Multidimensional ESPRIT for Damped and Undamped Signals: Algorithm, Computations, and Perturbation Analysis

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 ord...

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Veröffentlicht in:IEEE transactions on signal processing Jg. 65; H. 22; S. 5897 - 5910
Hauptverfasser: Sahnoun, Souleymen, Usevich, Konstantin, Comon, Pierre
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 15.11.2017
Institute of Electrical and Electronics Engineers
Schlagworte:
2-D ESPRIT
Algorithm design and analysis
Computational complexity
Computer Science
Frequency estimation
harmonic retrieval
Manganese
Matrix decomposition
multilevel Hankel matrix
perturbation analysis
Perturbation methods
Signal and Image Processing
Signal processing algorithms
Tensile stress
truncated SVD
multilevel Hankel matrix
harmonic retrieval
truncated SVD
Frequency estimation
perturbation analysis
2-D ESPRIT
ISSN:1053-587X, 1941-0476
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Zusammenfassung: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2736512