Robust R-D parameter estimation via closed-form PARAFAC

R-dimensional parameter estimation problems are common in a variety of signal processing applications. In order to solve such problems, we propose a robust multidimensional model order selection scheme and a robust multidimensional parameter estimation scheme using the closed-form PARAFAC algorithm, which is a recently proposed way to compute the PARAFAC decomposition based on several simultaneous diagonalizations. In general, R-dimensional (R-D) model order selection (MOS) techniques, e.g., the R-D Exponential Fitting Test (R-D EFT), are designed for multidimensional data by taking into account its multidimensional structure. However, the R-D MOS techniques assume that the data is contaminated by white Gaussian noise. To deal with colored noise, we propose the closed-form PARAFAC based model order selection (CFP-MOS) technique based on multiple estimates of the factor matrices provided as an intermediate step by the closed-form PARAFAC algorithm. Additionally, we propose the closed-form PARAFAC based parameter estimator (CFP-PE), which can be applied to extract spatial frequencies in case of arbitrary array geometries.