波达方向（Direction of Arrival，DOA）估计是阵列信号处理中的关键研究领域之一，被广泛应用于卫星导航、雷达、通信等各个方面。嵌套阵列（Nested array, NA）由于能够在相同的物理阵元下获得更大的阵列孔径和更高的自由度，因此基于嵌套阵的DOA估计成为研究热点问题之一。二级嵌套阵列和广义嵌套阵列是嵌套阵列中的常用阵型，然而在二级嵌套阵列的DOA估计方法中，往往忽略了对冗余信息的利用；广义嵌套阵列虽然具有更大的虚拟阵列孔径和自由度，但是虚拟阵列存在空洞，同时考虑到实际环境为非均匀噪声时DOA估计性能会下降，本文主要围绕二级嵌套阵列和广义嵌套阵列展开研究，主要研究内容如下：

1．针对二级嵌套阵列的DOA估计方法忽略了冗余信息的问题，提出一种基于平均化去冗余的二级嵌套阵列无网格实值DOA估计算法。所提算法首先设计矩阵变换对二级嵌套阵列的冗余虚拟阵元进行平均化去冗余处理，建立虚拟阵列接收信号模型；然后利用原子范数最小化方法估计接收信号的协方差矩阵；最后结合实值化与MUSIC算法进行高精度的DOA估计。仿真实验结果表明：该算法在信噪比较低和快拍数较小的情况下，提高了DOA估计的精度，对临近信号的分辨概率更高，并且具有更快的角度估计速度，实时性更好。

2．针对广义嵌套阵列的差分联合阵列存在空洞导致DOA估计算法性能降低的问题，同时考虑到非均匀噪声背景，提出一种基于协方差矩阵重构和加权截断核范数的广义嵌套阵列DOA估计算法。该算法首先将阵列接收数据的协方差矩阵分开表示为两个矩阵，用其中的对角矩阵中的最小值代替其他对角线元素。然后，采用截断核范数最小化的方法对重构后的协方差矩阵进行空洞加权填充，以增强DOA估计的准确性和稳健性。最后，通过子空间方法对填充后的协方差矩阵进行处理，实现DOA估计。通过仿真实验表明，该算法能够有效地填充空洞，提高了虚拟阵元的利用率，并且能够有效地抑制非均匀噪声，提高了小快拍、低信噪比下的DOA估计精度与分辨概率。

Direction of Arrival (DOA) estimation is an important problem in the field of array signal processing, which has a wide range of applications in radar, sonar, wireless communication and other military and civilian fields. In recent years, Nested array (NA) has been proposed to solve the contradiction between the performance and cost of Uniform Linear Array (ULA). However, the utilization of redundant information is neglected in the DOA estimation method of two-level nested arrays. Although the generalized nested array has a larger virtual array aperture and degrees of freedom, there are voids in the virtual array, also considering the non-uniform noise background. Therefore, the main research of this thesis is as follows:

1. Aiming at the problem that the DOA estimation method of the two-level nested array ignores the redundant information, a gridless real-valued DOA estimation algorithm for the two-level nested array based on averaging and de-redundancy is proposed. The proposed algorithm firstly designs the matrix transform to averaging and de-redundancy the redundant virtual array elements of the two-level nested array, and establishes the virtual array received signal model; then estimates the covariance matrix of the received signal by using the atomic norm minimization method; and finally combines the real-valued and MUSIC algorithms to carry out the high-precision DOA estimation. The results of simulation experiments show that the algorithm improves the accuracy of DOA estimation with lower signal-to-noise ratio and smaller number of snapshots, has a higher resolution probability of the neighboring signals, and has a faster angle estimation speed and better real-time performance.

2. Aiming at the problem of the performance degradation of DOA estimation algorithm due to the existence of holes in the difference joint array of generalized nested arrays, and taking into account the non-uniform noise background, a DOA estimation algorithm based on covariance reconstruction and matrix filling is proposed. The algorithm first decomposes the received data covariance matrix to obtain a diagonal array containing non-uniform noise terms, selects the minimum value in the diagonal elements to replace the remaining diagonal elements, and obtains the reconstructed covariance matrix; then uses the truncated nuclear norm minimization method to fill in the holes weighted covariance matrix of the reconstructed covariance matrix of the virtual array; and finally, utilizes the subspace method to carry out DOA estimation. The simulation experimental results show that the algorithm avoids the effect of holes on DOA estimation, improves the utilization rate of virtual array elements and can effectively suppress non-uniform noise, and improves the DOA estimation accuracy and resolution probability under small snapshot and low signal-to-noise ratio.

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