面向目标感知的盲信号处理算法研究
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摘要
盲信号处理是当前信号处理领域中的热点课题,其优势在于除了假定源信号之间相互独立外,不需要任何其它的先验知识,有广泛的应用前景。本论文针对盲信号处理中的挑战性课题,尝试通过理论和实验研究,针对目标感知系统,解决当前目标增强技术下难以解决的目标增强问题,从而提升系统的目标感知能力。重点研究了两个理论框架下的盲分离问题,一是日常办公环境下混响严重的卷积混合盲分离模型,这是本文所解决的盲分离中第1个难题,着重研究了卷积混合盲分离频域解法中的复值信号盲分离和次序不确定性问题;二是基于粒子滤波的含噪信号盲分离研究,为解决盲信号处理中噪声环境下的后非线性和欠定盲分离等难题提供了一个崭新的思路。在实际应用上,重点探讨了卷积混合盲分离频域算法在语音信号盲分离和主动声纳目标检测中的应用,前者是普遍性问题,后者是关于国防军事装备中迫切需要解决的问题。
本文首先对复值信号盲分离研究历史与现状进行简要回顾和论述,之后指出现行5个主流算法的优缺点:法国J.-F.Cardoso提出的JADE是用复值向量的共轭转置代替了实数的转置来建立累积量矩阵,再对累积量矩阵进行特征值分解求得分离矩阵;赫尔辛基理工大学Ella Bingham和Aapo Hyvarinen提出的ComplexFastICA是对复数绝对值运算,与实数算法形式相同;马里兰大学Calhoun Vince与T. Adali提出的Complex ICA是基于互信息最小化的自然梯度盲分离算法,但是忽略了复值信号的伪参数特性;赫尔辛基理工大学Jan Eriksson和Visa Koivunen提出的SUT算法是对非正则复值向量的伪自相关矩阵进行分解从而得到分离矩阵;美国Scott C. Douglas提出的Equivariant SUT利用了伪自相关矩阵的特性,不过算法是对实值信号算法直接进行改进得到的,没有建立代价函数。
鉴于此,本文先根据非正则复值向量的伪自相关矩阵构造了二阶统计量的代价函数,再通过梯度下降法推导出基于伪自相关矩阵的二阶复值信号盲分离算法Strong SOS;其次构建互信息最小化的代价函数,在推导过程中对复值信号分别进行共轭转置和转置运算,从而推导出基于伪互相关矩阵的高阶统计量复值信号盲分离算法Strong HOS,最后通过仿真试验与上述的5种算法进行比对。由于所发展的新算法充分利用了非正则复值向量“伪参数”的性质,从分离效果上看,Strong SOS和Strong HOS收敛效果更好,分离性能更强。进而得出结论:无论是理论分析还是仿真试验,都说明了非正则向量的“伪参数”使复值盲信号分离算法收敛更快、分离效果更好。这项工作是卷积混合盲分离频域算法的第一步,为更加准确地解决算法第二步的频率对准问题奠定了基础。
本文第二个研究重点是卷积混合盲分离频域解法中的次序不确定问题。结合非正则复向量的“伪参数”,首先提出了扩展自相关矩阵、扩展驾驶向量和扩展权值向量,提出了扩展MVDR波束形成方法ExMVDR,仿真试验表明该方法比MVDR输出的主波束信噪比高出2dB左右;其次,深入研究了互参数法的理论基础,公式推导和高斯白噪声下的仿真试验都揭示了互参数法有效的原因之一是由于离散傅立叶的计算方法提供了互参数的相关性,从而得出了互参数法的应用可以拓展至语音信号以外的信号的结论;通过对源信号计算互参数来反映相关系数和KL距离在语音信号卷积混合频域解法中的性能,发现KL距离的性能优于相关系数,但是在某些情况下,由于离散化带来的误差和信号长度太短而引起的独立性下降等因素,使得KL距离仍然存在着不能够进行有效进行频率对准的可能;最后论证了语音信号分段做FFT之后,不同窗对应的同频率下的复值信号是非正则的,从而进一步提出了卷积混和盲分离频域解法的方法: Strong SOS+ExMVDR, Strong HOS+ExMVDR和Strong HOS+KL。
为了检验上述算法的性能,对日常办公室环境下的卷积混合语音信号进行解卷积实验。混响时间是130毫秒,采样频率是8000赫兹,源信号是17个汉字组成的中文语音信号和一段轻音乐。实验中,混合信号是通过著名的Image算法模拟日常办公环境下房间内的传递函数与单独录制的源信号相卷积混合的。无论是频域内复值混合信号的盲分离计算,还是频率对准阶段,本文所提出的方法与主流算法比,都具有一定的优势,因此在与日本NTT的Shoji Makino等人的算法Polar ICA+MVDR比对中,Strong SOS+ExMVDR和Strong HOS+ExMVDR估计的源信号信噪比要高出Polar ICA+MVDR一个分贝以上,另外,本文还使用IBM Viavoice中文语音识别软件对不同方法估计的17个汉字进行识别,Strong SOS+ExMVDR和Strong HOS+ExMVDR估计的17个汉字,软件都可识别出,Polar ICA+MVDR估计的源信号,IBM Viavoice只能够认出14个汉字,而ICA Center上提供的FDICA算法估计的源信号,Viavoice只能够认出13个汉字,对于Strong HOS+KL估计的源信号,能够认出15个汉字,少于Strong SOS+ExMVDR和Strong HOS+ExMVDR,这是由于在频率对准阶段采用的互参数法KL不如ExMVDR准确。通过这些实验更加有效的证明了所提出算法的优越性,也充分说明了非正则复值向量“伪参数”在复值信号处理中的重要作用;通过比较Viavoice对混合信号和估计的源信号的识别率,说明了语音识别软件Viavoice在盲信号处理下识别能力得到提高,从而进一步证明了本文所提出的“面向目标感知的盲信号处理算法研究”的思路是正确的。无论是比较算法评价指标还是语音识别软件识别不同方法估计的源信号的准确率,都证明所提出的算法Strong SOS+ExMVDR, Strong HOS+ExMVDR和Strong HOS+KL比现存主流算法有优势,从而推动了严重混响条件下的卷积混合盲分离频域算法的发展。
粒子滤波是解决非线性非高斯过程的有效方法,在过去10多年里得到了迅速发展,而随着盲信号处理理论的发展,含噪、非线性盲分离受到越来越多的关注,本文通过粒子滤波来解决含噪的后非线性和欠定等多种盲分离模型,建立了粒子滤波+不含噪盲分离的框架。首先对含噪盲分离模型进行分解,提出了如果将不含噪的混合信号估计出来就可以将含噪模型转化为不含噪模型的思路;其次,通过建立不含噪混合信号的时变AR模型来构造状态空间方程中的状态方程,通过可观测到的含噪混合信号与要估计的不含噪混合信号的线性或者非线性关系,构造了状态空间方程中的观测方程,从而发现了动态状态空间方程与含噪盲分离相结合的可行性;按此思路,通过粒子滤波可将含噪盲分离模型转化为不含噪模型,在后非线性函数已知或者可估计出的情况下,可将非线性盲分离模型转化为线性模型,然后通过现有的不含噪盲分离算法估计出源信号。在这个框架下,本文从理论上解决了线性正定含噪、非线性正定含噪、线性欠定含噪、非线性欠定含噪等非常有挑战性的盲分离问题。
由于各种含噪盲分离模型成熟解法不多,首先进行相对简单的正定线性含噪盲分离实验,并与赫尔辛基理工大学J. Sarela和H.Valpola等人提出的Denoising Source Separation (DSS)算法进行比对,以验证所提出方案的可靠性。信号混合采用瞬时混合方式,噪声是加性的。在0至12dB的输入信噪比下,无论是高斯白噪声还是伽玛噪声环境,从算法评判标准上看,所提出的PF+FastICA方法对源信号的估计要好于DSS。紧接着,对正定非线性、欠定线性和欠定非线性盲分离算法进行试验,输入信噪比均为10dB。粒子滤波的贡献有5至6dB左右,对源信号的估计效果与正定线性含噪和不含噪混合两种情况下的效果相当。实验进一步证实了所提出方案的可行性、可靠性和有效性,为解决噪声环境下的非线性、欠定盲分离问题建立了崭新的理论框架。在卷积混合盲分离的应用上,本文还重点讨论了其在主动声纳目标检测中的应用。本文将目标回波看作第一个源信号,将近海的混响或者远海的背景干扰看作第二个源信号,通过选取波束形成后的主波束和与主波束相邻的波束作为盲分离中的两个接收信号,采用本文所发展的卷积混合盲分离频域算法对主波束目标信号进行增强。真实目标海上实验数据处理结果表明:通过盲分离,主波束的匹配滤波输出得到了2.5dB的增益,目标时频分析的特征更加清晰,证实了本文所提出方案的正确性,在盲分离算法的实际应用上迈出了有价值的一步,对主动声纳目标检测、特征提取以及目标识别技术的发展有重要的意义。
本文的工作得到国家自然科学基金项目“声信号盲分离算法研究”(信息学部,批准号60372075)的资助,同时还得到上海市科委基础研究项目“复杂环境下动态系统的结构学习研究”(No: 05JC14026)和国家重点实验室开放式基金“复值信号盲分离算法研究”(VSN-2006-04)的资助。本文同时还得到国防重点实验室基金项目“水声信息处理技术与系统研究”和国防重点攻关项目“主动拖曳式声纳研究”的数据支持。
Blind signal processing (BSP) is a very hot topic in the signal processing society. The advantage is that BSP does not require any prior knowledge except the independence among different sources, so BSP has been applied in many disciplines. This dissertation is targeted to the challenging problems in BSP. To improve the perception capacity is the final goal in the application with BSP enforcing the target in perception systems. Two frameworks are mainly studied. One is the blind separation of convolutive mixtures in heavy reverberation, which is the first hard problem the dissertation resolves. The complex-valued source separation and the permutation are studied for the blind separation of convolutive mixtures in the frequency domain. The second is the particle filtering based noisy source separation, which provides a novel approach for the post-nonlinear and underdetermined blind source separation under the noisy environment. In the real-word application, it is mainly discussed that how blind separation of convolutive mixtures are adopted in the speech source separation and the active sonar target detection.
The dissertation first deals with the blind separation of complex-valued sources. After the improper complex-valued vector and the characteristic of pseudo-autocorrelation matrix are explored, we find that JADE, Complex FastICA, Complex ICA, SUT and Equivariant SUT do not make full use of the good characteristics of the improper complex-valued vector. Then, based on the pseudo-autocorrelation matrix, we construct a second order statistics (SOS) cost function. With the decent gradient algorithm, a new SOS based blind separation of complex-valued sources algorithm is inferred. We name it as Strong SOS. Along the same idea, we construct the cost function based on the minimum of the mutual information between different independent sources. In the process to infer the new algorithm, we perform the conjugate transpose and transpose operation to the complex-valued vector and matrix, and the new algorithm is obtained based on the pseudo-crosscorrelation matrix. We name it as Strong HOS compared to Strong SOS. Through simulations, it is proved that Strong HOS and Strong SOS perform better than JADE, Complex FastICA, Complex ICA, SUT and Equivariant SUT. It is the reason that Strong HOS and Strong SOS explore the characteristics of improper complex-valued vectors entirely. Blind separation of complex-valued sources is the first step to the blind separation of convolutive mixtures in the frequency domain. Strong HOS and Strong SOS make much solider foundation to correct the permutation in the second step.
And then, the permutation indeterminacy of frequency domain approach to blind separation of convolutive mixtures is studied. Based on the pseudo-parameter of improper vectors, the traditional beamforming method——MVDR is revised. Simulation validates that the extended MVDR functions better than MVDR in low SNR situation.
After the mutual parameters are deeply analyzed, it is natural to find that the computation method of DFT introduces the correlation to the mutual parameters method, hence, the mutual parameters can be extended to other signals except speech. By different simulation, different current algorithms are compared. KL distance behaves better than correlation coefficient. However, in some frequency bins, mutual parameters still possibly can not correct the permutation indeterminacy. At last, Strong SOS+ExMVDR, Strong HOS+ExMVDR, and Strong HOS+KL are composed together for the frequency domain method.
To test the performance of algorithms we put forward, the experiment simulates the situation in the ordinary office. The reverberation time is 130 milliseconds and the sampling frequency is 8000 Hz. Sources are the Chinese speech of 17 words and the light music. The impulse filter is generated by the famous Image algorithm. Two standard algorithms are adopted, and they are the Polar ICA+MVDR of NTT in Japan and FDICA of ICA Center. The improved SNR from the Strong SOS+ExMVDR and Strong HOS+ExMVDR are over 1 dB than Polar ICA+MVDR. IBM Viavoice can recognize all the 17 words estimated by Strong SOS+ExMVDR and Strong HOS+ExMVDR, but only 14 by Polar ICA+MVDR and 13 by FDICA.
This experiment validates the effectiveness of the methods we put forward in this dissertation. Our work pushes the development of blind separation of convolutive mixtures in the frequency domain.
Particle filtering (PF) is an optimal solution to the nonlinear and nongaussian problem, and it has been a hot topic in the past ten years. With the development of BSP, noisy blind source separation and post nonlinear blind source separation gradually become more and more attractive. This dissertation revolves the noisy post nonlinear and underdetermined blind source separation through the application of PF. First, the noisy blind source separation model is decomposed to two parts which are the noise free model and the received signal contaminated by noises; second, in theory, the feasibility of the dynamic state space equations and noisy blind source separation is explored. Exactly, the Time Varying AR model of the noise free mixtures describes the state equation, and the relation of noisy mixtures and noise free mixtures constructs the observed equation in the state space problem; third, along this way, the noisy model can be converted to be the noise free model, and the post nonlinear model can turn into the linear model provided that the post nonlinear function is a priori or can be estimated. Thus, the current blind source separation algorithms can perform on the estimated noise free mixtures directly. Under this framework, the noisy linear determined problem, noisy nonlinear determined problem, noisy linear underdetermined problem and the noisy nonlinear underdetermined problem are resolved in the theory.
As the solutions to noisy nonlinear problem are still open, the linear determined experiment is done first. The denoising source separation (DSS) of J. Sarela and H.Valpola in HUT is selected for the comparison to PF+FastICA. The mixing is instantaneous, and the noise is additive. The input SNR is between 0 to 12dB. No matter in gaussian noises or gamma noises, PF+FastICA performs better than DSS. This experiment proves our approach is effective. Then, under 10dB SNR noisy environment, the noisy nonlinear determined, noisy linear underdetermined and the noisy nonlinear underdetermined experiments are done respectively. The benefit of PF is between 5 and 6dB. The performance in the three experiments is close to the linear determined one. All the experiments prove the validation of our approach. The framework of PF+ICA provides a novel approach to nonlinear and underdetermined blind source separation under the noisy environment.
In the application of blind separation of convolutive mixtures, we mainly explore the feasibility in the active sonar target detection. When the Doppler Effect is produced, both BNMF and whitening method are useful; or in the case that the target power has been already known, PCI may cancel the reverberation. However, these methods are no use provided that prior knowledge is not available. In this dissertation, the target echo is regarded as the first source, and the reverberation in shallow water or the background interference are the second source. After beamforming, the main beam and the adjacent beam are the observed signals. Strong SOS+Corr is adopted. The first experiment is about the simulated target, and the function of our approach is close to PCI. The second experiment is the true target. After Strong SOS+Corr is performed, the benefit of the matched filter output is about 2.5dB, and the characteristic of the time-frequency analysis is much better. The two experiments prove our approach and idea are helpful in the active sonar target detection, target feature extraction and target recognition.
This work is supported by National Science Fund under grant 60372075, and also supported by Shanghai No: 05JC14026 and opening fund of VSN-2006-04.
本文首先对复值信号盲分离研究历史与现状进行简要回顾和论述,之后指出现行5个主流算法的优缺点:法国J.-F.Cardoso提出的JADE是用复值向量的共轭转置代替了实数的转置来建立累积量矩阵,再对累积量矩阵进行特征值分解求得分离矩阵;赫尔辛基理工大学Ella Bingham和Aapo Hyvarinen提出的ComplexFastICA是对复数绝对值运算,与实数算法形式相同;马里兰大学Calhoun Vince与T. Adali提出的Complex ICA是基于互信息最小化的自然梯度盲分离算法,但是忽略了复值信号的伪参数特性;赫尔辛基理工大学Jan Eriksson和Visa Koivunen提出的SUT算法是对非正则复值向量的伪自相关矩阵进行分解从而得到分离矩阵;美国Scott C. Douglas提出的Equivariant SUT利用了伪自相关矩阵的特性,不过算法是对实值信号算法直接进行改进得到的,没有建立代价函数。
鉴于此,本文先根据非正则复值向量的伪自相关矩阵构造了二阶统计量的代价函数,再通过梯度下降法推导出基于伪自相关矩阵的二阶复值信号盲分离算法Strong SOS;其次构建互信息最小化的代价函数,在推导过程中对复值信号分别进行共轭转置和转置运算,从而推导出基于伪互相关矩阵的高阶统计量复值信号盲分离算法Strong HOS,最后通过仿真试验与上述的5种算法进行比对。由于所发展的新算法充分利用了非正则复值向量“伪参数”的性质,从分离效果上看,Strong SOS和Strong HOS收敛效果更好,分离性能更强。进而得出结论:无论是理论分析还是仿真试验,都说明了非正则向量的“伪参数”使复值盲信号分离算法收敛更快、分离效果更好。这项工作是卷积混合盲分离频域算法的第一步,为更加准确地解决算法第二步的频率对准问题奠定了基础。
本文第二个研究重点是卷积混合盲分离频域解法中的次序不确定问题。结合非正则复向量的“伪参数”,首先提出了扩展自相关矩阵、扩展驾驶向量和扩展权值向量,提出了扩展MVDR波束形成方法ExMVDR,仿真试验表明该方法比MVDR输出的主波束信噪比高出2dB左右;其次,深入研究了互参数法的理论基础,公式推导和高斯白噪声下的仿真试验都揭示了互参数法有效的原因之一是由于离散傅立叶的计算方法提供了互参数的相关性,从而得出了互参数法的应用可以拓展至语音信号以外的信号的结论;通过对源信号计算互参数来反映相关系数和KL距离在语音信号卷积混合频域解法中的性能,发现KL距离的性能优于相关系数,但是在某些情况下,由于离散化带来的误差和信号长度太短而引起的独立性下降等因素,使得KL距离仍然存在着不能够进行有效进行频率对准的可能;最后论证了语音信号分段做FFT之后,不同窗对应的同频率下的复值信号是非正则的,从而进一步提出了卷积混和盲分离频域解法的方法: Strong SOS+ExMVDR, Strong HOS+ExMVDR和Strong HOS+KL。
为了检验上述算法的性能,对日常办公室环境下的卷积混合语音信号进行解卷积实验。混响时间是130毫秒,采样频率是8000赫兹,源信号是17个汉字组成的中文语音信号和一段轻音乐。实验中,混合信号是通过著名的Image算法模拟日常办公环境下房间内的传递函数与单独录制的源信号相卷积混合的。无论是频域内复值混合信号的盲分离计算,还是频率对准阶段,本文所提出的方法与主流算法比,都具有一定的优势,因此在与日本NTT的Shoji Makino等人的算法Polar ICA+MVDR比对中,Strong SOS+ExMVDR和Strong HOS+ExMVDR估计的源信号信噪比要高出Polar ICA+MVDR一个分贝以上,另外,本文还使用IBM Viavoice中文语音识别软件对不同方法估计的17个汉字进行识别,Strong SOS+ExMVDR和Strong HOS+ExMVDR估计的17个汉字,软件都可识别出,Polar ICA+MVDR估计的源信号,IBM Viavoice只能够认出14个汉字,而ICA Center上提供的FDICA算法估计的源信号,Viavoice只能够认出13个汉字,对于Strong HOS+KL估计的源信号,能够认出15个汉字,少于Strong SOS+ExMVDR和Strong HOS+ExMVDR,这是由于在频率对准阶段采用的互参数法KL不如ExMVDR准确。通过这些实验更加有效的证明了所提出算法的优越性,也充分说明了非正则复值向量“伪参数”在复值信号处理中的重要作用;通过比较Viavoice对混合信号和估计的源信号的识别率,说明了语音识别软件Viavoice在盲信号处理下识别能力得到提高,从而进一步证明了本文所提出的“面向目标感知的盲信号处理算法研究”的思路是正确的。无论是比较算法评价指标还是语音识别软件识别不同方法估计的源信号的准确率,都证明所提出的算法Strong SOS+ExMVDR, Strong HOS+ExMVDR和Strong HOS+KL比现存主流算法有优势,从而推动了严重混响条件下的卷积混合盲分离频域算法的发展。
粒子滤波是解决非线性非高斯过程的有效方法,在过去10多年里得到了迅速发展,而随着盲信号处理理论的发展,含噪、非线性盲分离受到越来越多的关注,本文通过粒子滤波来解决含噪的后非线性和欠定等多种盲分离模型,建立了粒子滤波+不含噪盲分离的框架。首先对含噪盲分离模型进行分解,提出了如果将不含噪的混合信号估计出来就可以将含噪模型转化为不含噪模型的思路;其次,通过建立不含噪混合信号的时变AR模型来构造状态空间方程中的状态方程,通过可观测到的含噪混合信号与要估计的不含噪混合信号的线性或者非线性关系,构造了状态空间方程中的观测方程,从而发现了动态状态空间方程与含噪盲分离相结合的可行性;按此思路,通过粒子滤波可将含噪盲分离模型转化为不含噪模型,在后非线性函数已知或者可估计出的情况下,可将非线性盲分离模型转化为线性模型,然后通过现有的不含噪盲分离算法估计出源信号。在这个框架下,本文从理论上解决了线性正定含噪、非线性正定含噪、线性欠定含噪、非线性欠定含噪等非常有挑战性的盲分离问题。
由于各种含噪盲分离模型成熟解法不多,首先进行相对简单的正定线性含噪盲分离实验,并与赫尔辛基理工大学J. Sarela和H.Valpola等人提出的Denoising Source Separation (DSS)算法进行比对,以验证所提出方案的可靠性。信号混合采用瞬时混合方式,噪声是加性的。在0至12dB的输入信噪比下,无论是高斯白噪声还是伽玛噪声环境,从算法评判标准上看,所提出的PF+FastICA方法对源信号的估计要好于DSS。紧接着,对正定非线性、欠定线性和欠定非线性盲分离算法进行试验,输入信噪比均为10dB。粒子滤波的贡献有5至6dB左右,对源信号的估计效果与正定线性含噪和不含噪混合两种情况下的效果相当。实验进一步证实了所提出方案的可行性、可靠性和有效性,为解决噪声环境下的非线性、欠定盲分离问题建立了崭新的理论框架。在卷积混合盲分离的应用上,本文还重点讨论了其在主动声纳目标检测中的应用。本文将目标回波看作第一个源信号,将近海的混响或者远海的背景干扰看作第二个源信号,通过选取波束形成后的主波束和与主波束相邻的波束作为盲分离中的两个接收信号,采用本文所发展的卷积混合盲分离频域算法对主波束目标信号进行增强。真实目标海上实验数据处理结果表明:通过盲分离,主波束的匹配滤波输出得到了2.5dB的增益,目标时频分析的特征更加清晰,证实了本文所提出方案的正确性,在盲分离算法的实际应用上迈出了有价值的一步,对主动声纳目标检测、特征提取以及目标识别技术的发展有重要的意义。
本文的工作得到国家自然科学基金项目“声信号盲分离算法研究”(信息学部,批准号60372075)的资助,同时还得到上海市科委基础研究项目“复杂环境下动态系统的结构学习研究”(No: 05JC14026)和国家重点实验室开放式基金“复值信号盲分离算法研究”(VSN-2006-04)的资助。本文同时还得到国防重点实验室基金项目“水声信息处理技术与系统研究”和国防重点攻关项目“主动拖曳式声纳研究”的数据支持。
Blind signal processing (BSP) is a very hot topic in the signal processing society. The advantage is that BSP does not require any prior knowledge except the independence among different sources, so BSP has been applied in many disciplines. This dissertation is targeted to the challenging problems in BSP. To improve the perception capacity is the final goal in the application with BSP enforcing the target in perception systems. Two frameworks are mainly studied. One is the blind separation of convolutive mixtures in heavy reverberation, which is the first hard problem the dissertation resolves. The complex-valued source separation and the permutation are studied for the blind separation of convolutive mixtures in the frequency domain. The second is the particle filtering based noisy source separation, which provides a novel approach for the post-nonlinear and underdetermined blind source separation under the noisy environment. In the real-word application, it is mainly discussed that how blind separation of convolutive mixtures are adopted in the speech source separation and the active sonar target detection.
The dissertation first deals with the blind separation of complex-valued sources. After the improper complex-valued vector and the characteristic of pseudo-autocorrelation matrix are explored, we find that JADE, Complex FastICA, Complex ICA, SUT and Equivariant SUT do not make full use of the good characteristics of the improper complex-valued vector. Then, based on the pseudo-autocorrelation matrix, we construct a second order statistics (SOS) cost function. With the decent gradient algorithm, a new SOS based blind separation of complex-valued sources algorithm is inferred. We name it as Strong SOS. Along the same idea, we construct the cost function based on the minimum of the mutual information between different independent sources. In the process to infer the new algorithm, we perform the conjugate transpose and transpose operation to the complex-valued vector and matrix, and the new algorithm is obtained based on the pseudo-crosscorrelation matrix. We name it as Strong HOS compared to Strong SOS. Through simulations, it is proved that Strong HOS and Strong SOS perform better than JADE, Complex FastICA, Complex ICA, SUT and Equivariant SUT. It is the reason that Strong HOS and Strong SOS explore the characteristics of improper complex-valued vectors entirely. Blind separation of complex-valued sources is the first step to the blind separation of convolutive mixtures in the frequency domain. Strong HOS and Strong SOS make much solider foundation to correct the permutation in the second step.
And then, the permutation indeterminacy of frequency domain approach to blind separation of convolutive mixtures is studied. Based on the pseudo-parameter of improper vectors, the traditional beamforming method——MVDR is revised. Simulation validates that the extended MVDR functions better than MVDR in low SNR situation.
After the mutual parameters are deeply analyzed, it is natural to find that the computation method of DFT introduces the correlation to the mutual parameters method, hence, the mutual parameters can be extended to other signals except speech. By different simulation, different current algorithms are compared. KL distance behaves better than correlation coefficient. However, in some frequency bins, mutual parameters still possibly can not correct the permutation indeterminacy. At last, Strong SOS+ExMVDR, Strong HOS+ExMVDR, and Strong HOS+KL are composed together for the frequency domain method.
To test the performance of algorithms we put forward, the experiment simulates the situation in the ordinary office. The reverberation time is 130 milliseconds and the sampling frequency is 8000 Hz. Sources are the Chinese speech of 17 words and the light music. The impulse filter is generated by the famous Image algorithm. Two standard algorithms are adopted, and they are the Polar ICA+MVDR of NTT in Japan and FDICA of ICA Center. The improved SNR from the Strong SOS+ExMVDR and Strong HOS+ExMVDR are over 1 dB than Polar ICA+MVDR. IBM Viavoice can recognize all the 17 words estimated by Strong SOS+ExMVDR and Strong HOS+ExMVDR, but only 14 by Polar ICA+MVDR and 13 by FDICA.
This experiment validates the effectiveness of the methods we put forward in this dissertation. Our work pushes the development of blind separation of convolutive mixtures in the frequency domain.
Particle filtering (PF) is an optimal solution to the nonlinear and nongaussian problem, and it has been a hot topic in the past ten years. With the development of BSP, noisy blind source separation and post nonlinear blind source separation gradually become more and more attractive. This dissertation revolves the noisy post nonlinear and underdetermined blind source separation through the application of PF. First, the noisy blind source separation model is decomposed to two parts which are the noise free model and the received signal contaminated by noises; second, in theory, the feasibility of the dynamic state space equations and noisy blind source separation is explored. Exactly, the Time Varying AR model of the noise free mixtures describes the state equation, and the relation of noisy mixtures and noise free mixtures constructs the observed equation in the state space problem; third, along this way, the noisy model can be converted to be the noise free model, and the post nonlinear model can turn into the linear model provided that the post nonlinear function is a priori or can be estimated. Thus, the current blind source separation algorithms can perform on the estimated noise free mixtures directly. Under this framework, the noisy linear determined problem, noisy nonlinear determined problem, noisy linear underdetermined problem and the noisy nonlinear underdetermined problem are resolved in the theory.
As the solutions to noisy nonlinear problem are still open, the linear determined experiment is done first. The denoising source separation (DSS) of J. Sarela and H.Valpola in HUT is selected for the comparison to PF+FastICA. The mixing is instantaneous, and the noise is additive. The input SNR is between 0 to 12dB. No matter in gaussian noises or gamma noises, PF+FastICA performs better than DSS. This experiment proves our approach is effective. Then, under 10dB SNR noisy environment, the noisy nonlinear determined, noisy linear underdetermined and the noisy nonlinear underdetermined experiments are done respectively. The benefit of PF is between 5 and 6dB. The performance in the three experiments is close to the linear determined one. All the experiments prove the validation of our approach. The framework of PF+ICA provides a novel approach to nonlinear and underdetermined blind source separation under the noisy environment.
In the application of blind separation of convolutive mixtures, we mainly explore the feasibility in the active sonar target detection. When the Doppler Effect is produced, both BNMF and whitening method are useful; or in the case that the target power has been already known, PCI may cancel the reverberation. However, these methods are no use provided that prior knowledge is not available. In this dissertation, the target echo is regarded as the first source, and the reverberation in shallow water or the background interference are the second source. After beamforming, the main beam and the adjacent beam are the observed signals. Strong SOS+Corr is adopted. The first experiment is about the simulated target, and the function of our approach is close to PCI. The second experiment is the true target. After Strong SOS+Corr is performed, the benefit of the matched filter output is about 2.5dB, and the characteristic of the time-frequency analysis is much better. The two experiments prove our approach and idea are helpful in the active sonar target detection, target feature extraction and target recognition.
This work is supported by National Science Fund under grant 60372075, and also supported by Shanghai No: 05JC14026 and opening fund of VSN-2006-04.
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