Cumulant-Based Identification of Non Gaussian Moving Average Signals. Identification des Signaux à Moyenne Ajustée Non Gaussiens à L'aide de Cumulants

Cumulant-Based Identification of Non Gaussian Moving Average Signals

Identification des Signaux à Moyenne Ajustée Non Gaussiens à L'aide de Cumulants

M'hamed Bakrim | Driss Aboutajdine 

Dépt. de Physique, B.P. 618, Faculté des Sciences et Techniques, Marrakech, Maroc

GSC-LEESA, B.P. 1014, Faculté des Sciences, Rabat, Maroc

Page: 
175-186
 |
Received: 
2 April 1998
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

In this paper, an overview on higher-order statistics based identification methods is presented, and tree batch blind estimation methods are proposed. One of them use both autocorrelation and cumulant sequences, the others are cumulant-based only. The cumulant-based ones are respectively a generalization of Zhang et al.'s method and a reformulation of Giannakis-Mendel's method without autocorrelation . By simulations, we evaluate their performances and compare them together and with the existing approaches. The results show that the generalization of Zhang et al.'smethod give good estimates, specially in noise environment (white or colored noises). 

Résumé 

Dans ce papier, nous donnons un aperçu des méthodes classiques d'identification des signaux linéaires non gaussiens de type à moyenne ajustée basées sur les statistiques d'ordre supérieur (SOS) . Puis, nous proposons trois méthodes d'estimation globale: la première combine l'autocorrélation et les cumulants et les deux autres exploitent les cumulants seuls. L'une d'entre elles généralise la méthode de Zhang et al.. La deuxième est une modification de l'approche reformulée de Giannakis et Mendel. Elle est obtenue en remplaçant les moments d'ordre deux, sensibles aux bruits gaussiens, par des cumulants, grâce à une relation qu'on développera. Finalement nous testons par simulations les performances des trois méthodes proposées et nous les comparons à d'autres approches existantes . Les résultats montrent que la méthode proposée généralisant celle de Zhanget al.,fournit de bons résultats et qu'elle est plus résistante aux effets des bruits blancs ou colorés . 

Keywords: 

Higher-order statistics, blind identification, non minimum phase MA non gaussian signals, Batch identification methods .

Mots clés 

Statistiques d'ordre supérieur, Identification aveugle, signaux non gaussiens MA à non minimum de phase, méthodes d'identification globale.

1. Introduction
2. Modèle et Hypothèses
3. Relations Fondamentales
4. Méthodes Classiques Linéaires
5. Méthodes Proposées
6. Comparaison des Méthodes Proposées aux Méthodes Classiques
7. Simulation
8. Conclusion
  References

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