非理想阵列幅相响应下的空间谱估计算法研究
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摘要
空间谱估计是对空间某一区域内的多个感兴趣信号的方向进行估计的技术，是阵列信号处理最主要的研究方向之一。该技术广泛应用于雷达、声纳、通信、地震勘探、医学成像等多种军事和国民经济应用领域。
虽然高分辨空间谱估计算法在理论上具有分辨精度高的特点，但是大多数算法都是以阵列流型精确已知为前提的，而在实际中阵列流型误差不可避免，这将严重影响高分辨空间谱估计算法的性能。因此在进行空间谱估计之前，有必要对阵列流型误差进行校正。本文对阵列幅度相位响应（简称阵列响应）存在误差时，不同的阵列模型下的空间谱估计算法进行了深入研究。
本文对现有的空间谱估计算法进行改进，同时着重研究在阵列响应存在误差情况下的校正问题，在以下几个方面具有创新性成果：
1）提出了均匀线阵下的阵列响应误差的自校正算法。对于均匀线性阵列，由于其导向矢量的范德蒙特性，阵列响应迭代自校正技术会存在模糊性，也就是入射源DOA和阵列响应的迭代估计中的解不唯一。针对这一问题，本文详细讨论了入射源DOA和阵列响应迭代估计中存在的相位模糊性关系。基于这种模糊性关系，提出了一种入射源DOA和阵列响应进行迭代估计的算法，其中迭代过程中包括了消除相位模糊的步骤。为了消除相位模糊，这里需要设置一个相位响应已经事先校正过的阵元。和现有的迭代算法相比，本文提出的迭代算法具有较好的鲁棒性，不需要好的初始值，在较大的阵列响应误差情况下，同样具有较高的估计精度和较快的收敛速度。
2）提出了均匀平面阵列的二维DOA估计算法。该算法针对传统二维MUSIC算法计算量大的问题，对其进行了改进。根据均匀平面阵列流型向量的特点，把其分解成一个矩阵和一个向量相乘的形式，从而就可以把传统的二维MUSIC算法中需要的二维谱峰搜索转化成两个一维谱峰搜索，这样在保证估计精度的前提下，使算法的计算量大大降低。
3）提出了均匀平面阵列下的阵列响应误差的自校正算法。与均匀线性阵列类似，均匀平面阵列的阵列响应迭代自校正技术同样会存在模糊性，入射源二维DOA和阵列响应的迭代估计中的估计值不唯一。本文针对均匀平面阵列模型，详细讨论了入射源二维DOA和阵列响应联合估计中存在的相位模糊性关系。基于这种模糊性关系，提出了一种入射源二维DOA和阵列响应进行迭代估计的算法，其中迭代过程中包括了消除相位模糊的步骤。为了消除相位模糊，这里需要设置两个相位响应已经事先校正过的阵元。
4）提出了基于特殊累积量矩阵的近场源DOA和距离估计算法。该算法通过构建一个特殊的四阶累积量矩阵，消除一维待估计参数，然后应用ESPRIT算法，估计出一维参数；通过对协方差矩阵进行特征分解，应用MUSIC算法估计出另外一维参数。该算法只需要构建一个四阶累积量矩阵和一个协方差矩阵，仅需进行一维谱峰搜索，就能得出直接匹配的近场源DOA和距离参数。和现有算法相比，该算法计算量适中，估计性能好。
5）在新提出的近场源定位算法基础上，进一步提出了近场源方位参数和阵列响应联合估计算法。针对近场源均匀线性阵列模型，本文讨论了近场源方位参数和阵列响应联合估计中存在的相位模糊性关系。基于这种模糊性关系，提出了一种近场源方位参数和阵列响应进行迭代估计的算法，其中迭代过程中包括了消除相位模糊的步骤。为了消除相位模糊，这里需要设置两个相位响应已经事先校正过的阵元。
6）推导出了在阵列响应未知的情况下，近场源方位参数估计的CRB界（CramerRaoBound）的闭式表达式。该CRB表达式不包含复杂的矩阵操作，因此可以被直接有效的计算出。通过观察推导出的CRB表达式，对未知的阵列响应对CRB界的影响进行了分析。分析结果表明，阵列幅度响应是否已知不影响近场源参数估计的CRB界限，但是阵列相位响应是否已知会对近场源参数估计的CRB界限产生影响。
Estimating direction of arrival (DOA) and range of one or more interesting signals which are located in some spatial field simultaneously is one of the most important research area of array signal processing. It is widely used in various military and economic fields such as radar, sonar, communications, seismology and medical imaging.
Most high-resolution spatial spectrum estimation algorithms require precise knowledge about the receiving array manifold. However, in reality the array manifold errors are inevitable, the high-resolution spatial spectrum estimation algorithms wil suffer form severe performance degradation. Hence it is very necessary to calibrate the array manifold errors before spatial spectrum estimation. This dissertation has made deep research on the spatial spectrum estimation algorithms of different array manifold when the array exists gain and phase response errors.
This dissertation has made improvements on the existing source localization algorithms, and made deep research on the problem of array calibration when the array exists gain and phase response errors. Several new algorithms are proposed.
1) The author proposes a self-calibrated algorithm of array gain and phase response errors for uniform linear array. Considering the special manifold of uniform linear array, we discuss the ambiguities of the estimations of DOA and sensor gain and phase response errors. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of DOA and sensor gain and phase response errors. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume one sensor phase response of the array has been calibrated. Compared with the existing algorithms, the iterative algorithm is robust and doesn't need good initial value. It has high estimateion precision and fast convergent speed even when the array exists large gain and phase response errors.
2) The author proposes a2-D DOAs estimated algorithm for uniform rectangular array. Considering the large computational complexity of the classical2-D MUSIC algorithm, we make an improvement. Based on the property of the steering vector of uniform rectangular array, it can be transformed two matrices multiplication form. Then the proposed algorithm can avoid2-D searching by transforming2-D searching into two1-D searchings. The computation load of the proposed algorithm is relieved effectively. The estimated parameters are paired automatically. Simulation results show that the proposed algorithm can achieve accurate and stable estimated results.
3) A self-calibrated algorithm for unique planar equispaced array is proposed. Considering the special manifold of unique planar equispaced array, we discuss the ambiguities of the estimations of2-D DO As and sensor gain and phase response errors. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of2-D DOAs and sensor gain and phase response errors. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume two sensor phase responses of the array have been calibrated.
4) A new near-field source localization algorithm based on a uniform linear array was proposed. The proposed algorithm estimates each parameter separately but does not need pairing parameters. It can be divided into two important steps. The first step is bearing-related electric angle estimation based on the ESPRIT algorithm by constructing a special cumulant matrix. The second step is the other electric angle estimation based on the1-D MUSIC spectrum. It offers much lower computational complexity than the traditional near-field2-D MUSIC algorithm and has better performance than the high-order ESPRIT algorithm. Simulation results demonstrate that the performance of the proposed algorithm is close to the Cramer-Rao Bound (CRB).
5) Based on the new near-field localization algorithm, a method for joint estimation of near-field source parameters and array gain/phase response is proposed. Considering the special uniform linear array manifold for near-field source, we discuss the ambiguities of the estimations of near-field source parameters and sensor gain and phase response. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of near-field source parameters and sensor gain and phase response. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume two sensor phase responses of the array have been calibrated.
6) Closed-form expressions of the CRB for the estimation of near-field source location under unknown array gain/phase responses are derived. The expressions do not involve complicated matrix operations such as matrix inverse. Hence they can be efficiently calculated. Various affecting factors on the behaviour of the bounds are analyzed. From the CRB analysis, we conclude that any priori unknown gain uncertainty will not affect the CRB, but unknown phase response will lead to worse CRB.
虽然高分辨空间谱估计算法在理论上具有分辨精度高的特点，但是大多数算法都是以阵列流型精确已知为前提的，而在实际中阵列流型误差不可避免，这将严重影响高分辨空间谱估计算法的性能。因此在进行空间谱估计之前，有必要对阵列流型误差进行校正。本文对阵列幅度相位响应（简称阵列响应）存在误差时，不同的阵列模型下的空间谱估计算法进行了深入研究。
本文对现有的空间谱估计算法进行改进，同时着重研究在阵列响应存在误差情况下的校正问题，在以下几个方面具有创新性成果：
1）提出了均匀线阵下的阵列响应误差的自校正算法。对于均匀线性阵列，由于其导向矢量的范德蒙特性，阵列响应迭代自校正技术会存在模糊性，也就是入射源DOA和阵列响应的迭代估计中的解不唯一。针对这一问题，本文详细讨论了入射源DOA和阵列响应迭代估计中存在的相位模糊性关系。基于这种模糊性关系，提出了一种入射源DOA和阵列响应进行迭代估计的算法，其中迭代过程中包括了消除相位模糊的步骤。为了消除相位模糊，这里需要设置一个相位响应已经事先校正过的阵元。和现有的迭代算法相比，本文提出的迭代算法具有较好的鲁棒性，不需要好的初始值，在较大的阵列响应误差情况下，同样具有较高的估计精度和较快的收敛速度。
2）提出了均匀平面阵列的二维DOA估计算法。该算法针对传统二维MUSIC算法计算量大的问题，对其进行了改进。根据均匀平面阵列流型向量的特点，把其分解成一个矩阵和一个向量相乘的形式，从而就可以把传统的二维MUSIC算法中需要的二维谱峰搜索转化成两个一维谱峰搜索，这样在保证估计精度的前提下，使算法的计算量大大降低。
3）提出了均匀平面阵列下的阵列响应误差的自校正算法。与均匀线性阵列类似，均匀平面阵列的阵列响应迭代自校正技术同样会存在模糊性，入射源二维DOA和阵列响应的迭代估计中的估计值不唯一。本文针对均匀平面阵列模型，详细讨论了入射源二维DOA和阵列响应联合估计中存在的相位模糊性关系。基于这种模糊性关系，提出了一种入射源二维DOA和阵列响应进行迭代估计的算法，其中迭代过程中包括了消除相位模糊的步骤。为了消除相位模糊，这里需要设置两个相位响应已经事先校正过的阵元。
4）提出了基于特殊累积量矩阵的近场源DOA和距离估计算法。该算法通过构建一个特殊的四阶累积量矩阵，消除一维待估计参数，然后应用ESPRIT算法，估计出一维参数；通过对协方差矩阵进行特征分解，应用MUSIC算法估计出另外一维参数。该算法只需要构建一个四阶累积量矩阵和一个协方差矩阵，仅需进行一维谱峰搜索，就能得出直接匹配的近场源DOA和距离参数。和现有算法相比，该算法计算量适中，估计性能好。
5）在新提出的近场源定位算法基础上，进一步提出了近场源方位参数和阵列响应联合估计算法。针对近场源均匀线性阵列模型，本文讨论了近场源方位参数和阵列响应联合估计中存在的相位模糊性关系。基于这种模糊性关系，提出了一种近场源方位参数和阵列响应进行迭代估计的算法，其中迭代过程中包括了消除相位模糊的步骤。为了消除相位模糊，这里需要设置两个相位响应已经事先校正过的阵元。
6）推导出了在阵列响应未知的情况下，近场源方位参数估计的CRB界（CramerRaoBound）的闭式表达式。该CRB表达式不包含复杂的矩阵操作，因此可以被直接有效的计算出。通过观察推导出的CRB表达式，对未知的阵列响应对CRB界的影响进行了分析。分析结果表明，阵列幅度响应是否已知不影响近场源参数估计的CRB界限，但是阵列相位响应是否已知会对近场源参数估计的CRB界限产生影响。
Estimating direction of arrival (DOA) and range of one or more interesting signals which are located in some spatial field simultaneously is one of the most important research area of array signal processing. It is widely used in various military and economic fields such as radar, sonar, communications, seismology and medical imaging.
Most high-resolution spatial spectrum estimation algorithms require precise knowledge about the receiving array manifold. However, in reality the array manifold errors are inevitable, the high-resolution spatial spectrum estimation algorithms wil suffer form severe performance degradation. Hence it is very necessary to calibrate the array manifold errors before spatial spectrum estimation. This dissertation has made deep research on the spatial spectrum estimation algorithms of different array manifold when the array exists gain and phase response errors.
This dissertation has made improvements on the existing source localization algorithms, and made deep research on the problem of array calibration when the array exists gain and phase response errors. Several new algorithms are proposed.
1) The author proposes a self-calibrated algorithm of array gain and phase response errors for uniform linear array. Considering the special manifold of uniform linear array, we discuss the ambiguities of the estimations of DOA and sensor gain and phase response errors. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of DOA and sensor gain and phase response errors. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume one sensor phase response of the array has been calibrated. Compared with the existing algorithms, the iterative algorithm is robust and doesn't need good initial value. It has high estimateion precision and fast convergent speed even when the array exists large gain and phase response errors.
2) The author proposes a2-D DOAs estimated algorithm for uniform rectangular array. Considering the large computational complexity of the classical2-D MUSIC algorithm, we make an improvement. Based on the property of the steering vector of uniform rectangular array, it can be transformed two matrices multiplication form. Then the proposed algorithm can avoid2-D searching by transforming2-D searching into two1-D searchings. The computation load of the proposed algorithm is relieved effectively. The estimated parameters are paired automatically. Simulation results show that the proposed algorithm can achieve accurate and stable estimated results.
3) A self-calibrated algorithm for unique planar equispaced array is proposed. Considering the special manifold of unique planar equispaced array, we discuss the ambiguities of the estimations of2-D DO As and sensor gain and phase response errors. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of2-D DOAs and sensor gain and phase response errors. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume two sensor phase responses of the array have been calibrated.
4) A new near-field source localization algorithm based on a uniform linear array was proposed. The proposed algorithm estimates each parameter separately but does not need pairing parameters. It can be divided into two important steps. The first step is bearing-related electric angle estimation based on the ESPRIT algorithm by constructing a special cumulant matrix. The second step is the other electric angle estimation based on the1-D MUSIC spectrum. It offers much lower computational complexity than the traditional near-field2-D MUSIC algorithm and has better performance than the high-order ESPRIT algorithm. Simulation results demonstrate that the performance of the proposed algorithm is close to the Cramer-Rao Bound (CRB).
5) Based on the new near-field localization algorithm, a method for joint estimation of near-field source parameters and array gain/phase response is proposed. Considering the special uniform linear array manifold for near-field source, we discuss the ambiguities of the estimations of near-field source parameters and sensor gain and phase response. Based on the ambiguous relations, we propose an iterative algorithm for the estimation of near-field source parameters and sensor gain and phase response. The step of removing the phase ambiguities is included. We also show that the phase ambiguities can be removed if we assume two sensor phase responses of the array have been calibrated.
6) Closed-form expressions of the CRB for the estimation of near-field source location under unknown array gain/phase responses are derived. The expressions do not involve complicated matrix operations such as matrix inverse. Hence they can be efficiently calculated. Various affecting factors on the behaviour of the bounds are analyzed. From the CRB analysis, we conclude that any priori unknown gain uncertainty will not affect the CRB, but unknown phase response will lead to worse CRB.
引文
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