Statistical Resolution Limit for the Multidimensional Harmonic Retrieval Model: Hypothesis Test and Cramer-Rao Bound Approaches - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue EURASIP Journal on Advances in Signal Processing Année : 2011

Statistical Resolution Limit for the Multidimensional Harmonic Retrieval Model: Hypothesis Test and Cramer-Rao Bound Approaches

Remy Boyer
Alexandre Renaux
Sylvie Marcos

Résumé

The Statistical Resolution Limit (SRL), which is defined as the minimal separation between parameters to allow a correct resolvability, is an important statistical tool to quantify the ultimate performance for parametric estimation problems. In this paper we generalize the concept of the SRL to the Multidimensional SRL (MSRL) applied to the multidimensional harmonic retrieval model. In this paper, we derive the SRL for the so-called multidimensional harmonic retrieval model by using a generalization of the previously introduced SRL concepts that we call Multidimensional SRL (MSRL). We first derive the MSRL using an hypothesis test approach. This statistical test is shown to be asymptotically an uniformly most powerful test which is the strongest optimality statement that one could expect to obtain. Second, we link the proposed asymptotic MSRL based on the hypothesis test approach to a new extension of the SRL based on the Cramér-Rao Bound approach. Thus, a closed-form expression of the asymptotic MSRL is given and analyzed in the framework of the multidimensional harmonic retrieval model. Particularly, it is proved that the optimal MSRL is obtained for equi-powered sources and/or an equi-distributed number of sensors on each multi-way array.
Fichier principal
Vignette du fichier
SRL_MHM.pdf (619.17 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00579002 , version 1 (22-03-2011)

Identifiants

Citer

Mohammed Nabil El Korso, Remy Boyer, Alexandre Renaux, Sylvie Marcos. Statistical Resolution Limit for the Multidimensional Harmonic Retrieval Model: Hypothesis Test and Cramer-Rao Bound Approaches. EURASIP Journal on Advances in Signal Processing, 2011, 1 (12), pp.1-14. ⟨10.1186/1687-6180-2011-12⟩. ⟨hal-00579002⟩
279 Consultations
200 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More