Multi-dimensional model order selection

Martin Haardt,Florian Roemer,João Paulo Carvalho Lustosa Da Costa,Rafael Timóteo De Sousa

doi:10.1186/1687-6180-2011-26

Abstract

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 multi-dimensional 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.

Highlights

In the literature, matrix array signal processing techniques are extensively used in a variety of applications including radar, mobile communications, sonar, and seismology
For scenarios with colored noise, we present our proposed multi-dimensional model order selection technique called closed-form PARAFAC-based model order selection (CFP-MOS) scheme [3,5]
We evaluate the performance of the model order selection scheme in the presence of colored noise, which is given by replacing the white Gaussian white noise tensor N by the colored Gaussian noise tensor N (c) in (5)

Summary

Introduction

Matrix array signal processing techniques are extensively used in a variety of applications including radar, mobile communications, sonar, and seismology. For scenarios with colored noise, we present our proposed multi-dimensional model order selection technique called closed-form PARAFAC-based model order selection (CFP-MOS) scheme [3,5]. Besides the global eigenvalues-based schemes, we propose a tensor data-based multi-dimensional model order selection scheme.

Results

Conclusion