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

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 (fourth‐order 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.