分布式信源低复杂度参数估计算法研究
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摘要
分布式信源广泛存在于雷达、声纳和移动通信等领域。例如,在城区密集环境中,建筑物、道路和车辆等物体易引起多径传播现象,从而导致信号的能量发生一定程度的空间扩散。对于分布式信源,基于点源假设的传统参数估计算法已不再适用。为此,众多学者提出了一些分布源模型和相应的参数估计算法。然而,这些算法大多需要进行多维非线性优化或者多维谱搜索,计算复杂程度很高,不利于实时处理和工程实现。此外,现有的算法几乎都假设分布源是静止的,而不能对移动分布源的中心波达方向(DOA)进行实时跟踪估计。
针对上述问题,本文在对现有分布源模型和参数估计算法进行全面分析的基础上,重点对分布源的低复杂度参数估计和中心DOA的快速跟踪问题做了深入系统的研究,并取得了若干具有创新性的研究成果。论文的主要工作和创新点可概括如下:
1.在深入研究相干、非相干分布源模型及现有空时分布源模型的基础上,提出了两种新的分布源模型:角度相干时延相干分布源和角度非相干时延非相干分布源,并推导了相应的阵列接收矢量的表达式或阵列协方差矩阵的表达式。
2.提出了一种相干分布源的低复杂度参数估计算法。该算法利用了均匀线阵的平移子阵间的近似旋转不变性质和传播算子方法,能够实现中心DOA和角度扩展参数的解耦估计。由于避免了二维搜索和样本协方差矩阵的特征分解,该算法比现有算法有更少的计算花费,并且在低信噪比下的估计性能良好。
3.提出了两种低复杂度的相干分布源二维中心DOA估计算法。第一种算法利用了特殊的双平行线阵中存在的两个近似旋转不变关系,由总体最小二乘法求得两个对应的旋转不变矩阵,进而估计出分布源的中心方位角和中心俯仰角。第二种算法利用了特殊的三平行线阵中存在的三个近似旋转不变关系,由传播算子法求得对应的三个旋转不变矩阵,进而估计出分布源的二维中心DOA。与传统算法相比,上述两种算法无需谱搜索,计算复杂度更低,且能用于具有不同角分布的多源场合。
4.提出了两种非相干分布源的低复杂度参数估计算法。第一种算法利用了样本协方差矩阵次对角线元素的相位信息和无噪声协方差矩阵的首列矢量,能够实现中心DOA和角度扩展参数的解耦估计。该算法无需对样本协方差矩阵做特征分解,估计单个分布源的两个参数时仅需完成一次一维搜索,因而,计算复杂度较低。第二种算法基于空间靠得很近的两个平移线阵近似满足的旋转不变性质,由传播算子求得对应的旋转不变矩阵,进而利用旋转不变矩阵的特征值加权估计出分布源的中心DOA。该算法无需谱搜索和对样本协方差矩阵做特征分解,与现有算法相比,计算上更具优势,并且对模型误差稳健。
5.提出了两种二维非相干分布源的低复杂度参数估计算法。第一种算法利用L型阵列构造了两类空间互相关函数,并在小角度扩展假设下,由空间互相关函数的相位信息估计出分布源的中心方位角和中心俯仰角。该算法无需任何搜索和矩阵的特征分解运算,计算复杂度非常低,且对分布源的角分布形式不敏感。第二种算法首先利用空间靠得很近的两个平行线阵获得中心俯仰角的初始估计,然后由中心俯仰角初值将一个四维参数优化问题转化两个一维参数优化问题和一个二维参数优化问题。该算法大大减轻了计算负担,且能处理多个分布源。
6.提出了三种分布源中心DOA快速跟踪算法。其中,前两种算法基于子空间更新的思想,分别用于跟踪相干分布源的中心DOA和二维中心DOA。这两种算法避免了对样本协方差矩阵进行重复的特征分解,且可跟踪具有不同角分布的多个信号。第三种算法利用了最大似然估计和粒子群算法,用于跟踪非相干分布源的中心DOA。该算法无需重复确定伪信号子空间的维数,且在低信噪比时也具有优异的跟踪性能。
Distributed sources exist widely in radar, sonar and mobile communications fields. For example, in dense urban environments, some objects such as building, road and vehicle cause easily the multipath phenomena, and may lead to certain spatial spreading of the source energy. The traditional parameter estimation techniques based on point source model aren’t applicable to distributed sources. Therefore, a number of investigators have proposed some models of distributed sources and corresponding parameter estimation methods. However, most of them involve multi-dimensional nonlinear optimization or multi-dimensional spectrum search. The computational complexities of them are too high to be suited to real-time processing and engineering realization. In addition, all of them are based on the assumption that distributed sources are static, and cann’t be applied to track the nominal direction-of-arrivals (DOAs) of mobile distributed sources in real time.
Aiming at the above problems, based on an overall analysis of the existing models and parameter estimation methods of distributed sources, this dissertation focuses on two problems: the low-complexity parameter estimation and fast nominal DOA tracking of distributed sources, and gains several novel research achievements.
Our main works and innovations are summarized as follows:
1. Based on an intensive study on coherently distributed (CD) source model, incoherently distributed (ID) source model and the existing space-time distributed source model, two new distributed source models: temporal-angular coherently distributed sources and temporal-angular incoherently distributed sources are proposed. The expressions of corresponding array received vector and array covariance matrix are derived.
2. A low-complexity parameter estimation method for CD sources is proposed. Using the approximate rotational invariance property between two shifted subarrays in a uniform linear array (ULA) and the propagator method, the proposed method can realize the decoupled estimation of nominal DOA and angular spread. Avoiding two-dimensional (2-D) search and the eigendecomposition of the sample covariance matrix, our approach has a substantially reduced computational cost than the existing methods. Further, it can provide excellent performance even at low SNR.
3. Two low-complexity methods for the 2-D DOA estimation of CD sources are proposed. Based on two approximate rotational invariance relations in the special double parallel ULAs, the first method estimates the nominal azimuths and elevations of CD sources by obtaining two corresponding rotational invariance matrices using the total least squares (TLS) method. Based on three approximate rotational invariance relations in the special treble parallel ULAs, the second method obtains the 2-D nominal DOA estimates of CD sources by estimating three corresponding rotational invariance matrices using the propagator method. Without spectrum-peak search, the above methods provide lower computational complexity than the traditional methods, and can be applied to the multisource scenario with different angular distributions.
4. Two low-complexity parameter estimation methods for ID sources are proposed. The first method can realize the decoupled estimation of nominal DOA and angular spread by utilizing the phase information of the secondary diagonal elements of the sample covariance matrix and the first column vector of the noise-free covariance matrix. Without the eigendecomposition of the sample covariance matrix, the method can estimate two parameters of single ID source using only once one-dimensional (1-D) search. Therefore, it provides lower computational complexity. The second method exploits the approximate rotational invariance property between two closely spaced shifted ULAs. And it estimates the nominal DOAs of ID sources by using the weighted eigenvalues of the corresponding rotational invariance matrix which is estimated by propagator method. Without spectrum search and the eigendecomposition of the sample covariance matrix, our approach is computationally more attractive compared to the existing methods, and is robust to mismodeling.
5. Two low-complexity parameter estimation methods for 2-D ID sources are proposed. Using L-shape array, the first method formulated two types of spatial cross-correlation functions (SCFs). Under small angular spread, the nominal azimuth and elevation are estimated by using the phase information of the SCFs. Without any search and matrix eigendecomposition, our approach has a substantially reduced computational. Moreover, it is also a robust estimator which doesn’t depend on the angular distribution shape of the ID source. Based on two closely spaced parallel ULAs, the second method firstly obtains preliminary estimates of the nominal elevations. And then it transforms a four-dimensional parameter optimization problem into two 1-D parameter optimization problems and a 2-D parameter optimization problem with the help of preliminary values of the nominal elevations. The method reduces significantly the computational burden and can be used to deal with multiple ID sources.
6. Three fast methods for the nominal DOA tracking of distributed sources are proposed. Among the methods, two methods based on the subspace updating idea are used to track, respectively, the nominal DOAs and 2-D nominal DOAs of CD sources. Avoiding the repeated eigendecomposition of the sample covariance matrix, they can track multiple sources with different angular distributions. The third method takes advantage of the maximum likelihood (ML) estimator and particle swarm algorithm, and is used to track the nominal DOAs of ID sources. The method does not require the knowledge of the effective dimension of the pseudosignal subspace of ID sources, and can exhibit excellent tracking performance even at low SNR.
针对上述问题,本文在对现有分布源模型和参数估计算法进行全面分析的基础上,重点对分布源的低复杂度参数估计和中心DOA的快速跟踪问题做了深入系统的研究,并取得了若干具有创新性的研究成果。论文的主要工作和创新点可概括如下:
1.在深入研究相干、非相干分布源模型及现有空时分布源模型的基础上,提出了两种新的分布源模型:角度相干时延相干分布源和角度非相干时延非相干分布源,并推导了相应的阵列接收矢量的表达式或阵列协方差矩阵的表达式。
2.提出了一种相干分布源的低复杂度参数估计算法。该算法利用了均匀线阵的平移子阵间的近似旋转不变性质和传播算子方法,能够实现中心DOA和角度扩展参数的解耦估计。由于避免了二维搜索和样本协方差矩阵的特征分解,该算法比现有算法有更少的计算花费,并且在低信噪比下的估计性能良好。
3.提出了两种低复杂度的相干分布源二维中心DOA估计算法。第一种算法利用了特殊的双平行线阵中存在的两个近似旋转不变关系,由总体最小二乘法求得两个对应的旋转不变矩阵,进而估计出分布源的中心方位角和中心俯仰角。第二种算法利用了特殊的三平行线阵中存在的三个近似旋转不变关系,由传播算子法求得对应的三个旋转不变矩阵,进而估计出分布源的二维中心DOA。与传统算法相比,上述两种算法无需谱搜索,计算复杂度更低,且能用于具有不同角分布的多源场合。
4.提出了两种非相干分布源的低复杂度参数估计算法。第一种算法利用了样本协方差矩阵次对角线元素的相位信息和无噪声协方差矩阵的首列矢量,能够实现中心DOA和角度扩展参数的解耦估计。该算法无需对样本协方差矩阵做特征分解,估计单个分布源的两个参数时仅需完成一次一维搜索,因而,计算复杂度较低。第二种算法基于空间靠得很近的两个平移线阵近似满足的旋转不变性质,由传播算子求得对应的旋转不变矩阵,进而利用旋转不变矩阵的特征值加权估计出分布源的中心DOA。该算法无需谱搜索和对样本协方差矩阵做特征分解,与现有算法相比,计算上更具优势,并且对模型误差稳健。
5.提出了两种二维非相干分布源的低复杂度参数估计算法。第一种算法利用L型阵列构造了两类空间互相关函数,并在小角度扩展假设下,由空间互相关函数的相位信息估计出分布源的中心方位角和中心俯仰角。该算法无需任何搜索和矩阵的特征分解运算,计算复杂度非常低,且对分布源的角分布形式不敏感。第二种算法首先利用空间靠得很近的两个平行线阵获得中心俯仰角的初始估计,然后由中心俯仰角初值将一个四维参数优化问题转化两个一维参数优化问题和一个二维参数优化问题。该算法大大减轻了计算负担,且能处理多个分布源。
6.提出了三种分布源中心DOA快速跟踪算法。其中,前两种算法基于子空间更新的思想,分别用于跟踪相干分布源的中心DOA和二维中心DOA。这两种算法避免了对样本协方差矩阵进行重复的特征分解,且可跟踪具有不同角分布的多个信号。第三种算法利用了最大似然估计和粒子群算法,用于跟踪非相干分布源的中心DOA。该算法无需重复确定伪信号子空间的维数,且在低信噪比时也具有优异的跟踪性能。
Distributed sources exist widely in radar, sonar and mobile communications fields. For example, in dense urban environments, some objects such as building, road and vehicle cause easily the multipath phenomena, and may lead to certain spatial spreading of the source energy. The traditional parameter estimation techniques based on point source model aren’t applicable to distributed sources. Therefore, a number of investigators have proposed some models of distributed sources and corresponding parameter estimation methods. However, most of them involve multi-dimensional nonlinear optimization or multi-dimensional spectrum search. The computational complexities of them are too high to be suited to real-time processing and engineering realization. In addition, all of them are based on the assumption that distributed sources are static, and cann’t be applied to track the nominal direction-of-arrivals (DOAs) of mobile distributed sources in real time.
Aiming at the above problems, based on an overall analysis of the existing models and parameter estimation methods of distributed sources, this dissertation focuses on two problems: the low-complexity parameter estimation and fast nominal DOA tracking of distributed sources, and gains several novel research achievements.
Our main works and innovations are summarized as follows:
1. Based on an intensive study on coherently distributed (CD) source model, incoherently distributed (ID) source model and the existing space-time distributed source model, two new distributed source models: temporal-angular coherently distributed sources and temporal-angular incoherently distributed sources are proposed. The expressions of corresponding array received vector and array covariance matrix are derived.
2. A low-complexity parameter estimation method for CD sources is proposed. Using the approximate rotational invariance property between two shifted subarrays in a uniform linear array (ULA) and the propagator method, the proposed method can realize the decoupled estimation of nominal DOA and angular spread. Avoiding two-dimensional (2-D) search and the eigendecomposition of the sample covariance matrix, our approach has a substantially reduced computational cost than the existing methods. Further, it can provide excellent performance even at low SNR.
3. Two low-complexity methods for the 2-D DOA estimation of CD sources are proposed. Based on two approximate rotational invariance relations in the special double parallel ULAs, the first method estimates the nominal azimuths and elevations of CD sources by obtaining two corresponding rotational invariance matrices using the total least squares (TLS) method. Based on three approximate rotational invariance relations in the special treble parallel ULAs, the second method obtains the 2-D nominal DOA estimates of CD sources by estimating three corresponding rotational invariance matrices using the propagator method. Without spectrum-peak search, the above methods provide lower computational complexity than the traditional methods, and can be applied to the multisource scenario with different angular distributions.
4. Two low-complexity parameter estimation methods for ID sources are proposed. The first method can realize the decoupled estimation of nominal DOA and angular spread by utilizing the phase information of the secondary diagonal elements of the sample covariance matrix and the first column vector of the noise-free covariance matrix. Without the eigendecomposition of the sample covariance matrix, the method can estimate two parameters of single ID source using only once one-dimensional (1-D) search. Therefore, it provides lower computational complexity. The second method exploits the approximate rotational invariance property between two closely spaced shifted ULAs. And it estimates the nominal DOAs of ID sources by using the weighted eigenvalues of the corresponding rotational invariance matrix which is estimated by propagator method. Without spectrum search and the eigendecomposition of the sample covariance matrix, our approach is computationally more attractive compared to the existing methods, and is robust to mismodeling.
5. Two low-complexity parameter estimation methods for 2-D ID sources are proposed. Using L-shape array, the first method formulated two types of spatial cross-correlation functions (SCFs). Under small angular spread, the nominal azimuth and elevation are estimated by using the phase information of the SCFs. Without any search and matrix eigendecomposition, our approach has a substantially reduced computational. Moreover, it is also a robust estimator which doesn’t depend on the angular distribution shape of the ID source. Based on two closely spaced parallel ULAs, the second method firstly obtains preliminary estimates of the nominal elevations. And then it transforms a four-dimensional parameter optimization problem into two 1-D parameter optimization problems and a 2-D parameter optimization problem with the help of preliminary values of the nominal elevations. The method reduces significantly the computational burden and can be used to deal with multiple ID sources.
6. Three fast methods for the nominal DOA tracking of distributed sources are proposed. Among the methods, two methods based on the subspace updating idea are used to track, respectively, the nominal DOAs and 2-D nominal DOAs of CD sources. Avoiding the repeated eigendecomposition of the sample covariance matrix, they can track multiple sources with different angular distributions. The third method takes advantage of the maximum likelihood (ML) estimator and particle swarm algorithm, and is used to track the nominal DOAs of ID sources. The method does not require the knowledge of the effective dimension of the pseudosignal subspace of ID sources, and can exhibit excellent tracking performance even at low SNR.
引文
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