[92]Haykin S ed., Blind Deconvolution. New Jersey:Prentice-Hall, Inc.,1994.
[93]Haykin S. Adaptive Filter Theory.3rd ed., New Jersey:Prentice-Hall, Inc., 1996.
[94]Santamaria I, Pantaleón C, Vielva L, et al. Blind Equalization of Constant Modulus Signals Using Support Vector Machines. IEEE Transactions on Signal Processing.2004,52 (6):1773-1782.
[95]Benveniste A, Goursat G. Blind Equalizers. IEEE Transactions on Communications.1984,32:871-883.
[96]Shalvi O, Weinstein E. New Criteria for Blind Deconvolution of Nonminimum Phase Systems (Channels). IEEE Transaction on Information Theory.1990,36 (2):312-321.
[97]Torkkola K. Blind separation of delayed and convolved sources, Unsupervised Adaptive Filtering, Haykin S, ed., New York:Wiley,2000: 321-375.
[98]Amari S-I, Cichocki A, Yang H H. Blind Signal Separation and Extraction: Neural and Information-Theoretic Approaches, Unsupervised Adaptive Filtering, Haykin S, ed., New York:Wiley,2000:63-138.
[99]Tong L, Xu G, Kailath T. Blind channel identification and equalization using spectral correlation measurements, Part Ⅱ:A time-domain approach, Cyclostationary in communications and signal processing, Gardner W A, ed., New York:IEEE Press,1994:437-454.
[100]Dapena A, Serviere C, Castedo L. Inversion of the sliding Fourier transform using only two frequency bins and its application to source separation. Signal Processing.2003,83 (2):453-457.
[101]Rahbar K, Reilly J P. A Frequency Domain Method for Blind Source Separation of Convolutive Audio Mixtures. IEEE Transactions on Speech and Audio Processing.2005,13 (5):832-844.
[102]Xie P, Grant S L. A Fast and Efficient Frequency-Domain Method for Convolutive Blind Source Separation. Region 5 Conference,2008 IEEE, 2008:1-4.
[103]Buchner H, Kellermann W. Improved Kalman gain computation for multichannel frequency-domain adaptive filtering and application to acoustic echo cancellation.2002 IEEE International Conference on Acoustics, Speech, and Signal Processing, Orlando, FL, USA,2002: 1909-12.
[104]Buchner H, Aichner R, Kellermann W. TRINICON:A versatile framework for multichannel blind signal processing. Montreal, Que, Canada,2004: 889-892.
[105]Buchner H, Aichner R, Kellermann W. Blind Source Separation for Convolutive Mixtures:A Unified Treatment. Audio Signal Processing for Next-Generation Multimedia Communication Systems,2004:255-293.
[106]Buchner H, Aichner R, Kellermann W. A generalization of blind source separation algorithms for convolutive mixtures based on second-order statistics. IEEE Transactions on Speech and Audio Processing.2005,13 (1): 120-134.
[107]Buchner H, Aichner R, Stenglein J, et al. Simultaneous localization of multiple sound sources using blind adaptive MIMO filtering. Philadelphia, PA, United States,2005:97-100.
[108]Moulines E, Duhamel P, Cardoso J F, et al. Subspace Methods for the Blind Identification of Multichannel FIR Filters. IEEE Transactions on Signal Processing.1995,43 (2):516-525.
[109]Diamantaras K I, Papadimitriou T. Subspace-based channel shortening for the blind separation of convolutive mixtures. IEEE Transactions on Signal Processing.2006,54 (10):3669-3677.
[110]Peng C Y, Zhang X D. On recursive oblique projectors. Signal Processing Letters, IEEE.2005,12 (6):433-436.
[111]Judge G G, Hill R C, Griffiths W E, et al. Introduction to the Theory and Practice of Econometrics, New York:Wiley,1988.
[112]Conover W J. Practical Nonparametric Statistics, New York:Wiley,1980.
[113]Xiao J, Borgnat P, Flandrin P. Testing Stationarity With Time-Frequency Surrogates, EURASIP 2007, Poznan,2007:2020-2024.
[114]Xiao J, Borgnat P, Flandrin P, et al. Testing Stationarity with Surrogates-A One-Class SVM Approach. Borgnat P ed. Statistical Signal Processing, 2007. SSP'07. IEEE/SP 14th Workshop on,2007:720-724.
[115]Martin W, P.Flandrin. Detection of Changes of Signal Structure by Using the Wigner-Ville Spectrum. Signal Process.1985,8:215-233.
[116]Bayram M, Baraniuk R. Multiple Window Time-varying Spectrum Estimation, Nonlinear and Nonstationary Signal Processing, Fitzgerald W J, ed., London:Cambridge University Press,2000:292-316.
[117]吴国清,魏学环,周钢.提取螺旋桨识别特征的二种途径.声学学报.1993,18(3)：210-216.
[118]陶笃纯.舰船噪声节奏的研究(Ⅰ)-数学模型及功率谱密度.声学学报.1983,8(2)：65-76.
[119]陶笃纯.舰船噪声节奏的研究(Ⅱ)——自相关函数及节奏信息的提取.声学学报.1983,8(5)：280-289.
[120]王彪,杨志明,杨小东等.基于倒谱特征的舰船辐射噪声识别算法研究.西北师范大学学报(自然科学版).2006,42(6)：34-43.
[121]樊养余.舰船噪声的高阶统计量特征提取及其应用.西北工业大学博士论文,1999.
[122]吴国清.船辐射噪声高阶谱分析和标记图.声学学报.1996,21(1)：29-39.
[123]郭业才.基于高阶统计量的水下目标动态谱特征增强研究.西北工业大学博士论文,2003.
[124]李长柏.基于高阶谱和循环谱的舰船噪声多源特征分离研究.西北工业大学硕士论文,2005.
[125]侯铁双.舰船噪声通过特性的时频分析.西北工业大学硕士论文,2002.
[126]刘增力.基于小波变换的鱼雷辐射噪声分析.西北工业大学硕士论文,1999.
[127]张学林.基于小波变换的舰船辐射噪声特征提取.西北工业大学博士论文,2000.
[128]尤里克.工程水声原理,北京：国防工业出版社,1972.
[129]刘伯胜,雷家煜.水声学原理,哈尔滨：哈尔滨工程大学出版社,1993.
[130]Kay S M. Autoregressive Spectral Analysis of Narrowband Processes in White Noise with Application to SONAR Signals. Georgian Institute of Technology. Doc. D.,1980.
[131]熊紫英,朱锡清.基于LOFAR谱和DEMON谱特征的舰船辐射噪声研究.船舶力学.2007,11(2)：300-306.
[132]Hoyer E, Stork R. The zoom FFT using complex modulation. Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP 77.,1977:78-81.
[133]Fjell P, Lunde E. A modified cascade fast Fourier transform in a spectrum analysing system. Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP'77.,1977:873-876.
[134]罗利春.Zoom-FFT的改进、频谱反演与时-频局部化特性.电子学报.2006,(01)：
[135]侯朝焕,阎世尊,蒋银林.实用FFT信号处理技术,北京：海洋出版社,1990.
[136]Madisetti V K, Williams D B eds., Digital Signal Processing Handbook. Florida:CRC Press,1999.
[137]张贤达,保铮.非平稳信号分析与处理,北京：国防工业出版社,1998.
[138]黄知涛,周一宇,姜文利.循环平稳信号处理与应用,北京：科学出版社,2006.
[139]王宏禹.信号处理理论综合与统一法,北京：国防工业出版社,2005.
[140]Gardner W A, Napolitano A, Paura L. Cyclostationarity:Half a century of research. Signal Processing.2006,86 (4):639-697.
[141]Serpedin E, Panduru F, Sari I, et al. Bibliography on Cyclostationarity. Signal Processing.2005,85 (12):2233-2303.
[142]Gardner W A. The Spectral Correlation Theory of Cyclostationary Time-Series. Signal Processing.1986,11 (1):13-36.
[143]Gardner W. Measurement of spectral correlation. Acoustics, Speech and Signal Processing, IEEE Transactions on.1986,34 (5):1111-1123.
[144]Huang N E, Shen Z, Long S R, et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis. Proceedings:Mathematical, Physical and Engineering Sciences. 1998,454 (1971):903-995.
[145]杨建文,贾民平,许飞云.经验模式分解在循环平稳故障信号分析中的应用.东南大学学报(自然科学版).2006,36(1)：77-80.
[146]Dong Y, Li Y, Xiao M, et al. Analysis of earthquake ground motions using an improved Hilbert-Huang transform. Soil Dynamics and Earthquake Engineering.2007,5 (2):13.
[147]Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. Signal Processing Letters, IEEE.2004,11 (2):112-114.
[148]Wu Z, Huang N E. A study of the characteristics of white noise using the empirical mode decomposition method. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences.2004,460 (2046): 1597-1611.
[149]Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms. IEEE-EURASIP workshop on nonlinear signal and image processing NSIP-03, Grado (I).2003:
[150]Rilling G, Flandrin P. One or Two Frequencies? The Empirical Mode Decomposition Answers. Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on]. 2008,56 (1):85-95.
[151]Huang N, Attoh-Okine N O. The Hilbert-Huang Transform in Engineering, Florida:CRC Press.2005.
[152]钟佑明,秦树人,汤宝平.Hilbert Huang变换中的理论研究.振动与冲击.2002,21(4)：13-17.
[153]Flandrin P. Empirical Mode Decompositions as Data-driven Wavelet-like Expansions. International Journal of Waveletes, Multiresolution and Information Processing.2004,2 (4):477-496.
[154]Huang N E. Wu M L C, Long S R, et al. A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis. Proceedings: Mathematical, Physical and Engineering Sciences.2003,459 (2037): 2317-2345.
[155]Chen Q, Huang N, Riemenschneider S, et al. A B-spline approach for empirical mode decompositions. Advances in Computational Mathematics. 2006,24:171-195.
[156]钟佑明,金涛,秦树人.希尔伯特-黄变换中的一种新包络线算法.数据采集与处理.2005,20(1)：13-17.
[157]张郁山,梁建文.应用自回归模型处理EMD方法中的边界问题.自然科学进展.2003,13(10)：1054-1059.
[158]Fritsch F N, Carlson R E. Monotone Piecewise Cubic Interpolation. SIAM Journal on Numerical Analysis.1980,17(2):238-246.
[159]Broersen PMT. Autoregressive model orders for Durbin's MA and ARMA estimators. Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on].2000,48 (8): 2454-2457.
[160]Li W, Siu WC, Poon J C H. A new algorithm on multiple unknown source signals estimation and separation in a reverberant space. Circuits, Systems, and Signal Processing.1999,18 (5):489-504.
[161]Choi S, Cichocki A, Amari S. Equivariant nonstationary source separation. Nural Networks.2002,15 (1):121-130.
[162]MOLGEDEY L, SCHUSTER H G. Separation of a mixture of independent signals using time delayed correlations. Physical Review Letters.1994,19 (3):185-196.
[163]Belouchrani A, Cichocki A. Robust whitening procedure in blind source separation context. Electronics Letters.2000,36 (24):2050-2051.
[164]Gopi E S. Algorithm Collections, for Digital Signal Processing Applica-tions Using Matlab, Netherlands:Springer,2007.
[165]Manolakis D G, Ingle V K, Kogon S M. Statistical and Adaptive Signal Processing, Norwood:Artech House, Inc.,2005.
[166]Porter M. Ocean acoustic library,11-30,2005; http://www. hlsresearch. com/oalib/.
[167]MIT O A. The Santa Barbara channel experiment,01-26,2001; http://sbex. mit. edu/.
[168]Sun X, Douglas S C. Adaptive paraunitary filter banks for contrast-based multichannel blind deconvolution. Acoustics, Speech, and Signal Processing,2001. Proceedings. (ICASSP′01).2001 IEEE International Conference on,2001:2753-2756.
[169]Aichner R, Buchner H, Yan F, et al. A real-time blind source separation scheme and its application to reverberant and noisy acoustic environments. Signal Processing.2006,86 (6):1260-1277.
[170]Kopriva I, Serssic D. Wavelet packets approach to blind separation of statistically dependent sources. Neurocomputing.2008,71:1642-1655.
[171]Acharyya R. A novel approach for blind separation of convolutive mixtures. Florida Institute of Technology. Ph.D.,2007.
[172]Mallat S. A Wavelet Tour of Signal Processing.2nd ed., New York: Academic Press,1999.
[173]Coifman R R, Wickerhauser M V. Entropy-based algorithms for best basis selection. IEEE Trans. Info. Theory.1992,38 (2):713-718.
[174]Koprivaa I, Serssic D. Wavelet packets approach to blind separation of statistically dependent sources. Neurocomputing.2008,71 (1642-1655):
[175]Haykin S. Neural Networks:A Comprehensive Foundation.2nd ed., Singapore:Pentice Hall,2001.
[176]Vincent E, Gribonval R, Fevotte C. Performance Measurement in Blind Audio Source Separation. IEEE Transactions on Audio, Speech, and Language Processing.2006,14 (4):1462-1469.
[177]Bofill P, Zibulevsky M. Underdetermined blind source separation using sparse representations. Signal Processing.2001,81 (11):2353-2362.
[178]Li Y, Amari S-I, Cichocki A, et al. Underdetermined Blind Source Separation Based on Sparse Representation. IEEE Transaction on Signal Processing.2006,54 (2):423-437.
[179]A■ssa-El-Bey A, Linh-Trung N, Abed-Meraim K, et al. Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain. IEEE Transactions on Signal Processing.2007,55 (3):897-907.
[180]Shan Z, Swary J, Aviyente S. Underdetermined source separation in the time-frequency domain.2007 IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol III, Pts 1-3, Proceedings.2007: 945-948.
[181]Yilmaz O, Rickard S. Blind separation of speech mixtures via time-frequency masking. Signal Processing, IEEE Transactions on.2004, 52 (7):1830-1847.
[182]Bofill P. Underdetermined blind separation of delayed sound sources in the frequency domain. Neurocomputing.2003,55 (3-4):627-641.
[183]Araki S, Sawada H, Mukai R, et al. Underdetermined blind sparse source separation for arbitrarily arranged multiple sensors. Signal Processing. 2007,87 (8):1833-1847.
[184]Duda R O, Hart P E, Stork D G. Pattern Classification.2nd Ed. ed., New York:Wiley,2001.
[185]Kaufman L, Rousseeuw P J. Finding Groups in Data:An Introduction to Cluster Analysis, New Jersey:John Wiley & Sons, Inc.,2005.
[186]Sawada H, Araki S, Mukai R, et al. Grouping Separated Frequency Components by Estimating Propagation Model Parameters in Frequency-Domain Blind Source Separation. IEEE Transactions on Audio, Speech, and Language Processing.2007,15 (5):1592-1604.
[187]Bofill P. Identifying Single Source Data for Mixing Matrix Estimation in Instantaneous Blind Source Separation. ICANN 08,2008:759-767.
[188]RoomSim ToolBox; http://www.mathworks.com/matlabcentral/fileex-change/loadFile.do?objectId=5184&objectType=File.
[189]Vincent E. Complex nonconvex l(p) norm minimization for underdetermined source separation. Independent Component Analysis and Signal Separation, Proceedings,2007:430-437.
[190]Benesty J, Chen J, Huang Y. Microphone Array Signal Processing, Berlin: Springer-Verlag,2008.
[2]C.Jutten, J.Herault eds., Independent Component Analysis (INCA) versus Principal Component Analysis. Elsevier,1988.
[3]Chung W. Blind Parameter Estimation for Data Acquisition in Digital Communication Systems. Cornell University. Ph. D.,2002.
[4]James C J, Lowe D. Extracting multisource brain activity from a single electromagnetic channel. Artificial Intelligence in Medicine.2003,28 (1): 89-104.
[5]Mei T, Xi J, Yin F, et al. Blind Source Separation Based on Time-Domain Optimization of a Frequency-Domain Independence Criterion. Audio, Speech, and Language Processing, IEEE Transactions on [see also Speech and Audio Processing, IEEE Transactions on].2006,14 (6):2075-2085.
[6]Li W. Algorithms for blind FIR channel estimation and signal restoration. The Hong Kong Polytechnic University. Ph. D.,1999.
[7]Chi C-Y, Chen C-H, Chen C-Y. Blind MAI and ISI Suppression for DS/CDMA Systems Using HOS-Based Inverse Filter Criteria. IEEE Transactions on Signal Processing.2002,50 (6):1368-1381.
[8]Amari S-I, Cichocki A. Adaptive Blind Signal Processing-Neural Network Approaches. Proceedings of the IEEE.1998,86 (10):2026-2048.
[9]王之程,陈宗歧,于渢等.舰船噪声测量与分析,北京：国防工业出版社，2004.
[10]杨德森,战国辰,刘星.低噪声水下目标辐射噪声测量的新方法研究.中国声学学会2001青年学术会议,上海,2001：245-247.
[11]倪晋平.水声信号盲分离技术研究.西北工业大学博士论文,2002.
[12]孔薇,杨杰,周越.一种改进的最大熵方法在船舶辐射噪声盲分离中的应用.上海交通大学学报.2004,38(12)：1962-1965.
[13]姜卫东,陆佶人,张宏滔.基于单个频点的水声信号盲源分离.电子与信息学报.2005,27(04)：532-535.
[14]张安清,邱天爽,章新华.分数低阶矩的信号盲分离方法.通信学报.2006,27(3)：32-36.
[15]肖瑛.基于水声信道的盲均衡算法研究.哈尔滨工程大学博士论文,2006.
[16]袁连喜.线性盲源分离算法的理论与应用研究.哈尔滨工程大学博士论文,2006.
[17]张艳萍,赵俊渭,王尚斌等.基于判决导引的水声信道混合盲均衡算法研究.声学学报.2005,30(5)：442-446.
[18]张安清,章新华.基于信息理论的舰船噪声盲分离算法.系统工程与电子技术.2002,24(1)：38-51.
[19]倪晋平,马远良,孙超等.用独立成份分析算法实现水声信号盲分离.声学学报.2002,27(4)：321-326.
[20]郭业才,何龙庆,韩迎鸽等.盲均衡技术在水声信道均衡中的应用进展.舰船科学技术.2007,29(2)：22-27.
[21]Gomes J, Barras V. Acoustic channel equalization results for the ASIMOV high-speed coherent data link. OVEANS 2000 MTS/IEEE Coference and Exhibition,2002:1437-1442.
[22]Liu H, Xu G. Closed-form blind symbol estimation in digital communications. IEEE Trans. Signal Processing.1995,43 (11): 2714-2723.
[23]王峰,赵俊渭,李桂娟.一种常数模与判决引导相结合的盲均衡算法研究.通信学报.2002,23(6)：105-112.
[24]Halzinakos D, Nikias C L. Blind Decision Feedback Equalization Structure Based on Adaptive CumulantTechnigures. ICCS'89,1989:1278-1282.
[25]Tong L. Blind sequence estimation. IEEE Trans. On Communication.1995, 43:2986-2995.
[26]Shalvi O, Weistein E. Super-exponential methods for blind equalization. IEEE Trans. Information Theory.1993,39 (2):505-519.
[27]肖瑛,刘国枝,李振兴等.遗传优化神经网络的水声信道盲均衡.应用声学.2006,25(6)：340-345.
[28]Kechriotis G, Zervas E. Using recurrent neural network for adaptive communication channel equalization. IEEE Trans. On neural networks. 1994,5:267-278.
[29]王永川,陈自力,刘增田.基于小波分解的时变信道盲辨识.测试技术学报.2005,19(1)：79-82.
[30]韩迎鸽,郭业才,吴造林等.基于正交小波变换的多模盲均衡器设计与算法仿真研究.仪器仪表学报.2008,29(7)：1441-1445.
[31]张安清,邱天爽,章新华.扩展联合对角化法的水声信号盲分离技术.系统工程与电子技术.2003,25(9)：1058-1060.
[32]姜卫东,陆佶人,张宏滔.基于两个邻近频点相关特性的水声信号盲源分离.电子与信息学报.2006,28(9)：1555-1559.
[33]张安清,章新华,邱天爽等.基于线谱点的一种频域盲分离方法.系统工程与电子技术.2006,28(9)：1307-1310.
[34]姜卫东,张宏滔,陆佶人.噪声环境下水声信号瞬时盲源分离方法研究.声学技术.2006,25(3)：182-186.
[35]倪晋平,马远良,张忠兵.一种强干扰下超弱水声信号自适应盲分离的快速算法.声学技术.2002,3：
[36]Jutten C, Herault J. Blind separation of sources, part I. An adaptive algorithm based on neuromimetic architecture. Signal Processing.1991,24 (1):1-10.
[37]Comon P. Independent component analysis, A new concept? Signal Processing.1994,36 (3):287-314.
[38]Hyvarinen A, Karhunen J, Oja E. Independent component analysis, New York:John Wiley & Sons, Inc.,2001.
[39]Comon P, Jutten C, Herault J. Blind separation of sources, part II. Problems statement. Signal Processing.1991,24 (1):11-20.
[40]Sorouchyari E. Blind separation of sources, part III. Stability analysis. Signal Processing.1991,24 (1):21-29.
[41]Cardoso J-F. Source separation using higher order moments. Icassp'89, 1989:2109-2112.
[42]Cardoso J F. Super-symmetrical decomposition of the 4th-order cumulant tensor-blind identification of more sources than sensors. Icassp 91, Vols 1-5.1991:3109-3112.
[43]Tong L, Liu R-W, Soon V C, et al. Indeterminacy and identifiability of blinde identification. IEEE transactions on circuits and systems.1991,38 (5):499-509.
[44]Tong L, Inouye Y, Liu R-W. Waveform-Preserving Blind Estimation of Multiple Independent Sources. IEEE Transactions on Signal Processing. 1993,41 (7):2461-2470.
[45]Tong L, Soon V C, Huang Y. F, et al. AMUSE:a new blind identification algorithm. Circuits and Systems,1990., IEEE International Symposium on,, 1990:1784-1787.
[46]Cao X-R, Liu R-w. General approach to blind source separation. IEEE Transactions on Signal Processing.1996,44 (3):562-571.
[47]Hyvarinen A. A unifying model for blind separation of independent sources. Signal Processing.2005,85:1419-1427.
[48]Cardoso J F, Souloumiac A. Blind beamforming for non-Gaussian signals. lee Proceedings-F Radar and Signal Processing.1993,140 (6):362-370.
[49]Cardoso J F, Moulines E. Minimum contrast estimation with application to array-processing. Icassp-93:1993 Ieee International Conference on Acoustics, Speech, and Signal Processing, Vols 1-5.1993:D384-D387.
[50]Cardoso J F, Laheld B H. Equivariant adaptive source separation. IEEE Transactions on Signal Processing.1996,44 (12):3017-3030.
[51]Amari S, Cardoso J F. Blind source separation-Semiparametric statistical approach. IEEE Transactions on Signal Processing.1997,45 (11): 2692-2700.
[52]Yang H H, Amari S-I. Adaptive on-line learning algorithms for blind separation-maximum entropy and minimum mutal information. Neural Computation.1997,7 (9):1457-1482.
[53]Hyvarinen A. Fast and robust fixed-point algorithms for independent component analysis. Neural Networks, IEEE Transactions on.1999,10 (3): 626-634.
[54]Cichocki A, Unbehauen R, Rummert E. Robust learning algorithm for blind separation of signals. Electronic letters.1994,30 (17):1386-1387.
[55]Cichocki A, Unbehauen R. Robust neural networks with on-line learning for blind identification and blind separation of sources. IEEE transactions on circuits and systems.1996,43 (11):894-906.
[56]Karhunen J, Liuyue W, Vigario R. Nonlinear PCA type approaches for source separation and independent component analysis. Neural Networks, 1995. Proceedings., IEEE International Conference on,1995:995-1000.
[57]Karhunen J, Oja E, Wang L, et al. A class of neural networks for independent component analysis. Neural Networks, IEEE Transactions on. 1997,8 (3):486-504.
[58]Oja E. The nonlinear PCA learning rule in independent component analysis. Neurocomputing.1997,17 (1):25-45.
[59]Hyvarinen A. The Fixed-Point Algorithm and Maximum Likelihood Estimation for Independent Component Analysis. Neural Processing Letters.1999,10(1):1-5.
[60]Matsuoka K, Ohoya M, Kawamoto M. A neural net for blind separation of nonstationary signals. Neural Networks.1995,8 (3):411-419.
[61]Choi S, Cichocki A. Algebraic differential decorrelation for nonstationary source separation. Electronics Letters.2001,37 (23):1414-1415.
[62]Pham D T, Cardoso J F. Blind separation of instantaneous mixtures of nonstationary sources. IEEE Transactions on Signal Processing.2001,49 (9):1837-1848.
[63]Douglas S C, Kung S Y. Kuicnet Algorithms for Blind Deconvolution. IEEE Workshop on Neural Networks for Signal Processing, Cambridge, UK,1998:3-12.
[64]Hyvarinen A, Oja E. A Fast Fixed-Point Algorithm for Independent Component Analysis. Neural Computation.1997,9 (7):1483-1492.
[65]Bingham E, Hyvarinen A. A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals. International Journal of Neural Systems.2000,10 (1):1-8.
[66], Novey M, Adali T. On Extending the Complex FastICA Algorithm to Noncircular Sources. Signal Processing, IEEE Transactions on.2008,56 (5):2148-2154.
[67]Hyvarinen A, Koster U. FastISA:A fast fixed-point algorithm for Independent Subspace Analysis, ESANN'2006 proceedings-European Symposium on Artificial Neural Networks, Bruges, Belgium,2006: 371-376.
[68]Valpola H, Giannakopoulos X, Honkela A, et al. Nonlinear independent component analysis using ensemble learning:Experiments and discussion. Proc. Int. Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000), Helsinki, Finland,2000:351-356.
[69]Taleb A, Jutten C. Source separation in post-nonlinear mixtures. IEEE Transactions on Signal Processing.1999,47 (10):2807-2820.
[70]Jutten C, Taleb A. Source Separation:from Dusk till Dawn. Second International Workshop on Independent Component Analysis and Blind Signal Separation,2000:662-673.
[71]Hyvarinen A, Pajunen P. Nonlinear independent component analysis: Existence and uniqueness results. Neural Networks.1999,12 (3):429-439.
[72]Pajunen P, Hyvarinen A, Karhunen J. Nonlinear blind source separation by self-organizing maps, Proc. Int. Conf. on Neural Information Processing, Hong Kong,1996:1207-1210.
[73]Bishop C M, Svensen M, Williams C K I. GTM:The generative topographic mapping. Neural Computation.1998,10:215-234.
[74]Pajunen P, Karhunen J. A maximum likelihood approach to nonlinear blind source separation. Int. Conf. on Artificial Neural Networks (ICANN’97), Lausanne, Switzerland,1997:541-546.
[75]H.Valpola. Nonlinear independent component analysis using ensemble learning:Theory. Girolami M ed. Proc. Int.Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000), Helsinki, Finland,2000:251-256.
[76]Valpola H, Giannakopoulos X, Honkela A, et al. Nonlinear independent component analysis using ensemble learning:experiments and discussion, Proc. Int. Workshop on Independent Component Analysis and Blind Signal Separation, Helsinki, Finland,2000:351-356.
[77]Lappalainen H, Honkela A. Bayesian nonlinear independent component analysis by multi-layer perceptrons, Advances in Independent Component Analysis, Girolami M. ed., New York:Springer-Verlag,2000:93-121.
[78]Cichocki A, Sabala I, Choi S, et al. Self-adaptive independent component analysis for sub-gaussian and super-gaussian mixtures with unknown number of source signals and additive noise. Int. Symp. on Nonlinear Theory and Applications, Honolulu, HI,1997:731-734.
[79]Cichocki A, Sabala I, Amari S. Intelligent neural networks for blind signal processing with unknown number of sources. Int. Symp. on Engineering of Intelligent Systems, Tenerife, Spain,1998:148-154.
[80]Lathauwer L D, Castaing J, Cardoso J F. Fourth-order cumulant-based blind identification of underdetermined mixtures. IEEE Transactions on Signal Processing.2007,55 (6):2965-2973.
[81]Vielva L, Pereiro Y, Erdogmus D, et al. Inversion Techniques for Underdetermined Bss in an Arbitrary Number of Dimensions.4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA03), Nara, Japan,2003:131-136.
[82]Araki S, Makino S, Sawada H, et al. Underdetermined blind separation of convolutive mixtures of speech with directivity pattern based mask and ICA. Independent Component Analysis and Blind Signal Separation.2004, 3195:898-905.
[83]Luengo D, Santamaria I, Vielva L, et al. Underdetermined blind separation of sparse sources with instantaneous and convolutive mixtures.2003 IEEE Xiii Workshop on Neural Networks for Signal Processing-Nnsp'03.2003: 279-288.
[84]Bofill P, Monte E. Underdetermined convoluted source reconstruction using LP and SOCP, and a neural approximator of the optimizer. Independent Component Analysis and Blind Signal Separation, Proceedings,2006:569-576.
[85]Winter S, Kellermann W, Sawada H, et al. MAP based underdetermined blind source separation of convolutive mixtures by hierarchical clustering and 11-norm minimization. EURASIP J. Adv.2Signal Process.2007:
[86]Bofill P, Zibulevsky M. Blind separation of more sources than mixtures using sparasity of their short-time Fourier transform. International Workshop on ICA and BSS (ICA00), Helsinki, Finland,2000:87-92.
[87]Abed-Meraim K, Nguyen L-W, Belouchrani A. Underdetermined Blind Source Separation for FM-Like Signals, Time Frequency Signal Analysis and Processing, Boashash B, ed., Oxford, UK:ELSEVIER Ltd,2003: 357-368.
[88]Widrow B, Glover J R, McCool J M, et al. Adaptive noise canceling: Principles and applications. IEEE Proceedings.1975,63:1692-1716.
[89]Widrow B, Steams S D. Adaptive Signal Processing, New Jersey: Prentice-Hall, Inc.,1985.
[90]Haykin S. Adaptive Filter Theory.3rd Ed. ed., New Jersey:Prentice-Hall, Inc.,2002.
[91]Godrey R, Rocca F. Zero memory non-linear deconvolution. Geophysical Processing.1981,29:189-228.
[92]Haykin S ed., Blind Deconvolution. New Jersey:Prentice-Hall, Inc.,1994.
[93]Haykin S. Adaptive Filter Theory.3rd ed., New Jersey:Prentice-Hall, Inc., 1996.
[94]Santamaria I, Pantaleón C, Vielva L, et al. Blind Equalization of Constant Modulus Signals Using Support Vector Machines. IEEE Transactions on Signal Processing.2004,52 (6):1773-1782.
[95]Benveniste A, Goursat G. Blind Equalizers. IEEE Transactions on Communications.1984,32:871-883.
[96]Shalvi O, Weinstein E. New Criteria for Blind Deconvolution of Nonminimum Phase Systems (Channels). IEEE Transaction on Information Theory.1990,36 (2):312-321.
[97]Torkkola K. Blind separation of delayed and convolved sources, Unsupervised Adaptive Filtering, Haykin S, ed., New York:Wiley,2000: 321-375.
[98]Amari S-I, Cichocki A, Yang H H. Blind Signal Separation and Extraction: Neural and Information-Theoretic Approaches, Unsupervised Adaptive Filtering, Haykin S, ed., New York:Wiley,2000:63-138.
[99]Tong L, Xu G, Kailath T. Blind channel identification and equalization using spectral correlation measurements, Part Ⅱ:A time-domain approach, Cyclostationary in communications and signal processing, Gardner W A, ed., New York:IEEE Press,1994:437-454.
[100]Dapena A, Serviere C, Castedo L. Inversion of the sliding Fourier transform using only two frequency bins and its application to source separation. Signal Processing.2003,83 (2):453-457.
[101]Rahbar K, Reilly J P. A Frequency Domain Method for Blind Source Separation of Convolutive Audio Mixtures. IEEE Transactions on Speech and Audio Processing.2005,13 (5):832-844.
[102]Xie P, Grant S L. A Fast and Efficient Frequency-Domain Method for Convolutive Blind Source Separation. Region 5 Conference,2008 IEEE, 2008:1-4.
[103]Buchner H, Kellermann W. Improved Kalman gain computation for multichannel frequency-domain adaptive filtering and application to acoustic echo cancellation.2002 IEEE International Conference on Acoustics, Speech, and Signal Processing, Orlando, FL, USA,2002: 1909-12.
[104]Buchner H, Aichner R, Kellermann W. TRINICON:A versatile framework for multichannel blind signal processing. Montreal, Que, Canada,2004: 889-892.
[105]Buchner H, Aichner R, Kellermann W. Blind Source Separation for Convolutive Mixtures:A Unified Treatment. Audio Signal Processing for Next-Generation Multimedia Communication Systems,2004:255-293.
[106]Buchner H, Aichner R, Kellermann W. A generalization of blind source separation algorithms for convolutive mixtures based on second-order statistics. IEEE Transactions on Speech and Audio Processing.2005,13 (1): 120-134.
[107]Buchner H, Aichner R, Stenglein J, et al. Simultaneous localization of multiple sound sources using blind adaptive MIMO filtering. Philadelphia, PA, United States,2005:97-100.
[108]Moulines E, Duhamel P, Cardoso J F, et al. Subspace Methods for the Blind Identification of Multichannel FIR Filters. IEEE Transactions on Signal Processing.1995,43 (2):516-525.
[109]Diamantaras K I, Papadimitriou T. Subspace-based channel shortening for the blind separation of convolutive mixtures. IEEE Transactions on Signal Processing.2006,54 (10):3669-3677.
[110]Peng C Y, Zhang X D. On recursive oblique projectors. Signal Processing Letters, IEEE.2005,12 (6):433-436.
[111]Judge G G, Hill R C, Griffiths W E, et al. Introduction to the Theory and Practice of Econometrics, New York:Wiley,1988.
[112]Conover W J. Practical Nonparametric Statistics, New York:Wiley,1980.
[113]Xiao J, Borgnat P, Flandrin P. Testing Stationarity With Time-Frequency Surrogates, EURASIP 2007, Poznan,2007:2020-2024.
[114]Xiao J, Borgnat P, Flandrin P, et al. Testing Stationarity with Surrogates-A One-Class SVM Approach. Borgnat P ed. Statistical Signal Processing, 2007. SSP'07. IEEE/SP 14th Workshop on,2007:720-724.
[115]Martin W, P.Flandrin. Detection of Changes of Signal Structure by Using the Wigner-Ville Spectrum. Signal Process.1985,8:215-233.
[116]Bayram M, Baraniuk R. Multiple Window Time-varying Spectrum Estimation, Nonlinear and Nonstationary Signal Processing, Fitzgerald W J, ed., London:Cambridge University Press,2000:292-316.
[117]吴国清,魏学环,周钢.提取螺旋桨识别特征的二种途径.声学学报.1993,18(3)：210-216.
[118]陶笃纯.舰船噪声节奏的研究(Ⅰ)-数学模型及功率谱密度.声学学报.1983,8(2)：65-76.
[119]陶笃纯.舰船噪声节奏的研究(Ⅱ)——自相关函数及节奏信息的提取.声学学报.1983,8(5)：280-289.
[120]王彪,杨志明,杨小东等.基于倒谱特征的舰船辐射噪声识别算法研究.西北师范大学学报(自然科学版).2006,42(6)：34-43.
[121]樊养余.舰船噪声的高阶统计量特征提取及其应用.西北工业大学博士论文,1999.
[122]吴国清.船辐射噪声高阶谱分析和标记图.声学学报.1996,21(1)：29-39.
[123]郭业才.基于高阶统计量的水下目标动态谱特征增强研究.西北工业大学博士论文,2003.
[124]李长柏.基于高阶谱和循环谱的舰船噪声多源特征分离研究.西北工业大学硕士论文,2005.
[125]侯铁双.舰船噪声通过特性的时频分析.西北工业大学硕士论文,2002.
[126]刘增力.基于小波变换的鱼雷辐射噪声分析.西北工业大学硕士论文,1999.
[127]张学林.基于小波变换的舰船辐射噪声特征提取.西北工业大学博士论文,2000.
[128]尤里克.工程水声原理,北京：国防工业出版社,1972.
[129]刘伯胜,雷家煜.水声学原理,哈尔滨：哈尔滨工程大学出版社,1993.
[130]Kay S M. Autoregressive Spectral Analysis of Narrowband Processes in White Noise with Application to SONAR Signals. Georgian Institute of Technology. Doc. D.,1980.
[131]熊紫英,朱锡清.基于LOFAR谱和DEMON谱特征的舰船辐射噪声研究.船舶力学.2007,11(2)：300-306.
[132]Hoyer E, Stork R. The zoom FFT using complex modulation. Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP 77.,1977:78-81.
[133]Fjell P, Lunde E. A modified cascade fast Fourier transform in a spectrum analysing system. Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP'77.,1977:873-876.
[134]罗利春.Zoom-FFT的改进、频谱反演与时-频局部化特性.电子学报.2006,(01)：
[135]侯朝焕,阎世尊,蒋银林.实用FFT信号处理技术,北京：海洋出版社,1990.
[136]Madisetti V K, Williams D B eds., Digital Signal Processing Handbook. Florida:CRC Press,1999.
[137]张贤达,保铮.非平稳信号分析与处理,北京：国防工业出版社,1998.
[138]黄知涛,周一宇,姜文利.循环平稳信号处理与应用,北京：科学出版社,2006.
[139]王宏禹.信号处理理论综合与统一法,北京：国防工业出版社,2005.
[140]Gardner W A, Napolitano A, Paura L. Cyclostationarity:Half a century of research. Signal Processing.2006,86 (4):639-697.
[141]Serpedin E, Panduru F, Sari I, et al. Bibliography on Cyclostationarity. Signal Processing.2005,85 (12):2233-2303.
[142]Gardner W A. The Spectral Correlation Theory of Cyclostationary Time-Series. Signal Processing.1986,11 (1):13-36.
[143]Gardner W. Measurement of spectral correlation. Acoustics, Speech and Signal Processing, IEEE Transactions on.1986,34 (5):1111-1123.
[144]Huang N E, Shen Z, Long S R, et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis. Proceedings:Mathematical, Physical and Engineering Sciences. 1998,454 (1971):903-995.
[145]杨建文,贾民平,许飞云.经验模式分解在循环平稳故障信号分析中的应用.东南大学学报(自然科学版).2006,36(1)：77-80.
[146]Dong Y, Li Y, Xiao M, et al. Analysis of earthquake ground motions using an improved Hilbert-Huang transform. Soil Dynamics and Earthquake Engineering.2007,5 (2):13.
[147]Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. Signal Processing Letters, IEEE.2004,11 (2):112-114.
[148]Wu Z, Huang N E. A study of the characteristics of white noise using the empirical mode decomposition method. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences.2004,460 (2046): 1597-1611.
[149]Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms. IEEE-EURASIP workshop on nonlinear signal and image processing NSIP-03, Grado (I).2003:
[150]Rilling G, Flandrin P. One or Two Frequencies? The Empirical Mode Decomposition Answers. Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on]. 2008,56 (1):85-95.
[151]Huang N, Attoh-Okine N O. The Hilbert-Huang Transform in Engineering, Florida:CRC Press.2005.
[152]钟佑明,秦树人,汤宝平.Hilbert Huang变换中的理论研究.振动与冲击.2002,21(4)：13-17.
[153]Flandrin P. Empirical Mode Decompositions as Data-driven Wavelet-like Expansions. International Journal of Waveletes, Multiresolution and Information Processing.2004,2 (4):477-496.
[154]Huang N E. Wu M L C, Long S R, et al. A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectral Analysis. Proceedings: Mathematical, Physical and Engineering Sciences.2003,459 (2037): 2317-2345.
[155]Chen Q, Huang N, Riemenschneider S, et al. A B-spline approach for empirical mode decompositions. Advances in Computational Mathematics. 2006,24:171-195.
[156]钟佑明,金涛,秦树人.希尔伯特-黄变换中的一种新包络线算法.数据采集与处理.2005,20(1)：13-17.
[157]张郁山,梁建文.应用自回归模型处理EMD方法中的边界问题.自然科学进展.2003,13(10)：1054-1059.
[158]Fritsch F N, Carlson R E. Monotone Piecewise Cubic Interpolation. SIAM Journal on Numerical Analysis.1980,17(2):238-246.
[159]Broersen PMT. Autoregressive model orders for Durbin's MA and ARMA estimators. Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on].2000,48 (8): 2454-2457.
[160]Li W, Siu WC, Poon J C H. A new algorithm on multiple unknown source signals estimation and separation in a reverberant space. Circuits, Systems, and Signal Processing.1999,18 (5):489-504.
[161]Choi S, Cichocki A, Amari S. Equivariant nonstationary source separation. Nural Networks.2002,15 (1):121-130.
[162]MOLGEDEY L, SCHUSTER H G. Separation of a mixture of independent signals using time delayed correlations. Physical Review Letters.1994,19 (3):185-196.
[163]Belouchrani A, Cichocki A. Robust whitening procedure in blind source separation context. Electronics Letters.2000,36 (24):2050-2051.
[164]Gopi E S. Algorithm Collections, for Digital Signal Processing Applica-tions Using Matlab, Netherlands:Springer,2007.
[165]Manolakis D G, Ingle V K, Kogon S M. Statistical and Adaptive Signal Processing, Norwood:Artech House, Inc.,2005.
[166]Porter M. Ocean acoustic library,11-30,2005; http://www. hlsresearch. com/oalib/.
[167]MIT O A. The Santa Barbara channel experiment,01-26,2001; http://sbex. mit. edu/.
[168]Sun X, Douglas S C. Adaptive paraunitary filter banks for contrast-based multichannel blind deconvolution. Acoustics, Speech, and Signal Processing,2001. Proceedings. (ICASSP′01).2001 IEEE International Conference on,2001:2753-2756.
[169]Aichner R, Buchner H, Yan F, et al. A real-time blind source separation scheme and its application to reverberant and noisy acoustic environments. Signal Processing.2006,86 (6):1260-1277.
[170]Kopriva I, Serssic D. Wavelet packets approach to blind separation of statistically dependent sources. Neurocomputing.2008,71:1642-1655.
[171]Acharyya R. A novel approach for blind separation of convolutive mixtures. Florida Institute of Technology. Ph.D.,2007.
[172]Mallat S. A Wavelet Tour of Signal Processing.2nd ed., New York: Academic Press,1999.
[173]Coifman R R, Wickerhauser M V. Entropy-based algorithms for best basis selection. IEEE Trans. Info. Theory.1992,38 (2):713-718.
[174]Koprivaa I, Serssic D. Wavelet packets approach to blind separation of statistically dependent sources. Neurocomputing.2008,71 (1642-1655):
[175]Haykin S. Neural Networks:A Comprehensive Foundation.2nd ed., Singapore:Pentice Hall,2001.
[176]Vincent E, Gribonval R, Fevotte C. Performance Measurement in Blind Audio Source Separation. IEEE Transactions on Audio, Speech, and Language Processing.2006,14 (4):1462-1469.
[177]Bofill P, Zibulevsky M. Underdetermined blind source separation using sparse representations. Signal Processing.2001,81 (11):2353-2362.
[178]Li Y, Amari S-I, Cichocki A, et al. Underdetermined Blind Source Separation Based on Sparse Representation. IEEE Transaction on Signal Processing.2006,54 (2):423-437.
[179]A■ssa-El-Bey A, Linh-Trung N, Abed-Meraim K, et al. Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain. IEEE Transactions on Signal Processing.2007,55 (3):897-907.
[180]Shan Z, Swary J, Aviyente S. Underdetermined source separation in the time-frequency domain.2007 IEEE International Conference on Acoustics, Speech, and Signal Processing, Vol III, Pts 1-3, Proceedings.2007: 945-948.
[181]Yilmaz O, Rickard S. Blind separation of speech mixtures via time-frequency masking. Signal Processing, IEEE Transactions on.2004, 52 (7):1830-1847.
[182]Bofill P. Underdetermined blind separation of delayed sound sources in the frequency domain. Neurocomputing.2003,55 (3-4):627-641.
[183]Araki S, Sawada H, Mukai R, et al. Underdetermined blind sparse source separation for arbitrarily arranged multiple sensors. Signal Processing. 2007,87 (8):1833-1847.
[184]Duda R O, Hart P E, Stork D G. Pattern Classification.2nd Ed. ed., New York:Wiley,2001.
[185]Kaufman L, Rousseeuw P J. Finding Groups in Data:An Introduction to Cluster Analysis, New Jersey:John Wiley & Sons, Inc.,2005.
[186]Sawada H, Araki S, Mukai R, et al. Grouping Separated Frequency Components by Estimating Propagation Model Parameters in Frequency-Domain Blind Source Separation. IEEE Transactions on Audio, Speech, and Language Processing.2007,15 (5):1592-1604.
[187]Bofill P. Identifying Single Source Data for Mixing Matrix Estimation in Instantaneous Blind Source Separation. ICANN 08,2008:759-767.
[188]RoomSim ToolBox; http://www.mathworks.com/matlabcentral/fileex-change/loadFile.do?objectId=5184&objectType=File.
[189]Vincent E. Complex nonconvex l(p) norm minimization for underdetermined source separation. Independent Component Analysis and Signal Separation, Proceedings,2007:430-437.
[190]Benesty J, Chen J, Huang Y. Microphone Array Signal Processing, Berlin: Springer-Verlag,2008.