A hierarchical iterative algorithm for the canonical polyadic decomposition (CPD) of tensors is proposed by improving the traditional conjugate gradient least squares (CGLS) method. Methods based on algebraic operations are investigated with the objective of estimating the direction of arrival (DoA) and polarization parameters of signals impinging on an array with electromagnetic (EM) vector‐sensors. The proposed algorithm adopts a hierarchical iterative strategy, which enables the algorithm to obtain a fast recovery for the highly collinear factor matrix. Moreover, considering the same accuracy threshold, the proposed algorithm can achieve faster convergence compared with the alternating least squares (ALS) algorithm wherein the highly collinear factor matrix is absent. The results reveal that the proposed algorithm can achieve better performance under the condition of fewer snapshots, compared with the ALS‐based algorithm and the algorithm based on generalized eigenvalue decomposition (GEVD). Furthermore, with regard to an array with a small number of sensors, the observed advantage in estimating the DoA and polarization parameters of the signal is notable.

中文翻译：

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应用于张量分解的分层共轭梯度最小二乘估计信号参数

通过改进传统的共轭梯度最小二乘（CGLS）方法，提出了张量的规范多峰分解（CPD）的分层迭代算法。研究了基于代数运算的方法，目的是估计到达电磁（EM）矢量传感器阵列上的信号的到达方向（DoA）和极化参数。所提出的算法采用分层迭代策略，使得该算法能够快速恢复高共线因子矩阵。此外，考虑到相同的精度阈值，与不存在高度共线性因子矩阵的交替最小二乘（ALS）算法相比，该算法可以实现更快的收敛速度。结果表明，与基于ALS的算法和基于广义特征值分解（GEVD）的算法相比，该算法在较少快照的情况下可以实现更好的性能。此外，对于具有少量传感器的阵列，在估计信号的DoA和极化参数方面观察到的优势非常明显。