Performance of ESPRIT for Estimating Mixtures of Complex Exponentials Modulated by Polynomials: Supporting Document - Archive ouverte HAL Accéder directement au contenu
Rapport Année : 2007

Performance of ESPRIT for Estimating Mixtures of Complex Exponentials Modulated by Polynomials: Supporting Document

Résumé

High Resolution (HR) methods are known to provide accurate frequency estimates for discrete spectra [1]. The Polynomial Amplitude Complex Exponentials (PACE) model was presented as the most general model tractable by HR methods. A subspace-based estimation scheme was recently proposed in [2], derived from the ESPRIT algorithm [3]. In [4], we focused on the performance of this estimator. We first presented some asymptotic expansions of the estimated parameters, obtained at the first order under the assumption of a high signal-to-noise ratio (SNR). Then the performance of the generalized ESPRIT algorithm for estimating the parameters of this model was analyzed in terms of bias and variance, and compared to the Cramér-Rao bounds. In this supporting document, we present the proofs of the theoretical results introduced in [4]. This document, written as a sequel of [4], is not intended to be read separately. It is organized as follows: section I is devoted to the perturbation analysis, then the performance of the estimators is analyzed in section II.
Fichier principal
Vignette du fichier
ENST-07.pdf (153.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00180015 , version 1 (23-10-2007)
hal-00180015 , version 2 (20-02-2008)

Identifiants

  • HAL Id : hal-00180015 , version 2

Citer

Roland Badeau, Gaël Richard, Bertrand David. Performance of ESPRIT for Estimating Mixtures of Complex Exponentials Modulated by Polynomials: Supporting Document. 2007. ⟨hal-00180015v2⟩
170 Consultations
293 Téléchargements

Partager

Gmail Facebook X LinkedIn More