微弱核四极矩共振信号参数估计方法研究
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摘要
核四极矩共振是一种固态射频谱分析技术，可用于检测高危险爆炸物及违禁物品。然而，极低信噪比与射频干扰制约了核四极矩共振技术的实际应用。干扰抑制、微弱核四极矩共振信号的参数估计与检测技术成为核四极矩共振技术的核心及关键。本论文从信号处理的角度出发，对核四极矩共振的概念、信号模型、信号激励方法、干扰抑制以及微弱核四极矩共振信号参数估计与检测等方面做了比较全面的分析与阐述，深入研究了微弱核四极矩共振信号的干扰抑制，信号检测及参数估计等问题。具体工作概括如下：
1.针对干扰抑制与微弱核四极矩共振信号检测问题，提出了一种基于Hankel矩阵方式下奇异值分解的干扰抑制方法。该方法首先将原始数据构造成Hankel矩阵；然后对其进行奇异值分解，依据奇异值的大小可将原始信号分解为多个分量信号；最后对各分量信号进行谱估计，依据核四极矩共振信号的先验信息，滤除干扰信号与噪声；它有效地抑制了干扰信号，改善了信噪比。在干扰抑制的基础上，提出基于MUSIC谱估计的非线性最小二乘检测器，并以广义似然比统计量作为检测量；所提方法在降低了计算量的同时，提高了频率分辨率，达到有效检测微弱核四极矩共振信号的目的。
2.针对含有干扰信号与热噪声的自由衰减信号的参数估计问题，提出了基于总体最小二乘的线性预测类参数估计方法。所提方法同时考虑了线性预测方程两边数据矩阵的扰动量，并在计算总体最小二乘解时，考虑了干扰噪声项，克服了常规最小二乘方法仅考虑一边扰动量，致使估计方差较大的缺点。结合自由衰减信号的衰减特性与最大似然估计准则实现了微弱自由衰减信号参数有效估计。
3.针对强干扰信号遮蔽的微弱核四极矩共振信号参数估计问题，提出了基于改进的快速最大似然估计的残余信号迭代分解算法估计核四极矩共振信号参数。该方法将多维搜索问题转化为多个一维搜索，在频率维搜索时，结合了内插与类牛顿方法。所提方法在降低计算复杂度的同时提高了参数估计精度，解决了干扰信号对核四极矩共振信号的遮蔽问题。仿真和实测数据的结果验证了该算法的有效性。
4.针对核四极矩共振技术探测爆炸物中干扰信号的时变性，基于各信号采样模块包含有固定的核四极矩共振信号与时变干扰信号以及噪声的实际信号模型，提出改进的多模块HTLSstack算法。首先采用HTLS方法确定出共有极点的个数；其次构造新的筛选准则确定所有模块的共有极点；最后结合核四极矩共振信号的先验信息，实现核四极矩共振信号参数的有效估计。所提方法充分利用了原始数据的信息，在低信噪比下，避免了多模块HTLS方法在第一次奇异值分解时带来的性能损失，有效地提高了参数估计精度。
5.针对存在加性高斯白噪声多参数变量的单自旋回波串信号参数估计问题，提出一种参数分离化的2-D参数估计方法。利用2-D数据矩阵秩为1的特性，依照迭代加权最小二乘方法，从左、右主奇异值向量中以参数分离的方式分别估计出衰减因子和频率，基于最小二乘方法进一步获得信号幅度估计。该方法在相对高信噪比或大数据样本下可达到克拉美罗下界，且计算复杂度较低。
6.针对存在加性高斯白噪声多参数变量的多谱线自旋回波串信号参数估计问题，提出基于特征向量的2-D参数估计方法。将多谱线自旋回波串信号构造成2-D数据矩阵，按照不同的方式构造Hankel块矩阵束，利用子空间转移不变结构解得特征向量，依据特征向量的结构规律获得衰减因子和频率。该方法具有自动配对的能力，在相对高信噪比以及频率可分辨的情况下能够实现参数的有效估计。仿真数据结果验证了算法的有效性。
Nuclear quadrupole resonance (NQR) is a solid-state radio frequency (RF)spectroscopic technique, allowing the detection of various high explosives and illicitmaterials. Unfortunately, the practical use of NQR is restricted by the low signal tonoise ratio (SNR) and the radio frequency interference (RFI). The interferencemitigation, parameter estimation and detection of weak NQR signals are the core andthe key of the NQR technique. From the perspective of signal processing, some topicsrelated to NQR, such as the basic concept, the signal model, the signal excitationmethods, the interference mitigation, and parameter estimation and detection of weakNQR signals, are analyzed and elaborated comprehensively in this dissertation. Theinterference mitigation, detection and parameter estimation of weak NQR signals areresearched deeply. The specific work is summarized as follows:
1For the problem of interference mitigation and weak NQR signal detection, amethod of interference mitigation based on singular value decomposition (SVD) of theHankel matrix is proposed. In the proposed algorithm, a Hankel matrix is formed byoriginal data at first, and its SVD is implemented, then the original signal can bedecomposed into several component signals according to the singular values’ order.Finally, in accordance with the spectrum estimation of each component signal, theinterference and noise are removed on the basis of the prior information of NQR signals.It suppresses the interference effectively, and improves the SNR. After filtering theinterference, a nonlinear least square (NLS) detector based on MUSIC spectralestimation is presented, with the generalized likelihood ratio test (GLRT) as a detectionvariable. The proposed algoriyhm greatly reduces the computation load, simultaneously,guarantees a superior resolution of the frequency, so the motivation of the availabledetection for weak NQR signals is achieved.
2Be aimed at the parameters estimation problem of the free induction decay(FID) signal contained interference and thermal noise, the linear prediction estimatorbased on the total least squares (TLS) is presented to estimate the parameters of the FIDsignal. The perturbations of the linear prediction equation on the two sides areconsidered in the proposed method, and then solved in the total least squares sense, withthe consideration of the interference and noise terms, the drawback of the conventionalleast squares method which only considers one side disturbance and leads to a relativelylarge variance, is overcomed. With the combination of the damp character of the FID signal and the criterion of the maximum likelihood estimation, the estimation of theparameters of the weak FID signal is effectively accomplished.
3In allusion to the methods of parameters estimation of weak NQR signalsmasked by strong interference signals, residual signal iterative analysis algorithm(RSIAA) based on the improved fast maximum likelihood estimation (IFMLE) isproposed to estimate the parameters of the NQR signals. The proposed method turns themultidimensional search problem into multiple one-dimensional searches, and combinesthe interpolator and semi-Newton method. It solves the mask problem of theinterference to the NQR signal effectively, which simultaneously reduces thecomputational complexity and improves the estimated precision. The effectiveness ofthe proposed algorithm is demonstrated by the processing results of both simulated dataand experimental data.
4For the time-variation characteristic of interference signals in the explosivedetection using the NQR technique, and according to the real world signal model ofeach signal sample block including the fixed NQR signal, time-variation interferencesignals and noise, an improved multi-block Hankel total least squares stack (HTLSstack)method is presented. Firstly, the number of common poles is determined using theHTLS scheme; secondly, a new selection criterion is constructed to choose the commonpoles; finally, the prior knowledge is employed to realize the estimation of NQR signalseffectively. This method makes full use of the information of original data, and in thecase of low signal-to-noise ratio, it avoids the performance loss of multi-block HTLSmethod in the first SVD, and improves the precision of parameter estimation availably.
5To the problem of the multi-parameter estimation of a spin echo train (SET)signal in the presence of additive white Gaussian noise, a two-dimensional (2-D)parameter estimation method in a separable manner is proposed. By utilizing therank-one property of the2-D data matrix, and according to an iterative weighted leastsquares (WLS) method, the damping factor and frequency are estimated separately fromthe principal left and right singular vectors. The complex amplitude of SET is thenobtained on the basis of standard least squares. The parameter estimation performanceof this method achieves Cramer-Rao lower bound (CRLB) at a relatively large SNR ordata size conditions, and has a low computational complexity.
6In allusion to multi-parameter estimation of multi-spectrum SET signal in thepresence of additive white Gaussian noise, a two-dimensional (2-D) parameterestimation method based on eigenvector is proposed. In this method, by using the SETsignal, a2-D data matrix is constructed, and according to the different manners to form the Hankel block matrix pencil (MP), and the eigenvector is solved by utilizing theshift-invariance structure of the signal subspace, and further the damping factor as wellas the frequency are estimated with the structure rule of the eigenvector. The methodhas the capability of auto association, and under a relatively large SNR and availablefrequency resolution conditions, it can estimate the parameters effectively. Simulationresults show the effectiveness of the proposed algorithm.
1.针对干扰抑制与微弱核四极矩共振信号检测问题，提出了一种基于Hankel矩阵方式下奇异值分解的干扰抑制方法。该方法首先将原始数据构造成Hankel矩阵；然后对其进行奇异值分解，依据奇异值的大小可将原始信号分解为多个分量信号；最后对各分量信号进行谱估计，依据核四极矩共振信号的先验信息，滤除干扰信号与噪声；它有效地抑制了干扰信号，改善了信噪比。在干扰抑制的基础上，提出基于MUSIC谱估计的非线性最小二乘检测器，并以广义似然比统计量作为检测量；所提方法在降低了计算量的同时，提高了频率分辨率，达到有效检测微弱核四极矩共振信号的目的。
2.针对含有干扰信号与热噪声的自由衰减信号的参数估计问题，提出了基于总体最小二乘的线性预测类参数估计方法。所提方法同时考虑了线性预测方程两边数据矩阵的扰动量，并在计算总体最小二乘解时，考虑了干扰噪声项，克服了常规最小二乘方法仅考虑一边扰动量，致使估计方差较大的缺点。结合自由衰减信号的衰减特性与最大似然估计准则实现了微弱自由衰减信号参数有效估计。
3.针对强干扰信号遮蔽的微弱核四极矩共振信号参数估计问题，提出了基于改进的快速最大似然估计的残余信号迭代分解算法估计核四极矩共振信号参数。该方法将多维搜索问题转化为多个一维搜索，在频率维搜索时，结合了内插与类牛顿方法。所提方法在降低计算复杂度的同时提高了参数估计精度，解决了干扰信号对核四极矩共振信号的遮蔽问题。仿真和实测数据的结果验证了该算法的有效性。
4.针对核四极矩共振技术探测爆炸物中干扰信号的时变性，基于各信号采样模块包含有固定的核四极矩共振信号与时变干扰信号以及噪声的实际信号模型，提出改进的多模块HTLSstack算法。首先采用HTLS方法确定出共有极点的个数；其次构造新的筛选准则确定所有模块的共有极点；最后结合核四极矩共振信号的先验信息，实现核四极矩共振信号参数的有效估计。所提方法充分利用了原始数据的信息，在低信噪比下，避免了多模块HTLS方法在第一次奇异值分解时带来的性能损失，有效地提高了参数估计精度。
5.针对存在加性高斯白噪声多参数变量的单自旋回波串信号参数估计问题，提出一种参数分离化的2-D参数估计方法。利用2-D数据矩阵秩为1的特性，依照迭代加权最小二乘方法，从左、右主奇异值向量中以参数分离的方式分别估计出衰减因子和频率，基于最小二乘方法进一步获得信号幅度估计。该方法在相对高信噪比或大数据样本下可达到克拉美罗下界，且计算复杂度较低。
6.针对存在加性高斯白噪声多参数变量的多谱线自旋回波串信号参数估计问题，提出基于特征向量的2-D参数估计方法。将多谱线自旋回波串信号构造成2-D数据矩阵，按照不同的方式构造Hankel块矩阵束，利用子空间转移不变结构解得特征向量，依据特征向量的结构规律获得衰减因子和频率。该方法具有自动配对的能力，在相对高信噪比以及频率可分辨的情况下能够实现参数的有效估计。仿真数据结果验证了算法的有效性。
Nuclear quadrupole resonance (NQR) is a solid-state radio frequency (RF)spectroscopic technique, allowing the detection of various high explosives and illicitmaterials. Unfortunately, the practical use of NQR is restricted by the low signal tonoise ratio (SNR) and the radio frequency interference (RFI). The interferencemitigation, parameter estimation and detection of weak NQR signals are the core andthe key of the NQR technique. From the perspective of signal processing, some topicsrelated to NQR, such as the basic concept, the signal model, the signal excitationmethods, the interference mitigation, and parameter estimation and detection of weakNQR signals, are analyzed and elaborated comprehensively in this dissertation. Theinterference mitigation, detection and parameter estimation of weak NQR signals areresearched deeply. The specific work is summarized as follows:
1For the problem of interference mitigation and weak NQR signal detection, amethod of interference mitigation based on singular value decomposition (SVD) of theHankel matrix is proposed. In the proposed algorithm, a Hankel matrix is formed byoriginal data at first, and its SVD is implemented, then the original signal can bedecomposed into several component signals according to the singular values’ order.Finally, in accordance with the spectrum estimation of each component signal, theinterference and noise are removed on the basis of the prior information of NQR signals.It suppresses the interference effectively, and improves the SNR. After filtering theinterference, a nonlinear least square (NLS) detector based on MUSIC spectralestimation is presented, with the generalized likelihood ratio test (GLRT) as a detectionvariable. The proposed algoriyhm greatly reduces the computation load, simultaneously,guarantees a superior resolution of the frequency, so the motivation of the availabledetection for weak NQR signals is achieved.
2Be aimed at the parameters estimation problem of the free induction decay(FID) signal contained interference and thermal noise, the linear prediction estimatorbased on the total least squares (TLS) is presented to estimate the parameters of the FIDsignal. The perturbations of the linear prediction equation on the two sides areconsidered in the proposed method, and then solved in the total least squares sense, withthe consideration of the interference and noise terms, the drawback of the conventionalleast squares method which only considers one side disturbance and leads to a relativelylarge variance, is overcomed. With the combination of the damp character of the FID signal and the criterion of the maximum likelihood estimation, the estimation of theparameters of the weak FID signal is effectively accomplished.
3In allusion to the methods of parameters estimation of weak NQR signalsmasked by strong interference signals, residual signal iterative analysis algorithm(RSIAA) based on the improved fast maximum likelihood estimation (IFMLE) isproposed to estimate the parameters of the NQR signals. The proposed method turns themultidimensional search problem into multiple one-dimensional searches, and combinesthe interpolator and semi-Newton method. It solves the mask problem of theinterference to the NQR signal effectively, which simultaneously reduces thecomputational complexity and improves the estimated precision. The effectiveness ofthe proposed algorithm is demonstrated by the processing results of both simulated dataand experimental data.
4For the time-variation characteristic of interference signals in the explosivedetection using the NQR technique, and according to the real world signal model ofeach signal sample block including the fixed NQR signal, time-variation interferencesignals and noise, an improved multi-block Hankel total least squares stack (HTLSstack)method is presented. Firstly, the number of common poles is determined using theHTLS scheme; secondly, a new selection criterion is constructed to choose the commonpoles; finally, the prior knowledge is employed to realize the estimation of NQR signalseffectively. This method makes full use of the information of original data, and in thecase of low signal-to-noise ratio, it avoids the performance loss of multi-block HTLSmethod in the first SVD, and improves the precision of parameter estimation availably.
5To the problem of the multi-parameter estimation of a spin echo train (SET)signal in the presence of additive white Gaussian noise, a two-dimensional (2-D)parameter estimation method in a separable manner is proposed. By utilizing therank-one property of the2-D data matrix, and according to an iterative weighted leastsquares (WLS) method, the damping factor and frequency are estimated separately fromthe principal left and right singular vectors. The complex amplitude of SET is thenobtained on the basis of standard least squares. The parameter estimation performanceof this method achieves Cramer-Rao lower bound (CRLB) at a relatively large SNR ordata size conditions, and has a low computational complexity.
6In allusion to multi-parameter estimation of multi-spectrum SET signal in thepresence of additive white Gaussian noise, a two-dimensional (2-D) parameterestimation method based on eigenvector is proposed. In this method, by using the SETsignal, a2-D data matrix is constructed, and according to the different manners to form the Hankel block matrix pencil (MP), and the eigenvector is solved by utilizing theshift-invariance structure of the signal subspace, and further the damping factor as wellas the frequency are estimated with the structure rule of the eigenvector. The methodhas the capability of auto association, and under a relatively large SNR and availablefrequency resolution conditions, it can estimate the parameters effectively. Simulationresults show the effectiveness of the proposed algorithm.
引文
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