Abstract Recently proposed nested array can increase the number degrees of freedom (DOFs) greatly in comparison with uniform linear array, enabling us to extend it to tackle the problem of direction of arrival (DOA) estimation in the presence of gain-phase errors. By exploiting continuous multiplication operator and an auxiliary source, the gain-phase error matrix is efficiently estimated under the assumption that part of sensors are well calibrated. After compensating the gain-phase errors, a full-rank virtual covariance matrix is obtained by subvector division and the DOAs are successfully obtained via the ESPRIT technique. The proposed algorithm is a general one, and can be easily applied to coprime array and other mainstream DOA solving techniques (such as MUSIC and sparsity-based approaches). The performance analysis and Cramer-Rao Bound for DOA estimation with partly calibrated nested array are given and the effectiveness of the proposed algorithm is verified by numerical simulations.

中文翻译：

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使用连续乘法算子校准嵌套传感器阵列以进行 DOA 估计

摘要 与均匀线性阵列相比，最近提出的嵌套阵列可以大大增加自由度（DOF）的数量，使我们能够扩展它以解决存在增益相位误差的到达方向（DOA）估计问题。通过利用连续乘法算子和辅助源，在部分传感器校准良好的假设下有效地估计了增益相位误差矩阵。补偿增益相位误差后，通过子向量除法得到满秩虚拟协方差矩阵，并通过ESPRIT技术成功得到DOA。所提出的算法是通用的，可以很容易地应用于互质数组和其他主流的 DOA 求解技术（如 MUSIC 和基于稀疏性的方法）。