高分辨阵列信号处理方法研究
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摘要
阵列信号处理在雷达、声纳、通信等领域有着广泛的应用。随着阵列信号处理从理论到实际工程应用的发展,人们对算法稳健性和估计精度的要求越来越高。论文以提高阵列信号处理算法的稳健性和估计精度为目标,基于标量传感器阵列和矢量传感器阵列,对高分辨阵列信号处理方面展开研究,取得了一些有意义的成果。论文的主要内容由以下几个部分组成：
第一部分：SaS冲击噪声下高分辨阵列信号处理方法研究。
近年来,大量实验数据表明许多实际应用中的噪声都是非高斯分布的,适用于SaS分布来表示。由于SaS分布的随机变量不存在二阶及以上矩,因此传统基于二阶及以上统计量的阵列信号处理算法不能直接适用。针对这一问题,本文给出了几种冲击噪声背景下的阵列信号处理算法：首先论文研究了基于分数低阶矩的加权子空间拟合算法(FLOM-WSF)和基于Screened Ratio原理的加权子空间拟合算法(SR-WSF),该两种算法分别基于SaS型随机变量有界的分数低阶矩阵和共变系数矩阵,并用子空间拟合算法得到DOA估计值。仿真结果表明,该两种算法均可有效的提高冲击噪声背景下DOA的估计精度,其中SR-WSF算法无需对参数p进行选择,具有更强的稳健性。基于无穷范数归一化的ESPRIT算法(IN-ESPRIT)先对阵列接收的快拍数据进行预处理,构造一个伪协方差矩阵；然后,对伪协方差矩阵进行特征分析,并利用ESPRIT算法实现DOA的估计。与基于分数低阶矩的算法相比,IN-ESPRIT算法不仅具有更好的估计性能,可适用于多种冲击噪声,且无需已知冲击噪声特征指数的先验信息或估计。最小均方归一化误差(MMSNE)波束形成算法通过将期望信号和波束形成输出之间的归一化均方误差最小化求的最优权向量,根据瞬时自适应的无穷范数快拍归一化数据构造均方归一化误差,以此来代替均方误差,并采用采样协方差矩阵求逆(SMI)自适应算法的得到波束形成的权向量的估计。仿真结果表明,在多种冲击噪声背景下该算法都能有效提高估计精度,降低对干扰信号的零陷。
第二部分：扩展孔径高分辨阵列信号参数估计算法研究。
增加相邻传感器之间的间距可以实现阵列孔径扩展,从而提高参数估计的精度。但当相邻两阵元间的间距大于半波长时,会造成参数估计的模糊问题。针对该问题,论文给出两种基于双平行阵的扩展口径波达方向估计算法：扩展孔径ESPRIT算法和扩展孔径DOA矩阵算法。两种算法分别采用由4L+1个阵列单元和4L个阵列单元组成的双平行阵列几何结构,利用阵列传感器沿x轴和沿y轴的不同间距,分别计算出高精度模糊的方向余弦估计和低精度不模糊的方向余弦估计,利用低精度无模糊的方向余弦估计值对高精度模糊的方向余弦估计值进行解模糊处理,得到高精度无模糊的方向余弦的估计值。此外,论文还对由于阵列扩展孔径造成的特征值相等问题进行了研究,分别给出了两种有效的克服特征值相等问题的方法。
第三部分：基于声学和电磁矢量传感器阵列的二维DOA估计算法研究。
首先介绍了声学和电磁矢量传感器阵列的接收信号模型,然后研究了几种基于矢量传感器阵列的DOA估计算法：针对宽带Chirp信号,分别基于声学矢量传感器和电磁矢量传感器,研究了分数阶Fourier域滤波的算法。信号强度相同时,算法对信号进行分数阶Fourier变化后,分别用滤波器估计矢量传感器的导向矢量,信号强度不同时,算法用基于分数阶Fourier域滤波逐次消去强信号,然后分别估计导向矢量,根据导向矢量的性质得到方向估计值。该算法无需进行迭代搜索和二维DOA配对,可以估计具有相同或不同调频斜率的多个Chirp信号的二维DOA(极化)。针对相关噪声下的相干信号的DOA估计,基于面阵加远离的孤立传感器阵列几何结构,对声学矢量传感器和电磁矢量传感器,研究了基于传播算子的二维DOA(极化)估计算法。该算法首先定义了一个与信号相干性、噪声相关性无关的满秩矩阵,然后采用传播算子算法估计矢量传感器的导向矢量,最后得到自动配对的方位、仰角(极化参数)的估计值。针对基于声学矢量传感器阵列的高精度DOA估计,给出了一种基于传播算子的扩展孔径DOA估计算法,该算法无需特征分解或奇异值分解进行子空间的估计,因而在得到高精度的同时降低了运算量。最后研究了双子阵结构的电磁矢量传感器在空间相关噪声中的DOA-极化联合估计算法。算法基于任意空间位置的普通压力传感器和电磁矢量传感器组成的双子阵几何阵列结构,用两个子阵的互相关矩阵消除空间噪声,该算法对子阵几何结构无任何约束,也无需已知传感器的空间坐标,且具有较低的运算量,适用于实时处理。
Array signal processing technique has played a fundamental role in many appli-cations involving radar, sonar and communications. However, with the development of array signal processing approaches in practical applications, the investigations on robust and high accurate array signal processing methods have received great interest.
Following the recent advances of array signal processing, this dissertation inves-tigates robust and high accurate array signal processing methods using scalar sensors and vector sensors. This dissertation mainly consists of the following parts.
Part I:High accurate array signal processing methods in SaS impulsive noise
Recently, various experiment measurements have shown that atmospheric noise, underwater acoustic noise and electromagnetic disturbance noise have "impulsive" characteristics, which are inappropriatlly modeled as Gaussian noise in applications. As the SaS processes do not possess second-order and high order moments, conven-tional second-order-based array signal processing method can not apply to SaS noise environments directly. In order to deal with this problem, several array signal process-ing methods in impulsive noise environments are proposed in this chapter.
Firstly the fractional lower order moment based weighted subspace fitting (FLOM-WSF) algorithm and the Screened Ratio based weighted subspace fitting (SR-WSF) algorithm are proposed for direction finding under SaS noise. The FLOM-WSF and SR-WSF respectively form the array FLOM matrix and array covariation matrix, and then obtain DOA estimation using subspace fitting techniques. Comparing with the traditional DOA techniques, these two algorithms can improve estimation performance in impulsive noise. Incidentally, the SR-WSF algorithm requires no estimation of the noise parameter, hence showing high robustness. The infinity-norm normalization al-gorithm adaptively normalizes each sensor-array snapshot's spatial data vector by its infinity-norm, constructs a pseudo-correlation function, and then, ESPRIT algorithm is adapted to achieve DOA estimation. Simulations show that the IN-ESPRIT algo-rithm has superior estimation-accuracy over the FLOM-ESPRIT algorithm. Then a new minimum mean squared "normalized-error" (MMSNE) beamforming technique is investigated. This new beamformer aims to minimize the "normalized error " between the desired signal and the the beamformer's output. This normalized error is defined in terms of the instantaneously adaptive infinity-norm snapshot-normalized data, as an alter-native to the customary "fractional-order-error" for impulsive noise environ-ments. Sample matrix inversion (SMI) algorithm is used for updating the beamformer weights. Simulation results show the algorithm produces higher estimation-accuracy and offers better interference-rejection for several impulsive noise environments com-paring with the earlier FLOM-based beamformer.
Part II:Extended aperture high resolution parameter estimation
Extending the inter-sensor spacing beyond a half-wavelength can offer enhanced array resolution and direction-finding precision, but will lead to a set of cyclically am-biguous angle estimates. This chapter proposes two extended aperture two-directional DOA estimation algorithms using two parallel-shape-array:extended aperture ES-PRIT (EA-ESPRIT) algorithm and extended aperture DOA matrix (EA-DOAM) algo-rithm. The two algorithms use 4L+1 and 4L array elements to form two-parallel-shape array geometry, high-variance unambiguous direction cosine estimates and low-variance cyclically ambiguous direction cosine estimates are obtained from the different sensors space. The key idea underlying these two algorithms is to use the high-variance un-ambiguous direction cosine estimates to resolve the low-variance cyclically ambiguous direction cosine estimates to extract azimuth-elevation angle estimates. Two remedial methods to solve the identical eigenvalues problem have also been presented.
Part III:2D-DOA estimation using an array of acoustic and electro-magnetic vector sensors.
Firstly the data models of acoustic and electromagnetic vector sensor array are introduced. Then several DOA estimation methods using vector sensor array are developed.
A new azimuth, elevation angle (Polarization) estimation algorithm for multiple broadband chirp signals using a single acoustic or electromagnetic vector sensor is proposed in this chapter. Two distinct signal scenarios are considered. For multiple signals with same power, the proposed algorithm applies the fractional Fourier trans-form (FrFT) to estimate the steering vectors of vector sensors; For multiple signals with different powers, the proposed algorithm uses fractional Fourier domain filter-ing to estimate and eliminate steering vectors of vector sensors one by one, and then to get elevation-azimuth angle (Polarization) estimates of different signals separately. The proposed algorithm requires no iterative searching and pair matching procedures, works well for multiple chirps having the same or distinct chirp rates.
Then a propagator-based algorithm for two-dimensional direction finding of co-herent sources under spatially correlated noise is developed in this paper. The planar-plus-an-isolated array geometry based on acoustic or electromagnetic vector sensors is adopted, and a full rank cross-covariance matrix is defined. Then the propagator method is used to estimate the steering vectors of acoustic or electromagnetic vector sensor. The Characteristic of steering vector is developed to obtain the closed-form azimuth-elevation angle (Polarization) estimates.
A propagator-based algorithm for underwater acoustic 2-D direction-of-arrival (DOA) estimation with an array of acoustic vector sensors is proposed. The prop-agator method is exploited to extract extended aperture parameter estimation.The proposed algorithm requires no eigen-decomposition or singular value decomposition into the signal and noise subspaces. Comparing with its ESPRIT counterpart, the pro-posed propagator algorithm has its computational complexity reduced and the similar accuracy.
Finally a computationally simple azimuth-elevation direction finding algorithm in spatially correlated noise fields is developed. The algorithm uses two-far-separated subarray geometry based on electromagnetic vector sensors and scalar sensors, and all sensors are arbitrarily placed at unknown locations.A cross matrix to eliminate the effect of the spatially correlated noise is defined. The proposed algorithm has no restrict to the subarray geometry and sensors locations, does not need 2D iterative searching and shows low computational complexity.
第一部分：SaS冲击噪声下高分辨阵列信号处理方法研究。
近年来,大量实验数据表明许多实际应用中的噪声都是非高斯分布的,适用于SaS分布来表示。由于SaS分布的随机变量不存在二阶及以上矩,因此传统基于二阶及以上统计量的阵列信号处理算法不能直接适用。针对这一问题,本文给出了几种冲击噪声背景下的阵列信号处理算法：首先论文研究了基于分数低阶矩的加权子空间拟合算法(FLOM-WSF)和基于Screened Ratio原理的加权子空间拟合算法(SR-WSF),该两种算法分别基于SaS型随机变量有界的分数低阶矩阵和共变系数矩阵,并用子空间拟合算法得到DOA估计值。仿真结果表明,该两种算法均可有效的提高冲击噪声背景下DOA的估计精度,其中SR-WSF算法无需对参数p进行选择,具有更强的稳健性。基于无穷范数归一化的ESPRIT算法(IN-ESPRIT)先对阵列接收的快拍数据进行预处理,构造一个伪协方差矩阵；然后,对伪协方差矩阵进行特征分析,并利用ESPRIT算法实现DOA的估计。与基于分数低阶矩的算法相比,IN-ESPRIT算法不仅具有更好的估计性能,可适用于多种冲击噪声,且无需已知冲击噪声特征指数的先验信息或估计。最小均方归一化误差(MMSNE)波束形成算法通过将期望信号和波束形成输出之间的归一化均方误差最小化求的最优权向量,根据瞬时自适应的无穷范数快拍归一化数据构造均方归一化误差,以此来代替均方误差,并采用采样协方差矩阵求逆(SMI)自适应算法的得到波束形成的权向量的估计。仿真结果表明,在多种冲击噪声背景下该算法都能有效提高估计精度,降低对干扰信号的零陷。
第二部分：扩展孔径高分辨阵列信号参数估计算法研究。
增加相邻传感器之间的间距可以实现阵列孔径扩展,从而提高参数估计的精度。但当相邻两阵元间的间距大于半波长时,会造成参数估计的模糊问题。针对该问题,论文给出两种基于双平行阵的扩展口径波达方向估计算法：扩展孔径ESPRIT算法和扩展孔径DOA矩阵算法。两种算法分别采用由4L+1个阵列单元和4L个阵列单元组成的双平行阵列几何结构,利用阵列传感器沿x轴和沿y轴的不同间距,分别计算出高精度模糊的方向余弦估计和低精度不模糊的方向余弦估计,利用低精度无模糊的方向余弦估计值对高精度模糊的方向余弦估计值进行解模糊处理,得到高精度无模糊的方向余弦的估计值。此外,论文还对由于阵列扩展孔径造成的特征值相等问题进行了研究,分别给出了两种有效的克服特征值相等问题的方法。
第三部分：基于声学和电磁矢量传感器阵列的二维DOA估计算法研究。
首先介绍了声学和电磁矢量传感器阵列的接收信号模型,然后研究了几种基于矢量传感器阵列的DOA估计算法：针对宽带Chirp信号,分别基于声学矢量传感器和电磁矢量传感器,研究了分数阶Fourier域滤波的算法。信号强度相同时,算法对信号进行分数阶Fourier变化后,分别用滤波器估计矢量传感器的导向矢量,信号强度不同时,算法用基于分数阶Fourier域滤波逐次消去强信号,然后分别估计导向矢量,根据导向矢量的性质得到方向估计值。该算法无需进行迭代搜索和二维DOA配对,可以估计具有相同或不同调频斜率的多个Chirp信号的二维DOA(极化)。针对相关噪声下的相干信号的DOA估计,基于面阵加远离的孤立传感器阵列几何结构,对声学矢量传感器和电磁矢量传感器,研究了基于传播算子的二维DOA(极化)估计算法。该算法首先定义了一个与信号相干性、噪声相关性无关的满秩矩阵,然后采用传播算子算法估计矢量传感器的导向矢量,最后得到自动配对的方位、仰角(极化参数)的估计值。针对基于声学矢量传感器阵列的高精度DOA估计,给出了一种基于传播算子的扩展孔径DOA估计算法,该算法无需特征分解或奇异值分解进行子空间的估计,因而在得到高精度的同时降低了运算量。最后研究了双子阵结构的电磁矢量传感器在空间相关噪声中的DOA-极化联合估计算法。算法基于任意空间位置的普通压力传感器和电磁矢量传感器组成的双子阵几何阵列结构,用两个子阵的互相关矩阵消除空间噪声,该算法对子阵几何结构无任何约束,也无需已知传感器的空间坐标,且具有较低的运算量,适用于实时处理。
Array signal processing technique has played a fundamental role in many appli-cations involving radar, sonar and communications. However, with the development of array signal processing approaches in practical applications, the investigations on robust and high accurate array signal processing methods have received great interest.
Following the recent advances of array signal processing, this dissertation inves-tigates robust and high accurate array signal processing methods using scalar sensors and vector sensors. This dissertation mainly consists of the following parts.
Part I:High accurate array signal processing methods in SaS impulsive noise
Recently, various experiment measurements have shown that atmospheric noise, underwater acoustic noise and electromagnetic disturbance noise have "impulsive" characteristics, which are inappropriatlly modeled as Gaussian noise in applications. As the SaS processes do not possess second-order and high order moments, conven-tional second-order-based array signal processing method can not apply to SaS noise environments directly. In order to deal with this problem, several array signal process-ing methods in impulsive noise environments are proposed in this chapter.
Firstly the fractional lower order moment based weighted subspace fitting (FLOM-WSF) algorithm and the Screened Ratio based weighted subspace fitting (SR-WSF) algorithm are proposed for direction finding under SaS noise. The FLOM-WSF and SR-WSF respectively form the array FLOM matrix and array covariation matrix, and then obtain DOA estimation using subspace fitting techniques. Comparing with the traditional DOA techniques, these two algorithms can improve estimation performance in impulsive noise. Incidentally, the SR-WSF algorithm requires no estimation of the noise parameter, hence showing high robustness. The infinity-norm normalization al-gorithm adaptively normalizes each sensor-array snapshot's spatial data vector by its infinity-norm, constructs a pseudo-correlation function, and then, ESPRIT algorithm is adapted to achieve DOA estimation. Simulations show that the IN-ESPRIT algo-rithm has superior estimation-accuracy over the FLOM-ESPRIT algorithm. Then a new minimum mean squared "normalized-error" (MMSNE) beamforming technique is investigated. This new beamformer aims to minimize the "normalized error " between the desired signal and the the beamformer's output. This normalized error is defined in terms of the instantaneously adaptive infinity-norm snapshot-normalized data, as an alter-native to the customary "fractional-order-error" for impulsive noise environ-ments. Sample matrix inversion (SMI) algorithm is used for updating the beamformer weights. Simulation results show the algorithm produces higher estimation-accuracy and offers better interference-rejection for several impulsive noise environments com-paring with the earlier FLOM-based beamformer.
Part II:Extended aperture high resolution parameter estimation
Extending the inter-sensor spacing beyond a half-wavelength can offer enhanced array resolution and direction-finding precision, but will lead to a set of cyclically am-biguous angle estimates. This chapter proposes two extended aperture two-directional DOA estimation algorithms using two parallel-shape-array:extended aperture ES-PRIT (EA-ESPRIT) algorithm and extended aperture DOA matrix (EA-DOAM) algo-rithm. The two algorithms use 4L+1 and 4L array elements to form two-parallel-shape array geometry, high-variance unambiguous direction cosine estimates and low-variance cyclically ambiguous direction cosine estimates are obtained from the different sensors space. The key idea underlying these two algorithms is to use the high-variance un-ambiguous direction cosine estimates to resolve the low-variance cyclically ambiguous direction cosine estimates to extract azimuth-elevation angle estimates. Two remedial methods to solve the identical eigenvalues problem have also been presented.
Part III:2D-DOA estimation using an array of acoustic and electro-magnetic vector sensors.
Firstly the data models of acoustic and electromagnetic vector sensor array are introduced. Then several DOA estimation methods using vector sensor array are developed.
A new azimuth, elevation angle (Polarization) estimation algorithm for multiple broadband chirp signals using a single acoustic or electromagnetic vector sensor is proposed in this chapter. Two distinct signal scenarios are considered. For multiple signals with same power, the proposed algorithm applies the fractional Fourier trans-form (FrFT) to estimate the steering vectors of vector sensors; For multiple signals with different powers, the proposed algorithm uses fractional Fourier domain filter-ing to estimate and eliminate steering vectors of vector sensors one by one, and then to get elevation-azimuth angle (Polarization) estimates of different signals separately. The proposed algorithm requires no iterative searching and pair matching procedures, works well for multiple chirps having the same or distinct chirp rates.
Then a propagator-based algorithm for two-dimensional direction finding of co-herent sources under spatially correlated noise is developed in this paper. The planar-plus-an-isolated array geometry based on acoustic or electromagnetic vector sensors is adopted, and a full rank cross-covariance matrix is defined. Then the propagator method is used to estimate the steering vectors of acoustic or electromagnetic vector sensor. The Characteristic of steering vector is developed to obtain the closed-form azimuth-elevation angle (Polarization) estimates.
A propagator-based algorithm for underwater acoustic 2-D direction-of-arrival (DOA) estimation with an array of acoustic vector sensors is proposed. The prop-agator method is exploited to extract extended aperture parameter estimation.The proposed algorithm requires no eigen-decomposition or singular value decomposition into the signal and noise subspaces. Comparing with its ESPRIT counterpart, the pro-posed propagator algorithm has its computational complexity reduced and the similar accuracy.
Finally a computationally simple azimuth-elevation direction finding algorithm in spatially correlated noise fields is developed. The algorithm uses two-far-separated subarray geometry based on electromagnetic vector sensors and scalar sensors, and all sensors are arbitrarily placed at unknown locations.A cross matrix to eliminate the effect of the spatially correlated noise is defined. The proposed algorithm has no restrict to the subarray geometry and sensors locations, does not need 2D iterative searching and shows low computational complexity.
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