脉冲噪声下时间延迟估计方法及应用的研究
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摘要
时间延迟估计(TDE)是信号处理领域里一个十分活跃的研究课题。噪声是TDE需要考虑的主要问题之一。在实际应用中，常常会遇到一类具有明显脉冲性的非高斯噪声，基于高斯模型二阶统计量的传统TDE方法性能显著退化。因此，需要研究更具韧性的TDE方法。一种广义的高斯分布——Alpha稳定分布可以更准确地描述其统计特性。本文基于脉冲噪声Alpha稳定分布模型和分数低阶统计量(FLOS)，重点研究了单径条件下韧性TDE方法及其在生物医学信号分析中的应用、多径条件下韧性高分辨率TDE方法。该项研究有助于完善随机信号分析处理理论方法由传统的二阶统计量向FLOS方向的扩展，有助于提升TDE算法及其应用的整体水平和韧性程度，因而具有重要的理论和应用意义。
本文的主要工作如下：
(1)提出了韧性的自适应非整数TDE方法(LMPFTDE)。用Alpha稳定分布模型建模脉冲噪声，基于最小分散系数(MD)准则，对经典的ETDGE算法进行广义化，LMPFTDE算法在高斯及脉冲噪声下均可以较好的工作。为了避免基于FLOS算法中参数的选取问题，基于非线性变换，给出了适用于非时变TDE的Sigmoid相关算法；基于零阶统计量，给出了对数广义平稳性和对数遍历性的概念，提出了用几何功率对收敛因子归一化的自适应TDE方法(NZOSTDE)，这两种算法适合用于脉冲性较强的环境。将NZOSTDE算法应用于EP信号潜伏期延长的检测中，取得了较好的效果。
(2)在脉冲噪声多径TDE问题中，基于FLOS提出了三种韧性的、可以突破相关法分辨极限的高分辨率TDE方法：变换域多径TDE方法(FLOCCS-ESPRIT)、基于EM的韧性多径TDE方法(P-EM)及基于MD的松弛迭代多径TDE(RHMTDE)。FLOCCS-ESPRIT算法将多径信号的分数低阶互协方差谱序列看成时间序列，利用ESPRIT算法，得到高分辨率的多径TDE。P-EM、RHMTDE算法从不同角度将一个多维非线性优化问题转化为多个一维优化的问题。P-EM算法基于EM框架，通过信号分解构造完整数据，用p阶分数相关分别迭代得到各径时间延迟的最小平均p范数(LMP)估计；RHMTDE算法基于FLOS及MD，利用松弛搜索逐次迭代分解信号得到各径的TDE。该项研究有助于提高多径脉冲条件下的定位技术，有助于改善探地雷达在脉冲环境下的检测韧性。
(3)将脉冲噪声建模为Alpha稳定分布，提出了基于LMP盲信道辨识的韧性TDE算法(BCILMP)及韧性的自适应特征值分解TDE算法(RAED)。BCILMP算法和RAED算法的主要思想均是组合两个输入信号，使其共变矩阵最小特征值对应的特征向量为两个信道的估计，在LMP准则下自适应得到该特征向量，从而得到时间延迟信息。RAED算法对误差信号和输入向量均采用分数阶操作。这两种算法提高了基于高斯模型AED算法的韧性。
(4)研究了胃电信号及其噪声的特点。胃慢波决定胃电的传导，由于棘波和／或动作伪迹的影响，慢波中常常含有尖峰脉冲。因此，在对胃电信号空间特征的提取中，用Alpha稳定分布建模比用高斯分布建模更合适。基于BCILMP算法对仿真产生的带噪胃慢波信号的传导速率进行估计，与LMSTDE算法比较，该算法在高斯噪声和非高斯脉冲噪声环境下，均可以较好地估计出时间延迟。应用BCILMP算法对四位胃轻瘫病人胃电活动(GEA)的传导进行了估计，结果与医生的视觉评价基本一致。辅助医生人工判断，为胃电刺激(GES)治疗胃病参数的选取提供一定的参考。
Time Delay Estimation (TDE) is a popular issue in signal processing areas. Noise is one of the main problems in TDE. In practice, there is a kind of non-Gaussian noises with obvious impulsion in which cases the TDE algorithms based on second-order statistics of Gaussian model degenerate significantly. Therefore, robust methods in TDE need to be researched. A sort of generalized Gaussian distributions, Alpha-stable distribution, can more precisely describe the statistics of impulsive noise. Based on the impulsive noises of the Alpha-stable distribution model, this paper puts the emphases on the robust single path TDE methods and its applications in biological medical area, and also robust high-resolution multipaths TDE methods. The researches of the paper are helpful to the extension of the random signal analysesand processing theories from second-order statistics to FLOS statistics and upgrade the overall level and the robustness of the TDE algorithms and its applications. Therefore, the paper has great significances both in theories and applications.
The main work of the paper is as follows:
(1) A robust adaptive fractional TDE method, referred to as LMPFTDE, is proposed. By using impulsive noise modeled Alpha-stable distribution, ETDGE is generalized based on minimum dispersion (MD) criterion. LMPFTDE can work well both in Gaussian and impulsive noise environments. In order to avoid parameter selection, based on non-linear transformation, it proposes sigmoid correlation algorithm that fits for time delay invariance TDE; based on zero order statistics, it proposes the concepts of logarithmic wide sense stationary and logarithmic ergodic random process, and also an adaptive TDE method, referred to as NZOSTDE, with geometric power normalization step factor. These two methods are more suitable for much impulsive noise environments. Using NZOSTDE to detect EP latency delay, good results can be obtained.
(2) With regard to TDE in impulsive noise multipath environment, based on FLOS, it proposes three robust and high resolution TDE algorithms which could break through the limit of correlation algorithm. They are robust multipath TDE algorithm in transformation domain referred to as FLOCCS-ESPRIT, p-order fractional correlation EM algorithm referred to as P-EM, and robust and high resolution multipath TDE referred to as RHMTDE. The FLOCCS-ESPRIT regards the fractional lower-order cross-covariance spectrum of multipath signal as an equivalent time sequence, then makes use of ESPRIT to obtain high resolution multipath TDE. P-EM and RHMTDE transfer a multi-dimension nonlinearity optimization problem to a multiple one-dimensional optimization problem from different angles. Based on EM frame, P-EM constructs complete data by signal decomposition, iterates respectively by p-order fractional correlation, and obtains the TDE of each path under least mean p-norm (LMP) criterion. Based on FLOS and MD, RHMTDE makes use of relax iteration to acquire TDE of each path. This research can improve position technology and detection robust in ground-penetrating radar under multipath impulsive environment.
(3) Using Alpha-stable distribution to model impulsive noise, it proposes robust TDE algorithm based on LMP blind channel identification referred to as BCILMP and robust adaptive eigenvalue decomposition referred to as RAED. The main idea of BCILMP and RAED is to assemble two input signals so that the eigenvector corresponding to minimum eigenvalue of covariance matrix is the estimation of two channels. TDE is adaptive obtained under LMP criterion. RAED algorithm uses fractional order operation for error signal and input vector. Both of them improve robustness of AED algorithm based on Gaussian model.
(4) It studies the characteristics of gastric electrical activity (GEA) with noise. Gastric slow wave decides the propagation of GEA. Due to the effects of spikes and/or motion artifacts, the slow wave often contains sharp impulsion; therefore Alpha-stable distribution is more suitable than Gaussian in GEA research. Based on BCILMP, the propagation velocities of simulative slow wave with noises are estimated. Compared with LMSTDE, BCILMP provides well TDE both in Gaussian and impulsive noise environments. And then, BCILMP is applied to estimate the propagation velocities of GEA in four gastroparetic patients, and the results are mostly consistent with the evaluations of the doctor. It can be the assistant judgments for doctors and also provides the references to select the parameters of gastric electrical stimulation to cure gastric disasters.
本文的主要工作如下：
(1)提出了韧性的自适应非整数TDE方法(LMPFTDE)。用Alpha稳定分布模型建模脉冲噪声，基于最小分散系数(MD)准则，对经典的ETDGE算法进行广义化，LMPFTDE算法在高斯及脉冲噪声下均可以较好的工作。为了避免基于FLOS算法中参数的选取问题，基于非线性变换，给出了适用于非时变TDE的Sigmoid相关算法；基于零阶统计量，给出了对数广义平稳性和对数遍历性的概念，提出了用几何功率对收敛因子归一化的自适应TDE方法(NZOSTDE)，这两种算法适合用于脉冲性较强的环境。将NZOSTDE算法应用于EP信号潜伏期延长的检测中，取得了较好的效果。
(2)在脉冲噪声多径TDE问题中，基于FLOS提出了三种韧性的、可以突破相关法分辨极限的高分辨率TDE方法：变换域多径TDE方法(FLOCCS-ESPRIT)、基于EM的韧性多径TDE方法(P-EM)及基于MD的松弛迭代多径TDE(RHMTDE)。FLOCCS-ESPRIT算法将多径信号的分数低阶互协方差谱序列看成时间序列，利用ESPRIT算法，得到高分辨率的多径TDE。P-EM、RHMTDE算法从不同角度将一个多维非线性优化问题转化为多个一维优化的问题。P-EM算法基于EM框架，通过信号分解构造完整数据，用p阶分数相关分别迭代得到各径时间延迟的最小平均p范数(LMP)估计；RHMTDE算法基于FLOS及MD，利用松弛搜索逐次迭代分解信号得到各径的TDE。该项研究有助于提高多径脉冲条件下的定位技术，有助于改善探地雷达在脉冲环境下的检测韧性。
(3)将脉冲噪声建模为Alpha稳定分布，提出了基于LMP盲信道辨识的韧性TDE算法(BCILMP)及韧性的自适应特征值分解TDE算法(RAED)。BCILMP算法和RAED算法的主要思想均是组合两个输入信号，使其共变矩阵最小特征值对应的特征向量为两个信道的估计，在LMP准则下自适应得到该特征向量，从而得到时间延迟信息。RAED算法对误差信号和输入向量均采用分数阶操作。这两种算法提高了基于高斯模型AED算法的韧性。
(4)研究了胃电信号及其噪声的特点。胃慢波决定胃电的传导，由于棘波和／或动作伪迹的影响，慢波中常常含有尖峰脉冲。因此，在对胃电信号空间特征的提取中，用Alpha稳定分布建模比用高斯分布建模更合适。基于BCILMP算法对仿真产生的带噪胃慢波信号的传导速率进行估计，与LMSTDE算法比较，该算法在高斯噪声和非高斯脉冲噪声环境下，均可以较好地估计出时间延迟。应用BCILMP算法对四位胃轻瘫病人胃电活动(GEA)的传导进行了估计，结果与医生的视觉评价基本一致。辅助医生人工判断，为胃电刺激(GES)治疗胃病参数的选取提供一定的参考。
Time Delay Estimation (TDE) is a popular issue in signal processing areas. Noise is one of the main problems in TDE. In practice, there is a kind of non-Gaussian noises with obvious impulsion in which cases the TDE algorithms based on second-order statistics of Gaussian model degenerate significantly. Therefore, robust methods in TDE need to be researched. A sort of generalized Gaussian distributions, Alpha-stable distribution, can more precisely describe the statistics of impulsive noise. Based on the impulsive noises of the Alpha-stable distribution model, this paper puts the emphases on the robust single path TDE methods and its applications in biological medical area, and also robust high-resolution multipaths TDE methods. The researches of the paper are helpful to the extension of the random signal analysesand processing theories from second-order statistics to FLOS statistics and upgrade the overall level and the robustness of the TDE algorithms and its applications. Therefore, the paper has great significances both in theories and applications.
The main work of the paper is as follows:
(1) A robust adaptive fractional TDE method, referred to as LMPFTDE, is proposed. By using impulsive noise modeled Alpha-stable distribution, ETDGE is generalized based on minimum dispersion (MD) criterion. LMPFTDE can work well both in Gaussian and impulsive noise environments. In order to avoid parameter selection, based on non-linear transformation, it proposes sigmoid correlation algorithm that fits for time delay invariance TDE; based on zero order statistics, it proposes the concepts of logarithmic wide sense stationary and logarithmic ergodic random process, and also an adaptive TDE method, referred to as NZOSTDE, with geometric power normalization step factor. These two methods are more suitable for much impulsive noise environments. Using NZOSTDE to detect EP latency delay, good results can be obtained.
(2) With regard to TDE in impulsive noise multipath environment, based on FLOS, it proposes three robust and high resolution TDE algorithms which could break through the limit of correlation algorithm. They are robust multipath TDE algorithm in transformation domain referred to as FLOCCS-ESPRIT, p-order fractional correlation EM algorithm referred to as P-EM, and robust and high resolution multipath TDE referred to as RHMTDE. The FLOCCS-ESPRIT regards the fractional lower-order cross-covariance spectrum of multipath signal as an equivalent time sequence, then makes use of ESPRIT to obtain high resolution multipath TDE. P-EM and RHMTDE transfer a multi-dimension nonlinearity optimization problem to a multiple one-dimensional optimization problem from different angles. Based on EM frame, P-EM constructs complete data by signal decomposition, iterates respectively by p-order fractional correlation, and obtains the TDE of each path under least mean p-norm (LMP) criterion. Based on FLOS and MD, RHMTDE makes use of relax iteration to acquire TDE of each path. This research can improve position technology and detection robust in ground-penetrating radar under multipath impulsive environment.
(3) Using Alpha-stable distribution to model impulsive noise, it proposes robust TDE algorithm based on LMP blind channel identification referred to as BCILMP and robust adaptive eigenvalue decomposition referred to as RAED. The main idea of BCILMP and RAED is to assemble two input signals so that the eigenvector corresponding to minimum eigenvalue of covariance matrix is the estimation of two channels. TDE is adaptive obtained under LMP criterion. RAED algorithm uses fractional order operation for error signal and input vector. Both of them improve robustness of AED algorithm based on Gaussian model.
(4) It studies the characteristics of gastric electrical activity (GEA) with noise. Gastric slow wave decides the propagation of GEA. Due to the effects of spikes and/or motion artifacts, the slow wave often contains sharp impulsion; therefore Alpha-stable distribution is more suitable than Gaussian in GEA research. Based on BCILMP, the propagation velocities of simulative slow wave with noises are estimated. Compared with LMSTDE, BCILMP provides well TDE both in Gaussian and impulsive noise environments. And then, BCILMP is applied to estimate the propagation velocities of GEA in four gastroparetic patients, and the results are mostly consistent with the evaluations of the doctor. It can be the assistant judgments for doctors and also provides the references to select the parameters of gastric electrical stimulation to cure gastric disasters.
引文
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