Subspace based multi-dimensional model order selection in colored noise scenarios

Frequently, R-dimensional subspace-based methods are used to estimate the parameters in multidimensional 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 proposed eigenvalue based multi-dimensional model order selection schemes, which exploit the multidimensional structure of the data in order to achieve a higher probability of correct detection. However, our proposed multi-dimensional schemes are restricted to white noise scenarios. In this paper, we show how the Higher Order Singular Value Decomposition (HOSVD) of the measurement tensor enables us to improve the model order estimation of the estimation error (ESTER) scheme in colored noise scenarios. By using the matrix based ESTER, only one set of eigenvectors is taken into account, while by using the R-dimensional ESTER we obtain R sets of n-mode eigenvectors of the measurement tensor that are jointly used to improve significantly the accuracy of the estimated model order.