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