This paper aims to estimate the two dimensional (2D) direction-of-arrival (DOA) using a polarized uniform rectangular array (URA) under multipath propagation. To leverage the tensorial nature, a parallel factor (PARAFAC) model is established, in which it comprises two spatial response matrices, the polarization response matrix, and the source matrix. Unfortunately, the source matrix exhibits rank-deficiency, hindering effectively PARAFAC decomposition. Our analysis reveals that the rank-deficiency can be easily resolved by taking the KhatriRao product with a full column rank factor matrix. Consequently, three rearranged PARAFAC tensors are obtained that are free of the source matrix's rank-deficiency. The estimation of 2D-DOA is then performed using the vector cross product-auxiliary rotational invariance technique (VCPARIT). The proposed algorithms are insensitive to inter-sensor distance and are suitable for a one-snapshot scenario. Furthermore, they outperform existing smoothing methods from the perspective of estimation accuracy. Theoretical advantages of the proposed algorithms are corroborated by the simulations.

Multiple-input multiple-output (MIMO) sparse electromagnetic vector sensor (EMVS) arrays have brought new perspectives to signal processing due to their flexibility and higher resolution. In this study, we focus on angle estimation in a monostatic MIMO system using arbitrary geometry EMVS arrays. An improved parallel factor (PARAFAC)-based algorithm is introduced. By harnessing the natural multidimensional structure of the array output, we rearrange it into a PARAFAC model. The factor matrices are obtained using the complex parallel factor analysis (COMFAC), followed by applying vector cross-product (VCP)/phase compensation for rough/refined estimation. This approach achieves super-resolution estimation while automatically pairing angles and showing low computational complexity. As a result, it outperforms existing algorithms, and numerical simulation experiments validate the improvements achieved by the proposed method

Direction-of-arrival (DOA), also referred to as angle-of-arrival (AOA), is an excellent choice for unmanned aerial vehicle (UAV) localization and has garnered significant attention recently. In this article, we propose a novel two-dimensional (2D)-DOA auxiliary framework for anonymous UAV localization. At its core, this framework relies on measuring 2D-DOA using a monostatic multiple-input–multiple-output (MIMO) radar configured with electromagnetic vector sensors (EMVSs). Differing from existing mainstream methods, the multipath effect of the UAV is taken into account. A rearrangement multiple signal classification (R-MUSIC) algorithm is developed. The algorithm recovers the covariance matrix rank by connecting spatial responses from both transmitting (Tx) or receiving (Rx) arrays with radar cross-section (RCS) coefficients. Subsequently, rough 2D-DOA estimates are obtained using the vector cross-product (VCP) technique. These rough estimates are then used to establish good initialized values for refined 2-D spectral peak searching. Finally, leveraging the relationship between 2D-DOA and Tx/Rx array coordinates, a UAV’s 3-D position can be directly computed. This framework remains insensitive to the geometric configuration of Tx/Rx arrays while striking a balance between complexity and accuracy. Numerical simulation experiments confirm the improvements of our developed R-MUSIC algorithm.

Electromagnetic vector sensor (EMVS) arrays bring an epochal opportunity for direction finding, as they enable the estimation of two-dimensional direction of arrival (2D-DOA) and polarization characteristics. In this paper, we revisit the 2D-DOA estimation problem in an EMVS rectangle array under multipath propagation. An improved subspace estimator is proposed, which addresses the rank-deficit problem through matrix arrangement, and the 2D-DOA and polarization parameters are estimated via combining the normalized vector cross-product with the least squares method. Our proposed method is suitable for a single snapshot scenario and offers superior accuracy compared to existing methods. To validate its effectiveness, several numerical simulations have been designed and conducted.