Enhanced Model Order Estimation using Higher-Order Arrays

Abstract

Frequently, R-dimensional subspace-based methods are used to estimate the parameters in multi-dimensional harmonic retrieval problems in a variety of signal processing applications. Since the measured data is multi-dimensional, traditional approaches require stacking the dimensions into one highly structured matrix. Recently, we have shown how an HOSVD based low-rank approximation of the measurement tensor leads to an improved signal subspace estimate, which can be exploited in any multi-dimensional subspace-based parameter estimation scheme. To achieve this goal, it is required to estimate the model order of the multi-dimensional data. In this paper, we show how the HOSVD of the measurement tensor also enables us to improve the model order estimation step. This is due to the fact that only one set of eigenvalues is available in the matrix case. Applying the HOSVD, we obtain <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> + 1 sets of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -mode singular values of the measurement tensor that are used jointly to improve the accuracy of the model order selection significantly.