Multidimensional Harmonic Retrieval by N-D ESPRIT: Algorithm, Computations and Perturbation Analysis

Souleymen Sahnoun (1) , Konstantin Usevich (1) , Pierre Comon (1)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

In this paper we present and analyze the performance of multidimensional ESPRIT ($N$-D ESPRIT) method for estimating parameters of $N$-D superimposed damped exponentials. $N$-D ESPRIT algorithm is based on low-rank decomposition of multilevel Hankel matrices formed by the $N$-D data. In order to reduce the computational complexity for large signals, we propose a fast $N$-D ESPRIT using truncated singular value decomposition (SVD). Then, through a first-order perturbation analysis, we derive simple expressions of the variance of the estimates in $N$-D multiple-tones case. These expressions do not involve the factors of the SVD. We also derive closed-form expressions of the variances of the complex modes, frequencies and damping factors estimates in the $N$-D single-tone case. Computer results are presented to show effectiveness of the fast version of $N$-D ESPRIT and verify theoretical expressions.

Mots clés: Frequency estimation; harmonic retrieval; mul-tilevel Hankel matrix; 2-D ESPRIT; perturbation analysis

Domaines: Traitement du signal et de l'image [eess.SP]

Souleymen Sahnoun, Konstantin Usevich, Pierre Comon. Multidimensional Harmonic Retrieval by N-D ESPRIT: Algorithm, Computations and Perturbation Analysis. 2017. ⟨hal-01360438v2⟩