Polyadic Tensor Decomposition Research Articles

PMU Missing Data Recovery Using Tensor Decomposition

The paper proposes a new approach for the recovery of missing data from phasor measurement units (PMUs). The approach is based on the application of tensor decomposition to PMU data organized as three-dimensional tensors with respect to time, location and type of variables. The organization of the PMU data is in the form of a bus-oriented data structure and a branch-oriented data structure. Two versions of the approach are introduced. The first version uses polyadic tensor decomposition and the second version uses Tucker tensor decomposition. Several case studies are conducted validating the proposed approaches including measured PMU data in the New York transmission system. Comparison with existing approaches is performed to demonstrate the improvement in missing data recovery accuracy achieved by the new approach.

DOA and Polarization Parameters Estimation by Exploiting Canonical Polyadic Decomposition of Tensors

A new algorithm to estimate the direction of arrival (DOA) and polarization parameters of signals impinging on an array with electromagnetic (EM) vector-sensors is presented by exploiting the canonical polyadic decomposition (CPD) of tensors. In addition to spatial and temporal diversities, further information from the polarization domain is considered and used in this paper. Estimation errors of these parameters are evaluated by the Cramér-Rao lower bound (CRB) benchmark, in the presence of additive white Gaussian noise (AWGN). The superiority of the proposed algorithm is shown by comparing with the derivative algorithms of MUSIC and ESPRIT. In the proposed algorithm, the parameters can be estimated by virtue of the diversities of the spatial and polarization belonging to the factor matrices, rather than the conventional subspace which is the foundation of MUSIC and ESPRIT. Additionally, the classical CPD algorithm based on Alternating Least Squares (ALS) is introduced to verify the efficacy of the proposed CPD algorithm. Results demonstrate that when the number of snapshots is greater than 50, the proposed algorithm requires a smaller number of snapshots to achieve a high level of performance, compared against the subspace-based algorithms and the ALS-based algorithm. Furthermore, in the matter of the array with a small number of sensors, the discovered advantage concerning the Root Mean Square Error (RMSE) in estimating the DOA and the polarization state of the signal is noteworthy.