阵列多参数联合估计算法及应用的研究
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摘要
阵列多参数估计在通信、雷达、声纳等领域有着广泛的应用。随着阵列多参数估计从理论到实际工程的发展，人们对算法稳健性和估计精度的要求越来越高。本文以提高阵列多参数估计算法的稳健性和估计精度为目标，针对传统的标量传感器阵列、矢量传感器阵列下多信号源多参数联合估计以及双基地MIMO雷达中的多目标多参数联合估计展开了研究，取得了一些有意义的成果。论文的主要内容如下：
研究了空间二维角度和频率估计算法，本文将平行因子理论应用到阵列信号二维角度和频率估计中，首先针对L型阵列提出了基于平行因子三线性分解的二维角度和频率估计算法，根据阵列接收天线输出构建了一个平行因子三线性模型，通过对该模型三线性分解可以得到二维角度和频率的估计。在此基础上，针对双平行线阵列/面阵结构，提出了一种基于平行因子四线性分解的二维角度和频率联合估计算法。根据阵列输出数据构建一个四线性模型，通过对此模型分解可以得到二维角度和频率估计的参数。基于平行因子技术的参数估计方法是一种迭代算法，不需要特征值分解或奇异值分解，只需要一定的迭代次数算法就能收敛。该方法的优点是无需谱峰搜索，可实现多参数的联合估计与自动配对，与现有的算法进行了比较，具有更高的参数估计精度，而且在小样本数下也能较好的工作。
研究了任意声矢量传感器阵列下的角度和频率估计算法，相对于常规标量传感器而言，矢量传感器具备很多优势，可进行多维参数估计，得到更优越的性能。针对任意声矢量传感器阵列下的多参数估计，首先推导了阵列接收信号模型，提出了基于DOA矩阵和平行因子四线性分解的两种多参数估计算法。基于DOA矩阵法的算法具有计算复杂度低的优点，可适用于对计算复杂度有限制的声源定位场合。而基于平行因子四线性分解的方法无需谱峰搜索，可实现参数的同时估计与配对，与基于平行因子三线性分解的算法和ESPRIT算法进行了比较，具有更高的参数估计精度，为声源定位提供了一种新的选择。
研究了双基地MIMO雷达多目标的发射角（DOD）和接收角（DOA）联合估计，提出了一种降维MUSIC算法。该算法首先将二维MUSIC算法进行降维处理变成一维MUSIC，通过谱峰搜索得到DOA，进一步得到DOD方向矢量的估计值，再利用最小二乘法得到DOD的估计。该算法的优点是与二维MUSIC算法相比，避免了二维谱峰搜索，复杂度大大降低，而参数估计精度与其非常接近；与ESPRIT算法相比，参数估计性能优于ESPRIT算法；估计过程中参数自动配对，还可将该算法扩展到非规则阵列中。
研究了双基地MIMO雷达L型阵列和均匀圆阵列下多目标的二维DOD和二维DOA的联合估计，由于目前大部分参考文献对双基地MIMO雷达中多参数的研究都是针对均匀线阵建模，估计的是一维角度，L型阵列能估计方位角和仰角，与实际情形更为接近。均匀圆阵也是一种常用的阵列，能估计二维角度，由于其方向矢量不具备范得蒙特性，信号处理较为复杂。本文基于L型阵列和均匀圆阵列分别提出了基于平行因子技术的二维DOD和二维DOA联合估计算法。该算法利用L型阵列的结构特点和均匀圆阵本身的结构特点及最小二乘算法进行了四维角度的估计。算法的优点是参数估计精度优于ESPRIT算法，并接近克拉美罗界(CRB)，且估计过程中参数自动配对，在小样本数下也能较好的工作。
研究了L型阵列下双基地MIMO雷达的二维DOA、二维DOD及多普勒频率联合估计，提出了基于DOA矩阵的多维参数联合估计算法，该算法利用DOA矩阵法的思想构造矩阵，通过特征参数与估计参数之间关系，推导出了目标四维角度和多普勒频率联合估计公式，并得到闭式解。该算法与ESPRIT算法相比，只需一次特征值分解，计算量降低。随着信噪比的提高，估计性能越来越接近ESPRIT算法，估计过程不需要额外的配对运算就实现了参数的自动配对，并能有效克服空间色噪声的影响，仿真结果验证了算法的有效性。
Array signal parameters estimation techniques have played a fundamental role in manyapplications involving radar, sonar and communications. Howerer, with the development of arraysignal estimation algorithms in practical applications, the investigation on robust and high accuratearray signal parameter estimation algorithm have received great interest. Joint multiple parameterestimation of multiple sources for the conventional sensor array and the vector array, and thecorresponding estimation of multiple targets in bistatic MIMO-radar are investigated in thisdissertation. This research of the dissertation maily consists of the following parts:
The two dimensional direction of arrival and frequency estimation algorithm is investigated. Inthis paper the theory of parafac factor is applied for the joint estimation of2D-DOA and frequency.First the joint2D-DOA and frequency estimation using the parafac factor algorithm for L-shapedarray is proposed. The output signal of the array antennas is analyzed and it has trilinear modelcharacteristics. The frequency and2D-DOA can be estimated from trilinear model decomposition.Then the joint2D-DOA and frequency estimation using parallel factor quadrilinear decomposition foruniform square array and double linear array is studied. The output signal of the array antennas isanalyzed and it has quadrilinear model characteristics. The frequency and2D-DOA can be estimatedfrom the matrices via low-rank decomposition which utilizing the uniqueness of the parallel factordecomposition. The method, which does not need eigvalue decomposition or singular valuedecomposition is an iterative algorithm and it can convergence over certain iterative times. Theadvantages of the method require no searching spectral peak or pairing parameters. In constrast withthe conventional methods, the algorithm has higher precision estimation of parameters and works wellunder small sizes.
The joint angle and frequency estimation method for arbitrary acoustic vector sensor array isinvestigated. The main advantage of the vector-sensors over traditional scalar sensors is that theymake use of more available acoustic information and they can estimate multi-parameter of the soundwave. We drive the model of the received data for arbitrary acoustic vector array. Two algorithms ofmulti-parameters estimation have been proposed. DOA-matrix method has the advantage of lowcomputational complexity and can be applied in source orientation occasion which needs strictlycomplexity limit. The parallel factor quadrilinear decomposition algorithm does not require searchingspectral peak and can pair parameters automatically. Compared with the algorithm of ESPRIT and the parallel factor trilinear decomposition, The parallel factor quadrilinear decomposition algorithm hashigh precision in parameter estimation and supplys a new choice for source orientation.
The algorithm of the direction of departure(DOD) and direction of arrival(DOA) estimation ofmulti-target for bistatic MIMO radar is studied. We propose a reduced-dimension multiple signalclassification (MUSIC) algorithm. The algorithm reduces the dimension of2D-MUSIC and the DOAcan be get from searching spectral peak of the1D-MUSIC. The DOD steering vector can be estimatedfrom the relationship of DOA and then DOD can estimated via the least square method. The proposedalgorithm can avoid the high computational cost within two-dimension MUSIC (2D-MUSIC)algorithm and has very close performance to2D-MUSIC algorithm. We illustrate that thereduced-dimension MUSIC algorithm has better performance than ESPRIT algorithm and pair theparameters automatically and can work well in the other irregular array manifolds.
The joint estimation of2D-DOD and2D-DOA for bistatic MIMO radar with L-shaped array anduniform circular array is studied. Most of works develop models for uniform linear array which onlyidentifies one-dimensional angle. The L-shaped array can estimate two dimensional angle and is muchcloser to actual situation. Uniform circular array is a commonly array and can also estimate twodimensional angle. But the signal processing is more complicated because the direction vectors do nothave the Vandermonde characteristics. The algorithm of2D-DOA and2D-DOD for L-shaped anduniform circular array using the parallel factor analysis is presented. The proposed algorithm canestimate four-dimensional angle which uses the structure characteristics of L-shaped and circulararray and least square method. The advantages of the algorithm are that it has higher parameterestimation precision than ESPRIT algorithm and is close to Cramro-bound(CRB). The estimatedparameters pair automatically and it can works well under small sizes.
The four dimensional angle and Doppler frequency estimation for bistatic MIMO radar withL-shaped array is studied. The algorithm of multi-parameter joint estimation based on DOA-matrixmethod is proposed. The algorithm construsts the matrixs according to the DOA-matrix and derivesthe formula of joint four angle and Doppler frequency which use the relationship between theeigenvalue and corresponding eigenvector. The close-form solution can be obtained. Compared withESPRIT algorithm the proposed method only needs once eigenvalue decomposition and reduces thecomputation load. The performance of the proposed algorithm is very close to ESPRIT. It can pair theparameters automatically and eliminate the effect of the spatial colored noise. Simulation resultsverify its good performance.
研究了空间二维角度和频率估计算法，本文将平行因子理论应用到阵列信号二维角度和频率估计中，首先针对L型阵列提出了基于平行因子三线性分解的二维角度和频率估计算法，根据阵列接收天线输出构建了一个平行因子三线性模型，通过对该模型三线性分解可以得到二维角度和频率的估计。在此基础上，针对双平行线阵列/面阵结构，提出了一种基于平行因子四线性分解的二维角度和频率联合估计算法。根据阵列输出数据构建一个四线性模型，通过对此模型分解可以得到二维角度和频率估计的参数。基于平行因子技术的参数估计方法是一种迭代算法，不需要特征值分解或奇异值分解，只需要一定的迭代次数算法就能收敛。该方法的优点是无需谱峰搜索，可实现多参数的联合估计与自动配对，与现有的算法进行了比较，具有更高的参数估计精度，而且在小样本数下也能较好的工作。
研究了任意声矢量传感器阵列下的角度和频率估计算法，相对于常规标量传感器而言，矢量传感器具备很多优势，可进行多维参数估计，得到更优越的性能。针对任意声矢量传感器阵列下的多参数估计，首先推导了阵列接收信号模型，提出了基于DOA矩阵和平行因子四线性分解的两种多参数估计算法。基于DOA矩阵法的算法具有计算复杂度低的优点，可适用于对计算复杂度有限制的声源定位场合。而基于平行因子四线性分解的方法无需谱峰搜索，可实现参数的同时估计与配对，与基于平行因子三线性分解的算法和ESPRIT算法进行了比较，具有更高的参数估计精度，为声源定位提供了一种新的选择。
研究了双基地MIMO雷达多目标的发射角（DOD）和接收角（DOA）联合估计，提出了一种降维MUSIC算法。该算法首先将二维MUSIC算法进行降维处理变成一维MUSIC，通过谱峰搜索得到DOA，进一步得到DOD方向矢量的估计值，再利用最小二乘法得到DOD的估计。该算法的优点是与二维MUSIC算法相比，避免了二维谱峰搜索，复杂度大大降低，而参数估计精度与其非常接近；与ESPRIT算法相比，参数估计性能优于ESPRIT算法；估计过程中参数自动配对，还可将该算法扩展到非规则阵列中。
研究了双基地MIMO雷达L型阵列和均匀圆阵列下多目标的二维DOD和二维DOA的联合估计，由于目前大部分参考文献对双基地MIMO雷达中多参数的研究都是针对均匀线阵建模，估计的是一维角度，L型阵列能估计方位角和仰角，与实际情形更为接近。均匀圆阵也是一种常用的阵列，能估计二维角度，由于其方向矢量不具备范得蒙特性，信号处理较为复杂。本文基于L型阵列和均匀圆阵列分别提出了基于平行因子技术的二维DOD和二维DOA联合估计算法。该算法利用L型阵列的结构特点和均匀圆阵本身的结构特点及最小二乘算法进行了四维角度的估计。算法的优点是参数估计精度优于ESPRIT算法，并接近克拉美罗界(CRB)，且估计过程中参数自动配对，在小样本数下也能较好的工作。
研究了L型阵列下双基地MIMO雷达的二维DOA、二维DOD及多普勒频率联合估计，提出了基于DOA矩阵的多维参数联合估计算法，该算法利用DOA矩阵法的思想构造矩阵，通过特征参数与估计参数之间关系，推导出了目标四维角度和多普勒频率联合估计公式，并得到闭式解。该算法与ESPRIT算法相比，只需一次特征值分解，计算量降低。随着信噪比的提高，估计性能越来越接近ESPRIT算法，估计过程不需要额外的配对运算就实现了参数的自动配对，并能有效克服空间色噪声的影响，仿真结果验证了算法的有效性。
Array signal parameters estimation techniques have played a fundamental role in manyapplications involving radar, sonar and communications. Howerer, with the development of arraysignal estimation algorithms in practical applications, the investigation on robust and high accuratearray signal parameter estimation algorithm have received great interest. Joint multiple parameterestimation of multiple sources for the conventional sensor array and the vector array, and thecorresponding estimation of multiple targets in bistatic MIMO-radar are investigated in thisdissertation. This research of the dissertation maily consists of the following parts:
The two dimensional direction of arrival and frequency estimation algorithm is investigated. Inthis paper the theory of parafac factor is applied for the joint estimation of2D-DOA and frequency.First the joint2D-DOA and frequency estimation using the parafac factor algorithm for L-shapedarray is proposed. The output signal of the array antennas is analyzed and it has trilinear modelcharacteristics. The frequency and2D-DOA can be estimated from trilinear model decomposition.Then the joint2D-DOA and frequency estimation using parallel factor quadrilinear decomposition foruniform square array and double linear array is studied. The output signal of the array antennas isanalyzed and it has quadrilinear model characteristics. The frequency and2D-DOA can be estimatedfrom the matrices via low-rank decomposition which utilizing the uniqueness of the parallel factordecomposition. The method, which does not need eigvalue decomposition or singular valuedecomposition is an iterative algorithm and it can convergence over certain iterative times. Theadvantages of the method require no searching spectral peak or pairing parameters. In constrast withthe conventional methods, the algorithm has higher precision estimation of parameters and works wellunder small sizes.
The joint angle and frequency estimation method for arbitrary acoustic vector sensor array isinvestigated. The main advantage of the vector-sensors over traditional scalar sensors is that theymake use of more available acoustic information and they can estimate multi-parameter of the soundwave. We drive the model of the received data for arbitrary acoustic vector array. Two algorithms ofmulti-parameters estimation have been proposed. DOA-matrix method has the advantage of lowcomputational complexity and can be applied in source orientation occasion which needs strictlycomplexity limit. The parallel factor quadrilinear decomposition algorithm does not require searchingspectral peak and can pair parameters automatically. Compared with the algorithm of ESPRIT and the parallel factor trilinear decomposition, The parallel factor quadrilinear decomposition algorithm hashigh precision in parameter estimation and supplys a new choice for source orientation.
The algorithm of the direction of departure(DOD) and direction of arrival(DOA) estimation ofmulti-target for bistatic MIMO radar is studied. We propose a reduced-dimension multiple signalclassification (MUSIC) algorithm. The algorithm reduces the dimension of2D-MUSIC and the DOAcan be get from searching spectral peak of the1D-MUSIC. The DOD steering vector can be estimatedfrom the relationship of DOA and then DOD can estimated via the least square method. The proposedalgorithm can avoid the high computational cost within two-dimension MUSIC (2D-MUSIC)algorithm and has very close performance to2D-MUSIC algorithm. We illustrate that thereduced-dimension MUSIC algorithm has better performance than ESPRIT algorithm and pair theparameters automatically and can work well in the other irregular array manifolds.
The joint estimation of2D-DOD and2D-DOA for bistatic MIMO radar with L-shaped array anduniform circular array is studied. Most of works develop models for uniform linear array which onlyidentifies one-dimensional angle. The L-shaped array can estimate two dimensional angle and is muchcloser to actual situation. Uniform circular array is a commonly array and can also estimate twodimensional angle. But the signal processing is more complicated because the direction vectors do nothave the Vandermonde characteristics. The algorithm of2D-DOA and2D-DOD for L-shaped anduniform circular array using the parallel factor analysis is presented. The proposed algorithm canestimate four-dimensional angle which uses the structure characteristics of L-shaped and circulararray and least square method. The advantages of the algorithm are that it has higher parameterestimation precision than ESPRIT algorithm and is close to Cramro-bound(CRB). The estimatedparameters pair automatically and it can works well under small sizes.
The four dimensional angle and Doppler frequency estimation for bistatic MIMO radar withL-shaped array is studied. The algorithm of multi-parameter joint estimation based on DOA-matrixmethod is proposed. The algorithm construsts the matrixs according to the DOA-matrix and derivesthe formula of joint four angle and Doppler frequency which use the relationship between theeigenvalue and corresponding eigenvector. The close-form solution can be obtained. Compared withESPRIT algorithm the proposed method only needs once eigenvalue decomposition and reduces thecomputation load. The performance of the proposed algorithm is very close to ESPRIT. It can pair theparameters automatically and eliminate the effect of the spatial colored noise. Simulation resultsverify its good performance.
引文
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