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.
Parallel Factor (PARAFAC) analysis represents a decomposition of a tensor into a minimum sum of rank one tensors. For this task, one crucial problem is the estimation of the number of rank one components that are required to represent the tensor. This problem is also known as model order estimation. Recently we have developed new R-dimensional techniques based on the HOSVD to estimate the number of components in multi-dimensional harmonic retrieval problems (i.e., R-D EFT, R-D AIC, and R-D MDL). In this paper, we apply these R-D methods to the PARAFAC model, which is a more general multi-way data model, and show that they outperform T-CORCONDIA, a nonsubjective form of CORCON-DIA, in terms of the probability of detection as well as the required computational complexity.Joao Paulo C. L. da Costa is a scholarship holder of the National Counsel of Technological and Scientific Development (Conselho Nacional de Desenvolvimento Cientifico e Tecno16gico, CNPq) of the Brazilian Government and also a First Lieutenant of the Brazilian Army (Exercito Brasileiro).
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