Rectangular array of electromagnetic vector sensors: tensor modelling/decomposition and DOA‐polarisation estimation

Abstract

In this study, the authors propose a fast quadrilinear decomposition algorithm for estimation of the directions-of-arrival and polarisations of the incident sources via a uniform rectangular array of electromagnetic vector sensors (EMVSs). Conventional quadrilinear alternating least squares (QALS), involves computationally intensive Khatri-Rao products in each iteration, to update the parameter matrices (factors). Moreover, QALS is more likely to fall in a local minimum and tends to take more steps before an acceptable solution, which further slows down the convergence and often mis-converges, thereby yielding meaningless results. To preserve the quadrilinearity, they arrange the measurements as a four-dimensional (4D) data (fourthorder tensor), from which a third-order sub-tensor (3D slice) can be obtained by fixing one index along any dimension. These slices are used to create new cost functions that are alternately minimised while updating the factors until convergence. They show that the rows of parameter matrices form the diagonal elements of a tensor, which capture the internal quadrilinearity of data and significantly reduce the cost function in few iterations only. Simulation results verify that the authors' algorithm holds faster convergence, does not mis-converge, provides parameter estimation accuracy similarly to the QALS and superior of the Estimation of Signal Parameters via Rotational Invariance Technique and propagator method.

Two-Dimensional DOA Estimation for Coprime Planar Arrays Based on Self-Correlation Tensor

“…K � 13 sources are from φ � [18,28,38,48,22,32,42,52,62,26,36,46,56] e estimation performance of the proposed method is shown in Figure 3, where the number of snapshots is 5000, SNR � 15 dB, and the search step is 0.1 °.…”

“…In this regard, experts and scholars have introduced tensors into DOA estimation [27][28][29][30][31][32]. Tensors [33][34][35] are high-dimensional data, which can save information of different physical meanings in other dimensions.…”

Structural-Missing Tensor Completion for Robust DOA Estimation with Sensor Failure

“…Meanwhile, numerous tensor decomposition techniques such as the canonical polyadic decomposition (CPD) [31] and Tucker decomposition [32] have been proposed to retrieve parameters from the tensor data [33,34]. Based on tensor models and tensor decompositions, many tensor-based DOA estimation methods are proposed to enhance the estimation performance for multidimensional arrays [35,36]. Specifically, the CPD is applied to multiple-invariance array signals for effective DOA estimation [37].…”

Monopulse based DOA and polarization estimation with polarization sensitive arrays

“…Existing joint DOA and polarization estimation methods are normally designed for the VSAs composed of EMVSes, such as the vector cross product method in [5], the subspace-based methods in [21,22,23,24], and the tensor-based method in [25]. Some computationally efficient methods are also proposed, such as the dimensionreduction MUSIC [26], the propagator-based method [27], and the quaternion-based method [28,29].…”