Multidimensional ESPRIT for Damped and Undamped Signals: 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 and/or undamped 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; multilevel Hankel matrix; 2-D ESPRIT; perturbation analysis; truncated SVD

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

Souleymen Sahnoun, Konstantin Usevich, Pierre Comon. Multidimensional ESPRIT for Damped and Undamped Signals: Algorithm, Computations, and Perturbation Analysis. IEEE Transactions on Signal Processing, 2017, 65 (22), pp. 5897-5910. ⟨10.1109/TSP.2017.2736512⟩. ⟨hal-01360438v3⟩