Multi-dimensional model order selection (MOS) techniques achieve an improved accuracy, reliability, and robustness, since they consider all dimensions jointly during the estimation of parameters. Additionally, from fundamental identifiability results of multi-dimensional decompositions, it is known that the number of main components can be larger when compared to matrix-based decompositions. In this article, we show how to use tensor calculus to extend matrix-based MOS schemes and we also present our proposed multi-dimensional model order selection scheme based on the closed-form PARAFAC algorithm, which is only applicable to multidimensional data. In general, as shown by means of simulations, the Probability of correct Detection (PoD) of our proposed multi-dimensional MOS schemes is much better than the PoD of matrix-based schemes.
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 struetured 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 HIOSVD 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 IIOSVD, we obtain R + 1 sets of n-mode singular values of the measurement tensor that are used jointly to improve the accuracy of the model order selection significantly.
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