This paper presents a novel strategy to simultaneously estimate the direction of arrival (DOA) of a source signal and the phase error of a partly calibrated array with arbitrary geometry. We add up the snapshot data of two different sensors, and then extract a knowledge associated with the DOA and phase errors of these two elements by using singular value decomposition. In such a manner, we can establish a series of linear equations with respect to the unknown DOA and phase error, by simply conducting the procedure on any two sensor elements. On this basis, it can be shown that the problem of jointly estimating DOA and phase error is equivalent to a least square (LS) problem with a quadratic equality constraint. To solve this LS problem (so that the DOA and phase error can be obtained), an effective convex–concave procedure is employed. Different from the conventional algorithms that are limited to specific array geometries, the proposed one is suitable for arrays with arbitrary geometries. More importantly, the devised method only requires one extra calibrated sensor, which is not necessarily adjacently located with the reference one. Several simulations are carried out in this paper and the effectiveness of the devised method can be clearly observed.

中文翻译：

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具有任意几何形状的部分校准阵列的 DOA 和相位误差估计

本文提出了一种新颖的策略，可以同时估计源信号的到达方向 (DOA) 和具有任意几何形状的部分校准阵列的相位误差。我们将两个不同传感器的快照数据相加，然后通过奇异值分解提取与这两个元素的 DOA 和相位误差相关的知识。以这种方式，我们可以通过简单地在任意两个传感器元件上执行该过程来建立关于未知 DOA 和相位误差的一系列线性方程。在此基础上，可以证明联合估计DOA和相位误差的问题等价于具有二次等式约束的最小二乘(LS)问题。为了解决这个 LS 问题（以便可以获得 DOA 和相位误差），采用了有效的凸凹过程。与仅限于特定阵列几何形状的传​​统算法不同，所提出的算法适用于具有任意几何形状的阵列。更重要的是，设计的方法只需要一个额外的校准传感器，它不一定与参考传感器相邻。本文进行了多次模拟，可以清楚地观察到所设计方法的有效性。